This file is indexed.

/usr/share/doc/nettle-dev/nettle.html is in nettle-dev 3.3-1+b2.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

   1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
4513
4514
4515
4516
4517
4518
4519
4520
4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
4532
4533
4534
4535
4536
4537
4538
4539
4540
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555
4556
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
4580
4581
4582
4583
4584
4585
4586
4587
4588
4589
4590
4591
4592
4593
4594
4595
4596
4597
4598
4599
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
4621
4622
4623
4624
4625
4626
4627
4628
4629
4630
4631
4632
4633
4634
4635
4636
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
5236
5237
5238
5239
5240
5241
5242
5243
5244
5245
5246
5247
5248
5249
5250
5251
5252
5253
5254
5255
5256
5257
5258
5259
5260
5261
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
5277
5278
5279
5280
5281
5282
5283
5284
5285
5286
5287
5288
5289
5290
5291
5292
5293
5294
5295
5296
5297
5298
5299
5300
5301
5302
5303
5304
5305
5306
5307
5308
5309
5310
5311
5312
5313
5314
5315
5316
5317
5318
5319
5320
5321
5322
5323
5324
5325
5326
5327
5328
5329
5330
5331
5332
5333
5334
5335
5336
5337
5338
5339
5340
5341
5342
5343
5344
5345
5346
5347
5348
5349
5350
5351
5352
5353
5354
5355
5356
5357
5358
5359
5360
5361
5362
5363
5364
5365
5366
5367
5368
5369
5370
5371
5372
5373
5374
5375
5376
5377
5378
5379
5380
5381
5382
5383
5384
5385
5386
5387
5388
5389
5390
5391
5392
5393
5394
5395
5396
5397
5398
5399
5400
5401
5402
5403
5404
5405
5406
5407
5408
5409
5410
5411
5412
5413
5414
5415
5416
5417
5418
5419
5420
5421
5422
5423
5424
5425
5426
5427
5428
5429
5430
5431
5432
5433
5434
5435
5436
5437
5438
5439
5440
5441
5442
5443
5444
5445
5446
5447
5448
5449
5450
5451
5452
5453
5454
5455
5456
5457
5458
5459
5460
5461
5462
5463
5464
5465
5466
5467
5468
5469
5470
5471
5472
5473
5474
5475
5476
5477
5478
5479
5480
5481
5482
5483
5484
5485
5486
5487
5488
5489
5490
5491
5492
5493
5494
5495
5496
5497
5498
5499
5500
5501
5502
5503
5504
5505
5506
5507
5508
5509
5510
5511
5512
5513
5514
5515
5516
5517
5518
5519
5520
5521
5522
5523
5524
5525
5526
5527
5528
5529
5530
5531
5532
5533
5534
5535
5536
5537
5538
5539
5540
5541
5542
5543
5544
5545
5546
5547
5548
5549
5550
5551
5552
5553
5554
5555
5556
5557
5558
5559
5560
5561
5562
5563
5564
5565
5566
5567
5568
5569
5570
5571
5572
5573
5574
5575
5576
5577
5578
5579
5580
5581
5582
5583
5584
5585
5586
5587
5588
5589
5590
5591
5592
5593
5594
5595
5596
5597
5598
5599
5600
5601
5602
5603
5604
5605
5606
5607
5608
5609
5610
5611
5612
5613
5614
5615
5616
5617
5618
5619
5620
5621
5622
5623
5624
5625
5626
5627
5628
5629
5630
5631
5632
5633
5634
5635
5636
5637
5638
5639
5640
5641
5642
5643
5644
5645
5646
5647
5648
5649
5650
5651
5652
5653
5654
5655
5656
5657
5658
5659
5660
5661
5662
5663
5664
5665
5666
5667
5668
5669
5670
5671
5672
5673
5674
5675
5676
5677
5678
5679
5680
5681
5682
5683
5684
5685
5686
5687
5688
5689
5690
5691
5692
5693
5694
5695
5696
5697
5698
5699
5700
5701
5702
5703
5704
5705
5706
5707
5708
5709
5710
5711
5712
5713
5714
5715
5716
5717
5718
5719
5720
5721
5722
5723
5724
5725
5726
5727
5728
5729
5730
5731
5732
5733
5734
5735
5736
5737
5738
5739
5740
5741
5742
5743
5744
5745
5746
5747
5748
5749
5750
5751
5752
5753
5754
5755
5756
5757
5758
5759
5760
5761
5762
5763
5764
5765
5766
5767
5768
5769
5770
5771
5772
5773
5774
5775
5776
5777
5778
5779
5780
5781
5782
5783
5784
5785
5786
5787
5788
5789
5790
5791
5792
5793
5794
5795
5796
5797
5798
5799
5800
5801
5802
5803
5804
5805
5806
5807
5808
5809
5810
5811
5812
5813
5814
5815
5816
5817
5818
5819
5820
5821
5822
5823
5824
5825
5826
5827
5828
5829
5830
5831
5832
5833
5834
5835
5836
5837
5838
5839
5840
5841
5842
5843
5844
5845
5846
5847
5848
5849
5850
5851
5852
5853
5854
5855
5856
5857
5858
5859
5860
5861
5862
5863
5864
5865
5866
5867
5868
5869
5870
5871
5872
5873
5874
5875
5876
5877
5878
5879
5880
5881
5882
5883
5884
5885
5886
5887
5888
5889
5890
5891
5892
5893
5894
5895
5896
5897
5898
5899
5900
5901
5902
5903
5904
5905
5906
5907
5908
5909
5910
5911
5912
5913
5914
5915
5916
5917
5918
5919
5920
5921
5922
5923
5924
5925
5926
5927
5928
5929
5930
5931
5932
5933
5934
5935
5936
5937
5938
5939
5940
5941
5942
5943
5944
5945
5946
5947
5948
5949
5950
5951
5952
5953
5954
5955
5956
5957
5958
5959
5960
5961
5962
5963
5964
5965
5966
5967
5968
5969
5970
5971
5972
5973
5974
5975
5976
5977
5978
5979
5980
5981
5982
5983
5984
5985
5986
5987
5988
5989
5990
5991
5992
5993
5994
5995
5996
5997
5998
5999
6000
6001
6002
6003
6004
6005
6006
6007
6008
6009
6010
6011
6012
6013
6014
6015
6016
6017
6018
6019
6020
6021
6022
6023
6024
6025
6026
6027
6028
6029
6030
6031
6032
6033
6034
6035
6036
6037
6038
6039
6040
6041
6042
6043
6044
6045
6046
6047
6048
6049
6050
6051
6052
6053
6054
6055
6056
6057
6058
6059
6060
6061
6062
6063
6064
6065
6066
6067
6068
6069
6070
6071
6072
6073
6074
6075
6076
6077
6078
6079
6080
6081
6082
6083
6084
6085
6086
6087
6088
6089
6090
6091
6092
6093
6094
6095
6096
6097
6098
6099
6100
6101
6102
6103
6104
6105
6106
6107
6108
6109
6110
6111
6112
6113
6114
6115
6116
6117
6118
6119
6120
6121
6122
6123
6124
6125
6126
6127
6128
6129
6130
6131
6132
6133
6134
6135
6136
6137
6138
6139
6140
6141
6142
6143
6144
6145
6146
6147
6148
6149
6150
6151
6152
6153
6154
6155
6156
6157
6158
6159
6160
6161
6162
6163
6164
6165
6166
6167
6168
6169
6170
6171
6172
6173
6174
6175
6176
6177
6178
6179
6180
6181
6182
6183
6184
6185
6186
6187
6188
6189
6190
6191
6192
6193
6194
6195
6196
6197
6198
6199
6200
6201
6202
6203
6204
6205
6206
6207
6208
6209
6210
6211
6212
6213
6214
6215
6216
6217
6218
6219
6220
6221
6222
6223
6224
6225
6226
6227
6228
6229
6230
6231
6232
6233
6234
6235
6236
6237
6238
6239
6240
6241
6242
6243
6244
6245
6246
6247
6248
6249
6250
6251
6252
6253
6254
6255
6256
6257
6258
6259
6260
6261
6262
6263
6264
6265
6266
6267
6268
6269
6270
6271
6272
6273
6274
6275
6276
6277
6278
6279
6280
6281
6282
6283
6284
6285
6286
6287
6288
6289
6290
6291
6292
6293
6294
6295
6296
6297
6298
6299
6300
6301
6302
6303
6304
6305
6306
6307
6308
6309
6310
6311
6312
6313
6314
6315
6316
6317
6318
6319
6320
6321
6322
6323
6324
6325
6326
6327
6328
6329
6330
6331
6332
6333
6334
6335
6336
6337
6338
6339
6340
6341
6342
6343
6344
6345
6346
6347
6348
6349
6350
6351
6352
6353
6354
6355
6356
6357
6358
6359
6360
6361
6362
6363
6364
6365
6366
6367
6368
6369
6370
6371
6372
6373
6374
6375
6376
6377
6378
6379
6380
6381
6382
6383
6384
6385
6386
6387
6388
6389
6390
6391
6392
6393
6394
6395
6396
6397
6398
6399
6400
6401
6402
6403
6404
6405
6406
6407
6408
6409
6410
6411
6412
6413
6414
6415
6416
6417
6418
6419
6420
6421
6422
6423
6424
6425
6426
6427
6428
6429
6430
6431
6432
6433
6434
6435
6436
6437
6438
6439
6440
6441
6442
6443
6444
6445
6446
6447
6448
6449
6450
6451
6452
6453
6454
6455
6456
6457
6458
6459
6460
6461
6462
6463
6464
6465
6466
6467
6468
6469
6470
6471
6472
6473
6474
6475
6476
6477
6478
6479
6480
6481
6482
6483
6484
6485
6486
6487
6488
6489
6490
6491
6492
6493
6494
6495
6496
6497
6498
6499
6500
6501
6502
6503
6504
6505
6506
6507
6508
6509
6510
6511
6512
6513
6514
6515
6516
6517
6518
6519
6520
6521
6522
6523
6524
6525
6526
6527
6528
6529
6530
6531
6532
6533
6534
6535
6536
6537
6538
6539
6540
6541
6542
6543
6544
6545
6546
6547
6548
6549
6550
6551
6552
6553
6554
6555
6556
6557
6558
6559
6560
6561
6562
6563
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- This manual is for the Nettle library (version 3.2), a
low-level cryptographic library.

Originally written 2001 by Niels Möller, updated 2015.

This manual is placed in the public domain. You may freely copy it, in
whole or in part, with or without modification. Attribution is
appreciated, but not required. -->
<!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
<head>
<title>Nettle: a low-level cryptographic library</title>

<meta name="description" content="Nettle: a low-level cryptographic library">
<meta name="keywords" content="Nettle: a low-level cryptographic library">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="#Top" rel="start" title="Top">
<link href="#Index" rel="index" title="Index">
<link href="#SEC_Contents" rel="contents" title="Table of Contents">
<link href="dir.html#Top" rel="up" title="(dir)">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<h1 class="settitle" align="center">Nettle: a low-level cryptographic library</h1>






<a name="SEC_Contents"></a>
<h2 class="contents-heading">Table of Contents</h2>

<div class="contents">

<ul class="no-bullet">
  <li><a name="toc-Introduction-1" href="#Introduction">1 Introduction</a></li>
  <li><a name="toc-Copyright-1" href="#Copyright">2 Copyright</a></li>
  <li><a name="toc-Conventions-1" href="#Conventions">3 Conventions</a></li>
  <li><a name="toc-Example-1" href="#Example">4 Example</a></li>
  <li><a name="toc-Linking-1" href="#Linking">5 Linking</a></li>
  <li><a name="toc-Reference-1" href="#Reference">6 Reference</a>
  <ul class="no-bullet">
    <li><a name="toc-Hash-functions-1" href="#Hash-functions">6.1 Hash functions</a>
    <ul class="no-bullet">
      <li><a name="toc-Recommended-hash-functions-1" href="#Recommended-hash-functions">6.1.1 Recommended hash functions</a>
      <ul class="no-bullet">
        <li><a name="toc-SHA256" href="#SHA256">6.1.1.1 <acronym>SHA256</acronym></a></li>
        <li><a name="toc-SHA224" href="#SHA224">6.1.1.2 <acronym>SHA224</acronym></a></li>
        <li><a name="toc-SHA512" href="#SHA512">6.1.1.3 <acronym>SHA512</acronym></a></li>
        <li><a name="toc-SHA384-and-other-variants-of-SHA512" href="#SHA384-and-other-variants-of-SHA512">6.1.1.4 <acronym>SHA384 and other variants of SHA512</acronym></a></li>
        <li><a name="toc-SHA3_002d224" href="#SHA3_002d224">6.1.1.5 <acronym>SHA3-224</acronym></a></li>
        <li><a name="toc-SHA3_002d256" href="#SHA3_002d256">6.1.1.6 <acronym>SHA3-256</acronym></a></li>
        <li><a name="toc-SHA3_002d384" href="#SHA3_002d384">6.1.1.7 <acronym>SHA3-384</acronym></a></li>
        <li><a name="toc-SHA3_002d512" href="#SHA3_002d512">6.1.1.8 <acronym>SHA3-512</acronym></a></li>
      </ul></li>
      <li><a name="toc-Legacy-hash-functions-1" href="#Legacy-hash-functions">6.1.2 Legacy hash functions</a>
      <ul class="no-bullet">
        <li><a name="toc-MD5" href="#MD5">6.1.2.1 <acronym>MD5</acronym></a></li>
        <li><a name="toc-MD2" href="#MD2">6.1.2.2 <acronym>MD2</acronym></a></li>
        <li><a name="toc-MD4" href="#MD4">6.1.2.3 <acronym>MD4</acronym></a></li>
        <li><a name="toc-RIPEMD160" href="#RIPEMD160">6.1.2.4 <acronym>RIPEMD160</acronym></a></li>
        <li><a name="toc-SHA1" href="#SHA1">6.1.2.5 <acronym>SHA1</acronym></a></li>
        <li><a name="toc-GOSTHASH94" href="#GOSTHASH94">6.1.2.6 <acronym>GOSTHASH94</acronym></a></li>
      </ul></li>
      <li><a name="toc-The-struct-nettle_005fhash-abstraction" href="#nettle_005fhash-abstraction">6.1.3 The <code>struct nettle_hash</code> abstraction</a></li>
    </ul></li>
    <li><a name="toc-Cipher-functions-1" href="#Cipher-functions">6.2 Cipher functions</a>
    <ul class="no-bullet">
      <li><a name="toc-AES" href="#AES">6.2.1 AES</a></li>
      <li><a name="toc-ARCFOUR" href="#ARCFOUR">6.2.2 ARCFOUR</a></li>
      <li><a name="toc-ARCTWO" href="#ARCTWO">6.2.3 ARCTWO</a></li>
      <li><a name="toc-BLOWFISH" href="#BLOWFISH">6.2.4 BLOWFISH</a></li>
      <li><a name="toc-Camellia" href="#Camellia">6.2.5 Camellia</a></li>
      <li><a name="toc-CAST128" href="#CAST128">6.2.6 CAST128</a></li>
      <li><a name="toc-ChaCha" href="#ChaCha">6.2.7 ChaCha</a></li>
      <li><a name="toc-DES" href="#DES">6.2.8 DES</a></li>
      <li><a name="toc-DES3" href="#DES3">6.2.9 DES3</a></li>
      <li><a name="toc-Salsa20" href="#Salsa20">6.2.10 Salsa20</a></li>
      <li><a name="toc-SERPENT" href="#SERPENT">6.2.11 SERPENT</a></li>
      <li><a name="toc-TWOFISH" href="#TWOFISH">6.2.12 TWOFISH</a></li>
      <li><a name="toc-The-struct-nettle_005fcipher-abstraction" href="#The-struct-nettle_005fcipher-abstraction">6.2.13 The <code>struct nettle_cipher</code> abstraction</a></li>
    </ul></li>
    <li><a name="toc-Cipher-modes-1" href="#Cipher-modes">6.3 Cipher modes</a>
    <ul class="no-bullet">
      <li><a name="toc-Cipher-Block-Chaining" href="#CBC">6.3.1 Cipher Block Chaining</a></li>
      <li><a name="toc-Counter-mode" href="#CTR">6.3.2 Counter mode</a></li>
    </ul></li>
    <li><a name="toc-Authenticated-encryption-with-associated-data" href="#Authenticated-encryption">6.4 Authenticated encryption with associated data</a>
    <ul class="no-bullet">
      <li><a name="toc-EAX-1" href="#EAX">6.4.1 EAX</a>
      <ul class="no-bullet">
        <li><a name="toc-General-EAX-interface" href="#General-EAX-interface">6.4.1.1 General <acronym>EAX</acronym> interface</a></li>
        <li><a name="toc-EAX-helper-macros" href="#EAX-helper-macros">6.4.1.2 <acronym>EAX</acronym> helper macros</a></li>
        <li><a name="toc-EAX_002dAES128-interface" href="#EAX_002dAES128-interface">6.4.1.3 <acronym>EAX</acronym>-<acronym>AES</acronym>128 interface</a></li>
      </ul></li>
      <li><a name="toc-Galois-counter-mode" href="#GCM">6.4.2 Galois counter mode</a>
      <ul class="no-bullet">
        <li><a name="toc-General-GCM-interface" href="#General-GCM-interface">6.4.2.1 General <acronym>GCM</acronym> interface</a></li>
        <li><a name="toc-GCM-helper-macros" href="#GCM-helper-macros">6.4.2.2 <acronym>GCM</acronym> helper macros</a></li>
        <li><a name="toc-GCM_002dAES-interface" href="#GCM_002dAES-interface">6.4.2.3 <acronym>GCM</acronym>-<acronym>AES</acronym> interface</a></li>
        <li><a name="toc-GCM_002dCamellia-interface" href="#GCM_002dCamellia-interface">6.4.2.4 <acronym>GCM</acronym>-Camellia interface</a></li>
      </ul></li>
      <li><a name="toc-Counter-with-CBC_002dMAC-mode" href="#CCM">6.4.3 Counter with CBC-MAC mode</a>
      <ul class="no-bullet">
        <li><a name="toc-General-CCM-interface" href="#General-CCM-interface">6.4.3.1 General <acronym>CCM</acronym> interface</a></li>
        <li><a name="toc-CCM-message-interface" href="#CCM-message-interface">6.4.3.2 <acronym>CCM</acronym> message interface</a></li>
        <li><a name="toc-CCM_002dAES-interface" href="#CCM_002dAES-interface">6.4.3.3 <acronym>CCM</acronym>-<acronym>AES</acronym> interface</a></li>
      </ul></li>
      <li><a name="toc-ChaCha_002dPoly1305-1" href="#ChaCha_002dPoly1305">6.4.4 ChaCha-Poly1305</a></li>
      <li><a name="toc-The-struct-nettle_005faead-abstraction" href="#nettle_005faead-abstraction">6.4.5 The <code>struct nettle_aead</code> abstraction</a></li>
    </ul></li>
    <li><a name="toc-Keyed-Hash-Functions" href="#Keyed-hash-functions">6.5 Keyed Hash Functions</a>
    <ul class="no-bullet">
      <li><a name="toc-HMAC-1" href="#HMAC">6.5.1 <acronym>HMAC</acronym></a></li>
      <li><a name="toc-Concrete-HMAC-functions" href="#Concrete-HMAC-functions">6.5.2 Concrete <acronym>HMAC</acronym> functions</a>
      <ul class="no-bullet">
        <li><a name="toc-HMAC_002dMD5" href="#HMAC_002dMD5">6.5.2.1 <acronym>HMAC-MD5</acronym></a></li>
        <li><a name="toc-HMAC_002dRIPEMD160" href="#HMAC_002dRIPEMD160">6.5.2.2 <acronym>HMAC-RIPEMD160</acronym></a></li>
        <li><a name="toc-HMAC_002dSHA1" href="#HMAC_002dSHA1">6.5.2.3 <acronym>HMAC-SHA1</acronym></a></li>
        <li><a name="toc-HMAC_002dSHA256" href="#HMAC_002dSHA256">6.5.2.4 <acronym>HMAC-SHA256</acronym></a></li>
        <li><a name="toc-HMAC_002dSHA512" href="#HMAC_002dSHA512">6.5.2.5 <acronym>HMAC-SHA512</acronym></a></li>
      </ul></li>
      <li><a name="toc-UMAC-1" href="#UMAC">6.5.3 <acronym>UMAC</acronym></a></li>
      <li><a name="toc-Poly1305-1" href="#Poly1305">6.5.4 Poly1305</a></li>
    </ul></li>
    <li><a name="toc-Key-derivation-Functions" href="#Key-derivation-functions">6.6 Key derivation Functions</a>
    <ul class="no-bullet">
      <li><a name="toc-PBKDF2" href="#PBKDF2">6.6.1 <acronym>PBKDF2</acronym></a></li>
      <li><a name="toc-Concrete-PBKDF2-functions" href="#Concrete-PBKDF2-functions">6.6.2 Concrete <acronym>PBKDF2</acronym> functions</a>
      <ul class="no-bullet">
        <li><a name="toc-PBKDF2_002dHMAC_002dSHA1" href="#PBKDF2_002dHMAC_002dSHA1">6.6.2.1 <acronym>PBKDF2-HMAC-SHA1</acronym></a></li>
        <li><a name="toc-PBKDF2_002dHMAC_002dSHA256" href="#PBKDF2_002dHMAC_002dSHA256">6.6.2.2 <acronym>PBKDF2-HMAC-SHA256</acronym></a></li>
      </ul></li>
    </ul></li>
    <li><a name="toc-Public_002dkey-algorithms-1" href="#Public_002dkey-algorithms">6.7 Public-key algorithms</a>
    <ul class="no-bullet">
      <li><a name="toc-RSA-1" href="#RSA">6.7.1 <acronym>RSA</acronym></a>
      <ul class="no-bullet">
        <li><a name="toc-Nettle_0027s-RSA-support" href="#Nettle_0027s-RSA-support">6.7.1.1 Nettle&rsquo;s <acronym>RSA</acronym> support</a></li>
      </ul></li>
      <li><a name="toc-DSA-1" href="#DSA">6.7.2 <acronym>DSA</acronym></a>
      <ul class="no-bullet">
        <li><a name="toc-Nettle_0027s-DSA-support" href="#Nettle_0027s-DSA-support">6.7.2.1 Nettle&rsquo;s <acronym>DSA</acronym> support</a></li>
        <li><a name="toc-Old_002c-deprecated_002c-DSA-interface" href="#Old_002c-deprecated_002c-DSA-interface">6.7.2.2 Old, deprecated, <acronym>DSA</acronym> interface</a></li>
      </ul></li>
      <li><a name="toc-Elliptic-curves-1" href="#Elliptic-curves">6.7.3 <acronym>Elliptic curves</acronym></a>
      <ul class="no-bullet">
        <li><a name="toc-Side_002dchannel-silence-1" href="#Side_002dchannel-silence">6.7.3.1 Side-channel silence</a></li>
        <li><a name="toc-ECDSA-1" href="#ECDSA">6.7.3.2 ECDSA</a></li>
        <li><a name="toc-Curve25519" href="#Curve-25519">6.7.3.3 Curve25519</a></li>
        <li><a name="toc-EdDSA" href="#EdDSA">6.7.3.4 EdDSA</a></li>
      </ul></li>
    </ul></li>
    <li><a name="toc-Randomness-1" href="#Randomness">6.8 Randomness</a>
    <ul class="no-bullet">
      <li><a name="toc-Yarrow" href="#Yarrow">6.8.1 Yarrow</a></li>
    </ul></li>
    <li><a name="toc-ASCII-encoding-1" href="#ASCII-encoding">6.9 ASCII encoding</a></li>
    <li><a name="toc-Miscellaneous-functions-1" href="#Miscellaneous-functions">6.10 Miscellaneous functions</a></li>
    <li><a name="toc-Compatibility-functions-1" href="#Compatibility-functions">6.11 Compatibility functions</a></li>
  </ul></li>
  <li><a name="toc-Traditional-Nettle-Soup" href="#Nettle-soup">7 Traditional Nettle Soup</a></li>
  <li><a name="toc-Installation-1" href="#Installation">8 Installation</a></li>
  <li><a name="toc-Function-and-Concept-Index" href="#Index">Function and Concept Index</a></li>
</ul>
</div>


<a name="Top"></a>
<div class="header">
<p>
Next: <a href="#Introduction" accesskey="n" rel="next">Introduction</a>, Previous: <a href="dir.html#Top" accesskey="p" rel="prev">(dir)</a>, Up: <a href="dir.html#Top" accesskey="u" rel="up">(dir)</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Nettle"></a>
<h1 class="top">Nettle</h1>

<p>This document describes the Nettle low-level cryptographic library. You
can use the library directly from your C programs, or write or use an
object-oriented wrapper for your favorite language or application.
</p>
<p>This manual is for the Nettle library (version 3.2), a
low-level cryptographic library.
</p>
<p>Originally written 2001 by Niels Möller, updated 2015.
</p>
<blockquote>
<p>This manual is placed in the public domain. You may freely copy it, in
whole or in part, with or without modification. Attribution is
appreciated, but not required.
</p></blockquote>


<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#Introduction" accesskey="1">Introduction</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">What is Nettle?
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Copyright" accesskey="2">Copyright</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Your rights.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Conventions" accesskey="3">Conventions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">General interface conventions.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Example" accesskey="4">Example</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">An example program.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Linking" accesskey="5">Linking</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Linking with libnettle and libhogweed.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Reference" accesskey="6">Reference</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">All Nettle functions and features.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Nettle-soup" accesskey="7">Nettle soup</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">For the serious nettle hacker.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Installation" accesskey="8">Installation</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">How to install Nettle.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Index" accesskey="9">Index</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Function and concept index.
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
</pre></th></tr><tr><th colspan="3" align="left" valign="top"><pre class="menu-comment"> &mdash; The Detailed Node Listing &mdash;

Reference

</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#Hash-functions">Hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Cipher-functions">Cipher functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Cipher-modes">Cipher modes</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Keyed-hash-functions">Keyed hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Key-derivation-functions">Key derivation functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Public_002dkey-algorithms">Public-key algorithms</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Randomness">Randomness</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#ASCII-encoding">ASCII encoding</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Miscellaneous-functions">Miscellaneous functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Compatibility-functions">Compatibility functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Hash functions

</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#Recommended-hash-functions">Recommended hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Legacy-hash-functions">Legacy hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#nettle_005fhash-abstraction">nettle_hash abstraction</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Cipher modes

</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#CBC">CBC</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#CTR">CTR</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#GCM">GCM</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#CCM">CCM</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Keyed Hash Functions

</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#HMAC">HMAC</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#UMAC">UMAC</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
Public-key algorithms

</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#RSA">RSA</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">The RSA public key algorithm.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#DSA">DSA</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">The DSA digital signature algorithm.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Elliptic-curves">Elliptic curves</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Elliptic curves and ECDSA
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
<acronym>Elliptic curves</acronym>

</pre></th></tr><tr><td align="left" valign="top">&bull; <a href="#Side_002dchannel-silence">Side-channel silence</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#ECDSA">ECDSA</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Curve-25519">Curve 25519</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><th colspan="3" align="left" valign="top"><pre class="menu-comment">
</pre></th></tr></table>


<hr>
<a name="Introduction"></a>
<div class="header">
<p>
Next: <a href="#Copyright" accesskey="n" rel="next">Copyright</a>, Previous: <a href="#Top" accesskey="p" rel="prev">Top</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Introduction-1"></a>
<h2 class="chapter">1 Introduction</h2>

<p>Nettle is a cryptographic library that is designed to fit easily in more
or less any context: In crypto toolkits for object-oriented languages
(C++, Python, Pike, ...), in applications like LSH or GNUPG, or even in
kernel space. In most contexts, you need more than the basic
cryptographic algorithms, you also need some way to keep track of available
algorithms, their properties and variants. You often have some algorithm
selection process, often dictated by a protocol you want to implement.
</p>
<p>And as the requirements of applications differ in subtle and not so
subtle ways, an API that fits one application well can be a pain to use
in a different context. And that is why there are so many different
cryptographic libraries around.
</p>
<p>Nettle tries to avoid this problem by doing one thing, the low-level
crypto stuff, and providing a <em>simple</em> but general interface to it.
In particular, Nettle doesn&rsquo;t do algorithm selection. It doesn&rsquo;t do
memory allocation. It doesn&rsquo;t do any I/O.
</p>
<p>The idea is that one can build several application and context specific
interfaces on top of Nettle, and share the code, test cases, benchmarks,
documentation, etc. Examples are the Nettle module for the Pike
language, and LSH, which both use an object-oriented abstraction on top
of the library.
</p>
<p>This manual explains how to use the Nettle library. It also tries to
provide some background on the cryptography, and advice on how to best
put it to use.
</p>
<hr>
<a name="Copyright"></a>
<div class="header">
<p>
Next: <a href="#Conventions" accesskey="n" rel="next">Conventions</a>, Previous: <a href="#Introduction" accesskey="p" rel="prev">Introduction</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Copyright-1"></a>
<h2 class="chapter">2 Copyright</h2>

<p>Nettle is dual licenced under the GNU General Public License version 2
or later, and the GNU Lesser General Public License version 3 or later.
When using Nettle, you must comply fully with all conditions of at least
one of these licenses. A few of the individual files are licensed under
more permissive terms, or in the public domain. To find the current
status of particular files, you have to read the copyright notices at
the top of the files.
</p>
<p>This manual is in the public domain. You may freely copy it in whole or
in part, e.g., into documentation of programs that build on Nettle.
Attribution, as well as contribution of improvements to the text, is of
course appreciated, but it is not required.
</p>
<p>A list of the supported algorithms, their origins, and exceptions to the
above licensing:
</p>
<dl compact="compact">
<dt><em>AES</em></dt>
<dd><p>The implementation of the AES cipher (also known as rijndael) is written
by Rafael Sevilla. Assembler for x86 by Rafael Sevilla and
Niels Möller, Sparc assembler by Niels Möller.
</p>
</dd>
<dt><em>ARCFOUR</em></dt>
<dd><p>The implementation of the ARCFOUR (also known as RC4) cipher is written
by Niels Möller.
</p>
</dd>
<dt><em>ARCTWO</em></dt>
<dd><p>The implementation of the ARCTWO (also known as RC2) cipher is written
by Nikos Mavroyanopoulos and modified by Werner Koch and Simon
Josefsson.
</p>
</dd>
<dt><em>BLOWFISH</em></dt>
<dd><p>The implementation of the BLOWFISH cipher is written by Werner Koch,
copyright owned by the Free Software Foundation. Also hacked by Simon
Josefsson and Niels Möller.
</p>
</dd>
<dt><em>CAMELLIA</em></dt>
<dd><p>The C implementation is by Nippon Telegraph and Telephone Corporation
(NTT), heavily modified by Niels Möller. Assembler for x86 and x86_64
by Niels Möller.
</p>
</dd>
<dt><em>CAST128</em></dt>
<dd><p>The implementation of the CAST128 cipher is written by Steve Reid.
Released into the public domain.
</p>
</dd>
<dt><em>CHACHA</em></dt>
<dd><p>Implemented by Joachim Strömbergson, based on the implementation of
SALSA20 (see below). Assembly for x86_64 by Niels Möller.
</p>
</dd>
<dt><em>DES</em></dt>
<dd><p>The implementation of the DES cipher is written by Dana L. How, and
released under the LGPL, version 2 or later.
</p>
</dd>
<dt><em>GOSTHASH94</em></dt>
<dd><p>The C implementation of the GOST94 message digest is written by 
Aleksey Kravchenko and was ported from the rhash library by Nikos
Mavrogiannopoulos. It is released under the MIT license.
</p>
</dd>
<dt><em>MD2</em></dt>
<dd><p>The implementation of MD2 is written by Andrew Kuchling, and hacked
some by Andreas Sigfridsson and Niels Möller. Python Cryptography
Toolkit license (essentially public domain).
</p>
</dd>
<dt><em>MD4</em></dt>
<dd><p>This is almost the same code as for MD5 below, with modifications by
Marcus Comstedt. Released into the public domain.
</p>
</dd>
<dt><em>MD5</em></dt>
<dd><p>The implementation of the MD5 message digest is written by Colin Plumb.
It has been hacked some more by Andrew Kuchling and Niels Möller.
Released into the public domain.
</p>
</dd>
<dt><em>PBKDF2</em></dt>
<dd><p>The C implementation of PBKDF2 is based on earlier work for Shishi and
GnuTLS by Simon Josefsson.
</p>
</dd>
<dt><em>RIPEMD160</em></dt>
<dd><p>The implementation of RIPEMD160 message digest is based on the code in
libgcrypt, copyright owned by the Free Software Foundation. Ported to
Nettle by Andres Mejia.
</p>
</dd>
<dt><em>SALSA20</em></dt>
<dd><p>The C implementation of SALSA20 is based on D. J. Bernstein&rsquo;s reference
implementation (in the public domain), adapted to Nettle by Simon
Josefsson, and heavily modified by Niels Möller. Assembly for x86_64 and
ARM by Niels Möller.
</p>
</dd>
<dt><em>SERPENT</em></dt>
<dd><p>The implementation of the SERPENT cipher is based on the code in libgcrypt,
copyright owned by the Free Software Foundation. Adapted to Nettle by
Simon Josefsson and heavily modified by Niels Möller. Assembly for
x86_64 by Niels Möller.
</p>
</dd>
<dt><em>POLY1305</em></dt>
<dd><p>Based on the implementation by Andrew M. (floodyberry), modified by
Nikos Mavrogiannopoulos and Niels Möller. Assembly for x86_64 by Niels
Möller.
</p>
</dd>
<dt><em>SHA1</em></dt>
<dd><p>The C implementation of the SHA1 message digest is written by Peter
Gutmann, and hacked some more by Andrew Kuchling and Niels Möller.
Released into the public domain. Assembler for x86, x86_64 and ARM by
Niels Möller, released under the LGPL.
</p>
</dd>
<dt><em>SHA2</em></dt>
<dd><p>Written by Niels Möller, using Peter Gutmann&rsquo;s SHA1 code as a model. 
</p>
</dd>
<dt><em>SHA3</em></dt>
<dd><p>Written by Niels Möller.
</p>
</dd>
<dt><em>TWOFISH</em></dt>
<dd><p>The implementation of the TWOFISH cipher is written by Ruud de Rooij.
</p>
</dd>
<dt><em>UMAC</em></dt>
<dd><p>Written by Niels Möller.
</p>
</dd>
<dt><em>RSA</em></dt>
<dd><p>Written by Niels Möller. Uses the GMP library for bignum operations.
</p>
</dd>
<dt><em>DSA</em></dt>
<dd><p>Written by Niels Möller. Uses the GMP library for bignum operations.
</p>
</dd>
<dt><em>ECDSA</em></dt>
<dd><p>Written by Niels Möller. Uses the GMP library for bignum operations.
Development of Nettle&rsquo;s ECC support was funded by the .SE Internet Fund.
</p></dd>
</dl>

<hr>
<a name="Conventions"></a>
<div class="header">
<p>
Next: <a href="#Example" accesskey="n" rel="next">Example</a>, Previous: <a href="#Copyright" accesskey="p" rel="prev">Copyright</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Conventions-1"></a>
<h2 class="chapter">3 Conventions</h2>

<p>For each supported algorithm, there is an include file that defines a
<em>context struct</em>, a few constants, and declares functions for
operating on the context. The context struct encapsulates all information
needed by the algorithm, and it can be copied or moved in memory with no
unexpected effects.
</p>
<p>For consistency, functions for different algorithms are very similar,
but there are some differences, for instance reflecting if the key setup
or encryption function differ for encryption and decryption, and whether
or not key setup can fail. There are also differences between algorithms
that don&rsquo;t show in function prototypes, but which the application must
nevertheless be aware of. There is no big difference between the
functions for stream ciphers and for block ciphers, although they should
be used quite differently by the application.
</p>
<p>If your application uses more than one algorithm of the same type, you
should probably create an interface that is tailor-made for your needs,
and then write a few lines of glue code on top of Nettle.
</p>
<p>By convention, for an algorithm named <code>foo</code>, the struct tag for the
context struct is <code>foo_ctx</code>, constants and functions uses prefixes
like <code>FOO_BLOCK_SIZE</code> (a constant) and <code>foo_set_key</code> (a
function).
</p>
<p>In all functions, strings are represented with an explicit length, of
type <code>size_t</code>, and a pointer of type <code>uint8_t *</code> or
<code>const uint8_t *</code>. For functions that transform one string to
another, the argument order is length, destination pointer and source
pointer. Source and destination areas are usually of the same length.
When they differ, e.g., for <code>ccm_encrypt_message</code>, the length
argument specifies the size of the destination area. Source and
destination pointers may be equal, so that you can process strings in
place, but source and destination areas <em>must not</em> overlap in any
other way.
</p>
<p>Many of the functions lack return value and can never fail. Those
functions which can fail, return one on success and zero on failure.
</p>

<hr>
<a name="Example"></a>
<div class="header">
<p>
Next: <a href="#Linking" accesskey="n" rel="next">Linking</a>, Previous: <a href="#Conventions" accesskey="p" rel="prev">Conventions</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Example-1"></a>
<h2 class="chapter">4 Example</h2>

<p>A simple example program that reads a file from standard input and
writes its SHA1 check-sum on standard output should give the flavor of
Nettle.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

#include &lt;nettle/sha1.h&gt;

#define BUF_SIZE 1000

static void
display_hex(unsigned length, uint8_t *data)
{
  unsigned i;

  for (i = 0; i&lt;length; i++)
    printf(&quot;%02x &quot;, data[i]);

  printf(&quot;\n&quot;);
}

int
main(int argc, char **argv)
{
  struct sha1_ctx ctx;
  uint8_t buffer[BUF_SIZE];
  uint8_t digest[SHA1_DIGEST_SIZE];
  
  sha1_init(&amp;ctx);
  for (;;)
  {
    int done = fread(buffer, 1, sizeof(buffer), stdin);
    sha1_update(&amp;ctx, done, buffer);
    if (done &lt; sizeof(buffer))
      break;
  }
  if (ferror(stdin))
    return EXIT_FAILURE;

  sha1_digest(&amp;ctx, SHA1_DIGEST_SIZE, digest);

  display_hex(SHA1_DIGEST_SIZE, digest);
  return EXIT_SUCCESS;  
}
</pre></div>

<p>On a typical Unix system, this program can be compiled and linked with
the command line 
</p><div class="example">
<pre class="example">gcc sha-example.c -o sha-example -lnettle
</pre></div>

<hr>
<a name="Linking"></a>
<div class="header">
<p>
Next: <a href="#Reference" accesskey="n" rel="next">Reference</a>, Previous: <a href="#Example" accesskey="p" rel="prev">Example</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Linking-1"></a>
<h2 class="chapter">5 Linking</h2>

<p>Nettle actually consists of two libraries, <samp>libnettle</samp> and
<samp>libhogweed</samp>. The <samp>libhogweed</samp> library contains those
functions of Nettle that uses bignum operations, and depends on the GMP
library. With this division, linking works the same for both static and
dynamic libraries.
</p>
<p>If an application uses only the symmetric crypto algorithms of Nettle
(i.e., block ciphers, hash functions, and the like), it&rsquo;s sufficient to
link with <code>-lnettle</code>. If an application also uses public-key
algorithms, the recommended linker flags are <code>-lhogweed -lnettle
-lgmp</code>. If the involved libraries are installed as dynamic libraries, it
may be sufficient to link with just <code>-lhogweed</code>, and the loader
will resolve the dependencies automatically.
</p>
<hr>
<a name="Reference"></a>
<div class="header">
<p>
Next: <a href="#Nettle-soup" accesskey="n" rel="next">Nettle soup</a>, Previous: <a href="#Linking" accesskey="p" rel="prev">Linking</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Reference-1"></a>
<h2 class="chapter">6 Reference</h2>

<p>This chapter describes all the Nettle functions, grouped by family.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#Hash-functions" accesskey="1">Hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Cipher-functions" accesskey="2">Cipher functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Cipher-modes" accesskey="3">Cipher modes</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Authenticated-encryption" accesskey="4">Authenticated encryption</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Keyed-hash-functions" accesskey="5">Keyed hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Key-derivation-functions" accesskey="6">Key derivation functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Public_002dkey-algorithms" accesskey="7">Public-key algorithms</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Randomness" accesskey="8">Randomness</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#ASCII-encoding" accesskey="9">ASCII encoding</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Miscellaneous-functions">Miscellaneous functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Compatibility-functions">Compatibility functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<hr>
<a name="Hash-functions"></a>
<div class="header">
<p>
Next: <a href="#Cipher-functions" accesskey="n" rel="next">Cipher functions</a>, Previous: <a href="#Reference" accesskey="p" rel="prev">Reference</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>

<a name="Hash-functions-1"></a>
<h3 class="section">6.1 Hash functions</h3>
<a name="index-Hash-function"></a>
<p>A cryptographic <em>hash function</em> is a function that takes variable
size strings, and maps them to strings of fixed, short, length. There
are naturally lots of collisions, as there are more possible 1MB files
than 20 byte strings. But the function is constructed such that is hard
to find the collisions. More precisely, a cryptographic hash function
<code>H</code> should have the following properties:
</p>
<dl compact="compact">
<dt><em>One-way</em></dt>
<dd><a name="index-One_002dway"></a>
<p>Given a hash value <code>H(x)</code> it is hard to find a string <code>x</code>
that hashes to that value.
</p>
</dd>
<dt><em>Collision-resistant</em></dt>
<dd><a name="index-Collision_002dresistant"></a>
<p>It is hard to find two different strings, <code>x</code> and <code>y</code>, such
that <code>H(x)</code> = <code>H(y)</code>.
</p>
</dd>
</dl>

<p>Hash functions are useful as building blocks for digital signatures,
message authentication codes, pseudo random generators, association of
unique ids to documents, and many other things.
</p>
<p>The most commonly used hash functions are MD5 and SHA1. Unfortunately,
both these fail the collision-resistance requirement; cryptologists have
found ways to construct colliding inputs. The recommended hash functions
for new applications are SHA2 (with main variants SHA256 and SHA512). At
the time of this writing (Autumn 2015), SHA3 has recently been
standardized, and the new SHA3 and other top SHA3 candidates may also be
reasonable alternatives.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#Recommended-hash-functions" accesskey="1">Recommended hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Legacy-hash-functions" accesskey="2">Legacy hash functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#nettle_005fhash-abstraction" accesskey="3">nettle_hash abstraction</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<hr>
<a name="Recommended-hash-functions"></a>
<div class="header">
<p>
Next: <a href="#Legacy-hash-functions" accesskey="n" rel="next">Legacy hash functions</a>, Up: <a href="#Hash-functions" accesskey="u" rel="up">Hash functions</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Recommended-hash-functions-1"></a>
<h4 class="subsection">6.1.1 Recommended hash functions</h4>

<p>The following hash functions have no known weaknesses, and are suitable
for new applications. The SHA2 family of hash functions were specified
by <em>NIST</em>, intended as a replacement for <acronym>SHA1</acronym>.
</p>
<a name="SHA256"></a>
<h4 class="subsubsection">6.1.1.1 <acronym>SHA256</acronym></h4>

<p>SHA256 is a member of the SHA2 family. It outputs hash values of 256
bits, or 32 octets. Nettle defines SHA256 in <samp>&lt;nettle/sha2.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-sha256_005fctx"></a>Context struct: <strong>struct sha256_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA256_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA256_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA256 digest, i.e. 32.
</p></dd></dl>

<dl>
<dt><a name="index-SHA256_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA256_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA256. Useful for some special constructions,
in particular HMAC-SHA256.
</p></dd></dl>

<dl>
<dt><a name="index-sha256_005finit"></a>Function: <em>void</em> <strong>sha256_init</strong> <em>(struct sha256_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA256 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha256_005fupdate"></a>Function: <em>void</em> <strong>sha256_update</strong> <em>(struct sha256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha256_005fdigest"></a>Function: <em>void</em> <strong>sha256_digest</strong> <em>(struct sha256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA256_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>sha256_init</code>.
</p></dd></dl>

<p>Earlier versions of nettle defined SHA256 in the header file
<samp>&lt;nettle/sha.h&gt;</samp>, which is now deprecated, but kept for
compatibility.
</p>
<a name="SHA224"></a>
<h4 class="subsubsection">6.1.1.2 <acronym>SHA224</acronym></h4>

<p>SHA224 is a variant of SHA256, with a different initial state, and with
the output truncated to 224 bits, or 28 octets. Nettle defines SHA224 in
<samp>&lt;nettle/sha2.h&gt;</samp> (and in <samp>&lt;nettle/sha.h&gt;</samp>, for backwards
compatibility).
</p>
<dl>
<dt><a name="index-struct-sha224_005fctx"></a>Context struct: <strong>struct sha224_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA224_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA224_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA224 digest, i.e. 28.
</p></dd></dl>

<dl>
<dt><a name="index-SHA224_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA224_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA224. Useful for some special constructions,
in particular HMAC-SHA224.
</p></dd></dl>

<dl>
<dt><a name="index-sha224_005finit"></a>Function: <em>void</em> <strong>sha224_init</strong> <em>(struct sha224_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA224 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha224_005fupdate"></a>Function: <em>void</em> <strong>sha224_update</strong> <em>(struct sha224_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha224_005fdigest"></a>Function: <em>void</em> <strong>sha224_digest</strong> <em>(struct sha224_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA224_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>sha224_init</code>.
</p></dd></dl>

<a name="SHA512"></a>
<h4 class="subsubsection">6.1.1.3 <acronym>SHA512</acronym></h4>

<p>SHA512 is a larger sibling to SHA256, with a very similar structure but
with both the output and the internal variables of twice the size. The
internal variables are 64 bits rather than 32, making it significantly
slower on 32-bit computers. It outputs hash values of 512 bits, or 64
octets. Nettle defines SHA512 in <samp>&lt;nettle/sha2.h&gt;</samp> (and in
<samp>&lt;nettle/sha.h&gt;</samp>, for backwards compatibility).
</p>
<dl>
<dt><a name="index-struct-sha512_005fctx"></a>Context struct: <strong>struct sha512_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA512_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA512_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA512 digest, i.e. 64.
</p></dd></dl>

<dl>
<dt><a name="index-SHA512_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA512_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA512, 128. Useful for some special
constructions, in particular HMAC-SHA512.
</p></dd></dl>

<dl>
<dt><a name="index-sha512_005finit"></a>Function: <em>void</em> <strong>sha512_init</strong> <em>(struct sha512_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA512 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha512_005fupdate"></a>Function: <em>void</em> <strong>sha512_update</strong> <em>(struct sha512_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha512_005fdigest"></a>Function: <em>void</em> <strong>sha512_digest</strong> <em>(struct sha512_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA512_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>sha512_init</code>.
</p></dd></dl>

<a name="SHA384-and-other-variants-of-SHA512"></a>
<h4 class="subsubsection">6.1.1.4 <acronym>SHA384 and other variants of SHA512</acronym></h4>

<p>Several variants of SHA512 have been defined, with a different initial
state, and with the output truncated to shorter length than 512 bits.
Naming is a bit confused, these algorithms are called SHA512-224,
SHA512-256 and SHA384, for output sizes of 224, 256 and 384 bits,
respectively. Nettle defines these in <samp>&lt;nettle/sha2.h&gt;</samp> (and in
<samp>&lt;nettle/sha.h&gt;</samp>, for backwards compatibility).
</p>
<dl>
<dt><a name="index-struct-sha512_005f224_005fctx"></a>Context struct: <strong>struct sha512_224_ctx</strong></dt>
<dt><a name="index-struct-sha512_005f256_005fctx"></a>Context struct: <strong>struct sha512_256_ctx</strong></dt>
<dt><a name="index-struct-sha384_005fctx"></a>Context struct: <strong>struct sha384_ctx</strong></dt>
<dd><p>These context structs are all the same as sha512_ctx. They are defined as
simple preprocessor aliases, which may cause some problems if used as
identifiers for other purposes. So avoid doing that.
</p></dd></dl>

<dl>
<dt><a name="index-SHA512_005f224_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA512_224_DIGEST_SIZE</strong></dt>
<dt><a name="index-SHA512_005f256_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA512_256_DIGEST_SIZE</strong></dt>
<dt><a name="index-SHA384_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA384_DIGEST_SIZE</strong></dt>
<dd><p>The digest size for each variant, i.e., 28, 32, and 48, respectively.
</p></dd></dl>

<dl>
<dt><a name="index-SHA512_005f224_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA512_224_BLOCK_SIZE</strong></dt>
<dt><a name="index-SHA512_005f256_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA512_256_BLOCK_SIZE</strong></dt>
<dt><a name="index-SHA384_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA384_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size, same as SHA512_BLOCK_SIZE, i.e., 128. Useful for
some special constructions, in particular HMAC-SHA384.
</p></dd></dl>

<dl>
<dt><a name="index-sha512_005f224_005finit"></a>Function: <em>void</em> <strong>sha512_224_init</strong> <em>(struct sha512_224_ctx *<var>ctx</var>)</em></dt>
<dt><a name="index-sha512_005f256_005finit"></a>Function: <em>void</em> <strong>sha512_256_init</strong> <em>(struct sha512_256_ctx *<var>ctx</var>)</em></dt>
<dt><a name="index-sha384_005finit"></a>Function: <em>void</em> <strong>sha384_init</strong> <em>(struct sha384_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the context struct.
</p></dd></dl>

<dl>
<dt><a name="index-sha512_005f224_005fupdate"></a>Function: <em>void</em> <strong>sha512_224_update</strong> <em>(struct sha512_224_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-sha512_005f256_005fupdate"></a>Function: <em>void</em> <strong>sha512_256_update</strong> <em>(struct sha512_256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-sha384_005fupdate"></a>Function: <em>void</em> <strong>sha384_update</strong> <em>(struct sha384_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data. These are all aliases for sha512_update, which does
the same thing.
</p></dd></dl>

<dl>
<dt><a name="index-sha512_005f224_005fdigest"></a>Function: <em>void</em> <strong>sha512_224_digest</strong> <em>(struct sha512_224_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-sha512_005f256_005fdigest"></a>Function: <em>void</em> <strong>sha512_256_digest</strong> <em>(struct sha512_256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-sha384_005fdigest"></a>Function: <em>void</em> <strong>sha384_digest</strong> <em>(struct sha384_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it to
<var>digest</var>. <var>length</var> may be smaller than the specified digest
size, in which case only the first <var>length</var> octets of the digest are
written.
</p>
<p>These function also reset the context in the same way as the
corresponding init function.
</p></dd></dl>

<a name="SHA3_002d224"></a>
<h4 class="subsubsection">6.1.1.5 <acronym>SHA3-224</acronym></h4>
<a name="index-SHA3"></a>

<p>The SHA3 hash functions were specified by NIST in response to weaknesses
in SHA1, and doubts about SHA2 hash functions which structurally are
very similar to SHA1. SHA3 is a result of a competition, where the
winner, also known as Keccak, was designed by Guido Bertoni, Joan
Daemen, Michaël Peeters and Gilles Van Assche. It is structurally very
different from all widely used earlier hash functions. Like SHA2, there
are several variants, with output sizes of 224, 256, 384 and 512 bits
(28, 32, 48 and 64 octets, respectively). In August 2015, it was
formally standardized by NIST, as FIPS 202,
<a href="http://dx.doi.org/10.6028/NIST.FIPS.202">http://dx.doi.org/10.6028/NIST.FIPS.202</a>.
</p>
<p>Note that the SHA3 implementation in earlier versions of Nettle was
based on the specification at the time Keccak was announced as the
winner of the competition, which is incompatible with the final standard
and hence with current versions of Nettle. The <samp>nette/sha3.h</samp>
defines a preprocessor symbol <code>NETTLE_SHA3_FIPS202</code> to indicate
conformance with the standard.
</p>
<dl>
<dt><a name="index-NETTLE_005fSHA3_005fFIPS202"></a>Constant: <strong>NETTLE_SHA3_FIPS202</strong></dt>
<dd><p>Defined to 1 in Nettle versions supporting FIPS 202. Undefined in
earlier versions.
</p></dd></dl>

<p>Nettle defines SHA3-224 in <samp>&lt;nettle/sha3.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-sha3_005f224_005fctx"></a>Context struct: <strong>struct sha3_224_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA3_005f224_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA3_224_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA3_224 digest, i.e., 28.
</p></dd></dl>

<dl>
<dt><a name="index-SHA3_005f224_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA3_224_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA3_224.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f224_005finit"></a>Function: <em>void</em> <strong>sha3_224_init</strong> <em>(struct sha3_224_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA3-224 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f224_005fupdate"></a>Function: <em>void</em> <strong>sha3_224_update</strong> <em>(struct sha3_224_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f224_005fdigest"></a>Function: <em>void</em> <strong>sha3_224_digest</strong> <em>(struct sha3_224_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA3_224_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context.
</p></dd></dl>

<a name="SHA3_002d256"></a>
<h4 class="subsubsection">6.1.1.6 <acronym>SHA3-256</acronym></h4>

<p>This is SHA3 with 256-bit output size, and possibly the most useful
of the SHA3 hash functions.
</p>
<p>Nettle defines SHA3-256 in <samp>&lt;nettle/sha3.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-sha3_005f256_005fctx"></a>Context struct: <strong>struct sha3_256_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA3_005f256_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA3_256_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA3_256 digest, i.e., 32.
</p></dd></dl>

<dl>
<dt><a name="index-SHA3_005f256_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA3_256_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA3_256.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f256_005finit"></a>Function: <em>void</em> <strong>sha3_256_init</strong> <em>(struct sha3_256_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA3-256 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f256_005fupdate"></a>Function: <em>void</em> <strong>sha3_256_update</strong> <em>(struct sha3_256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f256_005fdigest"></a>Function: <em>void</em> <strong>sha3_256_digest</strong> <em>(struct sha3_256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA3_256_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context.
</p></dd></dl>

<a name="SHA3_002d384"></a>
<h4 class="subsubsection">6.1.1.7 <acronym>SHA3-384</acronym></h4>

<p>This is SHA3 with 384-bit output size.
</p>
<p>Nettle defines SHA3-384 in <samp>&lt;nettle/sha3.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-sha3_005f384_005fctx"></a>Context struct: <strong>struct sha3_384_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA3_005f384_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA3_384_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA3_384 digest, i.e., 48.
</p></dd></dl>

<dl>
<dt><a name="index-SHA3_005f384_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA3_384_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA3_384.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f384_005finit"></a>Function: <em>void</em> <strong>sha3_384_init</strong> <em>(struct sha3_384_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA3-384 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f384_005fupdate"></a>Function: <em>void</em> <strong>sha3_384_update</strong> <em>(struct sha3_384_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f384_005fdigest"></a>Function: <em>void</em> <strong>sha3_384_digest</strong> <em>(struct sha3_384_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA3_384_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context.
</p></dd></dl>

<a name="SHA3_002d512"></a>
<h4 class="subsubsection">6.1.1.8 <acronym>SHA3-512</acronym></h4>

<p>This is SHA3 with 512-bit output size.
</p>
<p>Nettle defines SHA3-512 in <samp>&lt;nettle/sha3.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-sha3_005f512_005fctx"></a>Context struct: <strong>struct sha3_512_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA3_005f512_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA3_512_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA3_512 digest, i.e. 64.
</p></dd></dl>

<dl>
<dt><a name="index-SHA3_005f512_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA3_512_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA3_512.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f512_005finit"></a>Function: <em>void</em> <strong>sha3_512_init</strong> <em>(struct sha3_512_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA3-512 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f512_005fupdate"></a>Function: <em>void</em> <strong>sha3_512_update</strong> <em>(struct sha3_512_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha3_005f512_005fdigest"></a>Function: <em>void</em> <strong>sha3_512_digest</strong> <em>(struct sha3_512_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA3_512_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context.
</p></dd></dl>

<hr>
<a name="Legacy-hash-functions"></a>
<div class="header">
<p>
Next: <a href="#nettle_005fhash-abstraction" accesskey="n" rel="next">nettle_hash abstraction</a>, Previous: <a href="#Recommended-hash-functions" accesskey="p" rel="prev">Recommended hash functions</a>, Up: <a href="#Hash-functions" accesskey="u" rel="up">Hash functions</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Legacy-hash-functions-1"></a>
<h4 class="subsection">6.1.2 Legacy hash functions</h4>

<p>The hash functions in this section all have some known weaknesses, and
should be avoided for new applications. These hash functions are mainly
useful for compatibility with old applications and protocols. Some are
still considered safe as building blocks for particular constructions,
e.g., there seems to be no known attacks against HMAC-SHA1 or even
HMAC-MD5. In some important cases, use of a &ldquo;legacy&rdquo; hash function
does not in itself make the application insecure; if a known weakness is
relevant depends on how the hash function is used, and on the threat
model.
</p>
<a name="MD5"></a>
<h4 class="subsubsection">6.1.2.1 <acronym>MD5</acronym></h4>

<p>MD5 is a message digest function constructed by Ronald Rivest, and
described in <cite>RFC 1321</cite>. It outputs message digests of 128 bits, or
16 octets. Nettle defines MD5 in <samp>&lt;nettle/md5.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-md5_005fctx"></a>Context struct: <strong>struct md5_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-MD5_005fDIGEST_005fSIZE"></a>Constant: <strong>MD5_DIGEST_SIZE</strong></dt>
<dd><p>The size of an MD5 digest, i.e. 16.
</p></dd></dl>

<dl>
<dt><a name="index-MD5_005fBLOCK_005fSIZE"></a>Constant: <strong>MD5_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of MD5. Useful for some special constructions,
in particular HMAC-MD5.
</p></dd></dl>

<dl>
<dt><a name="index-md5_005finit"></a>Function: <em>void</em> <strong>md5_init</strong> <em>(struct md5_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the MD5 state.
</p></dd></dl>

<dl>
<dt><a name="index-md5_005fupdate"></a>Function: <em>void</em> <strong>md5_update</strong> <em>(struct md5_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-md5_005fdigest"></a>Function: <em>void</em> <strong>md5_digest</strong> <em>(struct md5_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>MD5_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>md5_init</code>.
</p></dd></dl>

<p>The normal way to use MD5 is to call the functions in order: First
<code>md5_init</code>, then <code>md5_update</code> zero or more times, and finally
<code>md5_digest</code>. After <code>md5_digest</code>, the context is reset to
its initial state, so you can start over calling <code>md5_update</code> to
hash new data.
</p>
<p>To start over, you can call <code>md5_init</code> at any time.
</p>
<a name="MD2"></a>
<h4 class="subsubsection">6.1.2.2 <acronym>MD2</acronym></h4>

<p>MD2 is another hash function of Ronald Rivest&rsquo;s, described in
<cite>RFC 1319</cite>. It outputs message digests of 128 bits, or 16 octets.
Nettle defines MD2 in <samp>&lt;nettle/md2.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-md2_005fctx"></a>Context struct: <strong>struct md2_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-MD2_005fDIGEST_005fSIZE"></a>Constant: <strong>MD2_DIGEST_SIZE</strong></dt>
<dd><p>The size of an MD2 digest, i.e. 16.
</p></dd></dl>

<dl>
<dt><a name="index-MD2_005fBLOCK_005fSIZE"></a>Constant: <strong>MD2_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of MD2.
</p></dd></dl>

<dl>
<dt><a name="index-md2_005finit"></a>Function: <em>void</em> <strong>md2_init</strong> <em>(struct md2_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the MD2 state.
</p></dd></dl>

<dl>
<dt><a name="index-md2_005fupdate"></a>Function: <em>void</em> <strong>md2_update</strong> <em>(struct md2_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-md2_005fdigest"></a>Function: <em>void</em> <strong>md2_digest</strong> <em>(struct md2_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>MD2_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>md2_init</code>.
</p></dd></dl>

<a name="MD4"></a>
<h4 class="subsubsection">6.1.2.3 <acronym>MD4</acronym></h4>

<p>MD4 is a predecessor of MD5, described in <cite>RFC 1320</cite>. Like MD5, it
is constructed by Ronald Rivest. It outputs message digests of 128 bits,
or 16 octets. Nettle defines MD4 in <samp>&lt;nettle/md4.h&gt;</samp>. Use of MD4 is
not recommended, but it is sometimes needed for compatibility with
existing applications and protocols.
</p>
<dl>
<dt><a name="index-struct-md4_005fctx"></a>Context struct: <strong>struct md4_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-MD4_005fDIGEST_005fSIZE"></a>Constant: <strong>MD4_DIGEST_SIZE</strong></dt>
<dd><p>The size of an MD4 digest, i.e. 16.
</p></dd></dl>

<dl>
<dt><a name="index-MD4_005fBLOCK_005fSIZE"></a>Constant: <strong>MD4_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of MD4.
</p></dd></dl>

<dl>
<dt><a name="index-md4_005finit"></a>Function: <em>void</em> <strong>md4_init</strong> <em>(struct md4_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the MD4 state.
</p></dd></dl>

<dl>
<dt><a name="index-md4_005fupdate"></a>Function: <em>void</em> <strong>md4_update</strong> <em>(struct md4_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-md4_005fdigest"></a>Function: <em>void</em> <strong>md4_digest</strong> <em>(struct md4_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>MD4_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>md4_init</code>.
</p></dd></dl>

<a name="RIPEMD160"></a>
<h4 class="subsubsection">6.1.2.4 <acronym>RIPEMD160</acronym></h4>

<p>RIPEMD160 is a hash function designed by Hans Dobbertin, Antoon
Bosselaers, and Bart Preneel, as a strengthened version of RIPEMD
(which, like MD4 and MD5, fails the collision-resistance requirement).
It produces message digests of 160 bits, or 20 octets. Nettle defined
RIPEMD160 in <samp>nettle/ripemd160.h</samp>.
</p>
<dl>
<dt><a name="index-struct-ripemd160_005fctx"></a>Context struct: <strong>struct ripemd160_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-RIPEMD160_005fDIGEST_005fSIZE"></a>Constant: <strong>RIPEMD160_DIGEST_SIZE</strong></dt>
<dd><p>The size of a RIPEMD160 digest, i.e. 20.
</p></dd></dl>

<dl>
<dt><a name="index-RIPEMD160_005fBLOCK_005fSIZE"></a>Constant: <strong>RIPEMD160_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of RIPEMD160.
</p></dd></dl>

<dl>
<dt><a name="index-ripemd160_005finit"></a>Function: <em>void</em> <strong>ripemd160_init</strong> <em>(struct ripemd160_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the RIPEMD160 state.
</p></dd></dl>

<dl>
<dt><a name="index-ripemd160_005fupdate"></a>Function: <em>void</em> <strong>ripemd160_update</strong> <em>(struct ripemd160_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-ripemd160_005fdigest"></a>Function: <em>void</em> <strong>ripemd160_digest</strong> <em>(struct ripemd160_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>RIPEMD160_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>ripemd160_init</code>.
</p></dd></dl>

<a name="SHA1"></a>
<h4 class="subsubsection">6.1.2.5 <acronym>SHA1</acronym></h4>

<p>SHA1 is a hash function specified by <em>NIST</em> (The U.S. National
Institute for Standards and Technology). It outputs hash values of 160
bits, or 20 octets. Nettle defines SHA1 in <samp>&lt;nettle/sha1.h&gt;</samp> (and
in <samp>&lt;nettle/sha.h&gt;</samp>, for backwards compatibility).
</p>
<dl>
<dt><a name="index-struct-sha1_005fctx"></a>Context struct: <strong>struct sha1_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SHA1_005fDIGEST_005fSIZE"></a>Constant: <strong>SHA1_DIGEST_SIZE</strong></dt>
<dd><p>The size of a SHA1 digest, i.e. 20.
</p></dd></dl>

<dl>
<dt><a name="index-SHA1_005fBLOCK_005fSIZE"></a>Constant: <strong>SHA1_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of SHA1. Useful for some special constructions,
in particular HMAC-SHA1.
</p></dd></dl>

<dl>
<dt><a name="index-sha1_005finit"></a>Function: <em>void</em> <strong>sha1_init</strong> <em>(struct sha1_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the SHA1 state.
</p></dd></dl>

<dl>
<dt><a name="index-sha1_005fupdate"></a>Function: <em>void</em> <strong>sha1_update</strong> <em>(struct sha1_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-sha1_005fdigest"></a>Function: <em>void</em> <strong>sha1_digest</strong> <em>(struct sha1_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA1_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>sha1_init</code>.
</p></dd></dl>


<a name="GOSTHASH94"></a>
<h4 class="subsubsection">6.1.2.6 <acronym>GOSTHASH94</acronym></h4>

<p>The GOST94 or GOST R 34.11-94 hash algorithm is a Soviet-era algorithm 
used in Russian government standards (see <cite>RFC 4357</cite>).
It outputs message digests of 256 bits, or 32 octets.
Nettle defines GOSTHASH94 in <samp>&lt;nettle/gosthash94.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-gosthash94_005fctx"></a>Context struct: <strong>struct gosthash94_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-GOSTHASH94_005fDIGEST_005fSIZE"></a>Constant: <strong>GOSTHASH94_DIGEST_SIZE</strong></dt>
<dd><p>The size of a GOSTHASH94 digest, i.e. 32.
</p></dd></dl>

<dl>
<dt><a name="index-GOSTHASH94_005fBLOCK_005fSIZE"></a>Constant: <strong>GOSTHASH94_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of GOSTHASH94, i.e., 32.
</p></dd></dl>

<dl>
<dt><a name="index-gosthash94_005finit"></a>Function: <em>void</em> <strong>gosthash94_init</strong> <em>(struct gosthash94_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initialize the GOSTHASH94 state.
</p></dd></dl>

<dl>
<dt><a name="index-gosthash94_005fupdate"></a>Function: <em>void</em> <strong>gosthash94_update</strong> <em>(struct gosthash94_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Hash some more data.
</p></dd></dl>

<dl>
<dt><a name="index-gosthash94_005fdigest"></a>Function: <em>void</em> <strong>gosthash94_digest</strong> <em>(struct gosthash94_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Performs final processing and extracts the message digest, writing it
to <var>digest</var>. <var>length</var> may be smaller than
<code>GOSTHASH94_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the digest are written.
</p>
<p>This function also resets the context in the same way as
<code>gosthash94_init</code>.
</p></dd></dl>

<hr>
<a name="nettle_005fhash-abstraction"></a>
<div class="header">
<p>
Previous: <a href="#Legacy-hash-functions" accesskey="p" rel="prev">Legacy hash functions</a>, Up: <a href="#Hash-functions" accesskey="u" rel="up">Hash functions</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="The-struct-nettle_005fhash-abstraction"></a>
<h4 class="subsection">6.1.3 The <code>struct nettle_hash</code> abstraction</h4>
<a name="index-nettle_005fhash"></a>
<a name="index-nettle_005fhashes"></a>

<p>Nettle includes a struct including information about the supported hash
functions. It is defined in <samp>&lt;nettle/nettle-meta.h&gt;</samp>, and is used
by Nettle&rsquo;s implementation of <acronym>HMAC</acronym> (see <a href="#Keyed-hash-functions">Keyed hash functions</a>).
</p>
<dl>
<dt><a name="index-struct-nettle_005fhash"></a>Meta struct: <strong><code>struct nettle_hash</code></strong> <em>name context_size digest_size block_size init update digest</em></dt>
<dd><p>The last three attributes are function pointers, of types
<code>nettle_hash_init_func *</code>, <code>nettle_hash_update_func *</code>, and
<code>nettle_hash_digest_func *</code>. The first argument to these functions is
<code>void *</code> pointer to a context struct, which is of size
<code>context_size</code>.
</p></dd></dl>

<dl>
<dt><a name="index-nettle_005fmd2"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_md2</strong></dt>
<dt><a name="index-nettle_005fmd4"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_md4</strong></dt>
<dt><a name="index-nettle_005fmd5"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_md5</strong></dt>
<dt><a name="index-nettle_005fripemd160"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_ripemd160</strong></dt>
<dt><a name="index-nettle_005fsha1"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_sha1</strong></dt>
<dt><a name="index-nettle_005fsha224"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_sha224</strong></dt>
<dt><a name="index-nettle_005fsha256"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_sha256</strong></dt>
<dt><a name="index-nettle_005fsha384"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_sha384</strong></dt>
<dt><a name="index-nettle_005fsha512"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_sha512</strong></dt>
<dt><a name="index-nettle_005fsha3_005f256"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_sha3_256</strong></dt>
<dt><a name="index-nettle_005fgosthash94"></a>Constant Struct: <em>struct nettle_hash</em> <strong>nettle_gosthash94</strong></dt>
<dd><p>These are all the hash functions that Nettle implements.
</p></dd></dl>

<p>Nettle also exports a list of all these hashes.
</p>
<dl>
<dt><a name="index-nettle_005fhashes-1"></a>Constant Array: <em>struct nettle_hash **</em> <strong>nettle_hashes</strong></dt>
<dd><p>This list can be used to dynamically enumerate or search the supported
algorithms. NULL-terminated.
</p></dd></dl>

<hr>
<a name="Cipher-functions"></a>
<div class="header">
<p>
Next: <a href="#Cipher-modes" accesskey="n" rel="next">Cipher modes</a>, Previous: <a href="#Hash-functions" accesskey="p" rel="prev">Hash functions</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Cipher-functions-1"></a>
<h3 class="section">6.2 Cipher functions</h3>
<a name="index-Cipher"></a>

<p>A <em>cipher</em> is a function that takes a message or <em>plaintext</em>
and a secret <em>key</em> and transforms it to a <em>ciphertext</em>. Given
only the ciphertext, but not the key, it should be hard to find the
plaintext. Given matching pairs of plaintext and ciphertext, it should
be hard to find the key.
</p>
<a name="index-Block-Cipher"></a>
<a name="index-Stream-Cipher"></a>

<p>There are two main classes of ciphers: Block ciphers and stream ciphers.
</p>
<p>A block cipher can process data only in fixed size chunks, called
<em>blocks</em>. Typical block sizes are 8 or 16 octets. To encrypt
arbitrary messages, you usually have to pad it to an integral number of
blocks, split it into blocks, and then process each block. The simplest
way is to process one block at a time, independent of each other. That
mode of operation is called <em>ECB</em>, Electronic Code Book mode.
However, using <acronym>ECB</acronym> is usually a bad idea. For a start, plaintext blocks
that are equal are transformed to ciphertext blocks that are equal; that
leaks information about the plaintext. Usually you should apply the
cipher is some &ldquo;feedback mode&rdquo;, <em>CBC</em> (Cipher Block Chaining) and
<em>CTR</em> (Counter mode) being two of
of the most popular. See See <a href="#Cipher-modes">Cipher modes</a>, for information on
how to apply <acronym>CBC</acronym> and <acronym>CTR</acronym> with Nettle.
</p>
<p>A stream cipher can be used for messages of arbitrary length. A typical
stream cipher is a keyed pseudo-random generator. To encrypt a plaintext
message of <var>n</var> octets, you key the generator, generate <var>n</var>
octets of pseudo-random data, and XOR it with the plaintext. To decrypt,
regenerate the same stream using the key, XOR it to the ciphertext, and
the plaintext is recovered.
</p>
<p><strong>Caution:</strong> The first rule for this kind of cipher is the
same as for a One Time Pad: <em>never</em> ever use the same key twice.
</p>
<p>A common misconception is that encryption, by itself, implies
authentication. Say that you and a friend share a secret key, and you
receive an encrypted message. You apply the key, and get a plaintext
message that makes sense to you. Can you then be sure that it really was
your friend that wrote the message you&rsquo;re reading? The answer is no. For
example, if you were using a block cipher in ECB mode, an attacker may
pick up the message on its way, and reorder, delete or repeat some of
the blocks. Even if the attacker can&rsquo;t decrypt the message, he can
change it so that you are not reading the same message as your friend
wrote. If you are using a block cipher in <acronym>CBC</acronym> mode rather than
ECB, or are using a stream cipher, the possibilities for this sort of
attack are different, but the attacker can still make predictable
changes to the message.
</p>
<p>It is recommended to <em>always</em> use an authentication mechanism in
addition to encrypting the messages. Popular choices are Message
Authentication Codes like <acronym>HMAC-SHA1</acronym> (see <a href="#Keyed-hash-functions">Keyed hash functions</a>), or digital signatures like <acronym>RSA</acronym>.
</p>
<p>Some ciphers have so called &ldquo;weak keys&rdquo;, keys that results in
undesirable structure after the key setup processing, and should be
avoided. In Nettle, most key setup functions have no return value, but
for ciphers with weak keys, the return value indicates whether or not
the given key is weak. For good keys, key setup returns 1, and for weak
keys, it returns 0. When possible, avoid algorithms that
have weak keys. There are several good ciphers that don&rsquo;t have any weak
keys.
</p>
<p>To encrypt a message, you first initialize a cipher context for
encryption or decryption with a particular key. You then use the context
to process plaintext or ciphertext messages. The initialization is known
as <em>key setup</em>. With Nettle, it is recommended to use each
context struct for only one direction, even if some of the ciphers use a
single key setup function that can be used for both encryption and
decryption.
</p>
<a name="AES"></a>
<h4 class="subsection">6.2.1 AES</h4>
<p>AES is a block cipher, specified by NIST as a replacement for
the older DES standard. The standard is the result of a competition
between cipher designers. The winning design, also known as RIJNDAEL,
was constructed by Joan Daemen and Vincent Rijnmen.
</p>
<p>Like all the AES candidates, the winning design uses a block size of 128
bits, or 16 octets, and three possible key-size, 128, 192 and 256 bits
(16, 24 and 32 octets) being the allowed key sizes. It does not have any
weak keys. Nettle defines AES in <samp>&lt;nettle/aes.h&gt;</samp>, and there is one
context struct for each key size. (Earlier versions of Nettle used a
single context struct, <code>struct aes_ctx</code>, for all key sizes. This
interface kept for backwards compatibility).
</p> 
<dl>
<dt><a name="index-struct-aes128_005fctx"></a>Context struct: <strong>struct aes128_ctx</strong></dt>
<dt><a name="index-struct-aes192_005fctx"></a>Context struct: <strong>struct aes192_ctx</strong></dt>
<dt><a name="index-struct-aes256_005fctx"></a>Context struct: <strong>struct aes256_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-struct-aes_005fctx"></a>Context struct: <strong>struct aes_ctx</strong></dt>
<dd><p>Alternative struct, for the old AES interface.
</p></dd></dl>

<dl>
<dt><a name="index-AES_005fBLOCK_005fSIZE"></a>Constant: <strong>AES_BLOCK_SIZE</strong></dt>
<dd><p>The AES block-size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-AES128_005fKEY_005fSIZE"></a>Constant: <strong>AES128_KEY_SIZE</strong></dt>
<dt><a name="index-AES192_005fKEY_005fSIZE"></a>Constant: <strong>AES192_KEY_SIZE</strong></dt>
<dt><a name="index-AES256_005fKEY_005fSIZE"></a>Constant: <strong>AES256_KEY_SIZE</strong></dt>
<dt><a name="index-AES_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>AES_MIN_KEY_SIZE</strong></dt>
<dt><a name="index-AES_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>AES_MAX_KEY_SIZE</strong></dt>
</dl>

<dl>
<dt><a name="index-AES_005fKEY_005fSIZE"></a>Constant: <strong>AES_KEY_SIZE</strong></dt>
<dd><p>Default AES key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-aes128_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>aes128_set_encrypt_key</strong> <em>(struct aes128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-aes128_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>aes128_set_decrypt_key</strong> <em>(struct aes128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-aes192_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>aes192_set_encrypt_key</strong> <em>(struct aes192_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-aes192_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>aes192_set_decrypt_key</strong> <em>(struct aes192_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-aes256_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>aes256_set_encrypt_key</strong> <em>(struct aes256_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-aes256_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>aes256_set_decrypt_key</strong> <em>(struct aes256_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-aes_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>aes_set_encrypt_key</strong> <em>(struct aes_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-aes_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>aes_set_decrypt_key</strong> <em>(struct aes_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher, for encryption or decryption, respectively.
</p></dd></dl>

<dl>
<dt><a name="index-aes128_005finvert_005fkey"></a>Function: <em>void</em> <strong>aes128_invert_key</strong> <em>(struct aes128_ctx *<var>dst</var>, const struct aes128_ctx *<var>src</var>)</em></dt>
<dt><a name="index-aes192_005finvert_005fkey"></a>Function: <em>void</em> <strong>aes192_invert_key</strong> <em>(struct aes192_ctx *<var>dst</var>, const struct aes192_ctx *<var>src</var>)</em></dt>
<dt><a name="index-aes256_005finvert_005fkey"></a>Function: <em>void</em> <strong>aes256_invert_key</strong> <em>(struct aes256_ctx *<var>dst</var>, const struct aes256_ctx *<var>src</var>)</em></dt>
<dt><a name="index-aes_005finvert_005fkey"></a>Function: <em>void</em> <strong>aes_invert_key</strong> <em>(struct aes_ctx *<var>dst</var>, const struct aes_ctx *<var>src</var>)</em></dt>
<dd><p>Given a context <var>src</var> initialized for encryption, initializes the
context struct <var>dst</var> for decryption, using the same key. If the same
context struct is passed for both <code>src</code> and <code>dst</code>, it is
converted in place. These functions are mainly useful for applications
which needs to both encrypt and decrypt using the <em>same</em> key,
because calling, e.g., <code>aes128_set_encrypt_key</code> and
<code>aes128_invert_key</code>, is more efficient than calling
<code>aes128_set_encrypt_key</code> and <code>aes128_set_decrypt_key</code>.
</p></dd></dl>

<dl>
<dt><a name="index-aes128_005fencrypt"></a>Function: <em>void</em> <strong>aes128_encrypt</strong> <em>(struct aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-aes192_005fencrypt"></a>Function: <em>void</em> <strong>aes192_encrypt</strong> <em>(struct aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-aes256_005fencrypt"></a>Function: <em>void</em> <strong>aes256_encrypt</strong> <em>(struct aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-aes_005fencrypt"></a>Function: <em>void</em> <strong>aes_encrypt</strong> <em>(struct aes_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not overlap
in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-aes128_005fdecrypt"></a>Function: <em>void</em> <strong>aes128_decrypt</strong> <em>(struct aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-aes192_005fdecrypt"></a>Function: <em>void</em> <strong>aes192_decrypt</strong> <em>(struct aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-aes256_005fdecrypt"></a>Function: <em>void</em> <strong>aes256_decrypt</strong> <em>(struct aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-aes_005fdecrypt"></a>Function: <em>void</em> <strong>aes_decrypt</strong> <em>(struct aes_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to the encryption functions above.
</p></dd></dl>

<a name="ARCFOUR"></a>
<h4 class="subsection">6.2.2 ARCFOUR</h4>
<p>ARCFOUR is a stream cipher, also known under the trade marked name RC4,
and it is one of the fastest ciphers around. A problem is that the key
setup of ARCFOUR is quite weak, you should never use keys with
structure, keys that are ordinary passwords, or sequences of keys like
&ldquo;secret:1&rdquo;, &ldquo;secret:2&rdquo;, <small class="enddots">...</small>. If you have keys that don&rsquo;t look
like random bit strings, and you want to use ARCFOUR, always hash the
key before feeding it to ARCFOUR. Furthermore, the initial bytes of the
generated key stream leak information about the key; for this reason, it
is recommended to discard the first 512 bytes of the key stream.
</p>
<div class="example">
<pre class="example">/* A more robust key setup function for ARCFOUR */
void
arcfour_set_key_hashed(struct arcfour_ctx *ctx,
                       size_t length, const uint8_t *key)
{
  struct sha256_ctx hash;
  uint8_t digest[SHA256_DIGEST_SIZE];
  uint8_t buffer[0x200];

  sha256_init(&amp;hash);
  sha256_update(&amp;hash, length, key);
  sha256_digest(&amp;hash, SHA256_DIGEST_SIZE, digest);

  arcfour_set_key(ctx, SHA256_DIGEST_SIZE, digest);
  arcfour_crypt(ctx, sizeof(buffer), buffer, buffer);
}
</pre></div>

<p>Nettle defines ARCFOUR in <samp>&lt;nettle/arcfour.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-arcfour_005fctx"></a>Context struct: <strong>struct arcfour_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-ARCFOUR_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>ARCFOUR_MIN_KEY_SIZE</strong></dt>
<dd><p>Minimum key size, 1.
</p></dd></dl>

<dl>
<dt><a name="index-ARCFOUR_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>ARCFOUR_MAX_KEY_SIZE</strong></dt>
<dd><p>Maximum key size, 256.
</p></dd></dl>

<dl>
<dt><a name="index-ARCFOUR_005fKEY_005fSIZE"></a>Constant: <strong>ARCFOUR_KEY_SIZE</strong></dt>
<dd><p>Default ARCFOUR key size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-arcfour_005fset_005fkey"></a>Function: <em>void</em> <strong>arcfour_set_key</strong> <em>(struct arcfour_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. 
</p></dd></dl>

<dl>
<dt><a name="index-arcfour_005fcrypt"></a>Function: <em>void</em> <strong>arcfour_crypt</strong> <em>(struct arcfour_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypt some data. The same function is used for both encryption and
decryption. Unlike the block ciphers, this function modifies the
context, so you can split the data into arbitrary chunks and encrypt
them one after another. The result is the same as if you had called
<code>arcfour_crypt</code> only once with all the data.
</p></dd></dl>

<a name="ARCTWO"></a>
<h4 class="subsection">6.2.3 ARCTWO</h4>
<p>ARCTWO (also known as the trade marked name RC2) is a block cipher
specified in RFC 2268. Nettle also include a variation of the ARCTWO
set key operation that lack one step, to be compatible with the
reverse engineered RC2 cipher description, as described in a Usenet
post to <code>sci.crypt</code> by Peter Gutmann.
</p>
<p>ARCTWO uses a block size of 64 bits, and variable key-size ranging
from 1 to 128 octets. Besides the key, ARCTWO also has a second
parameter to key setup, the number of effective key bits, <code>ekb</code>.
This parameter can be used to artificially reduce the key size. In
practice, <code>ekb</code> is usually set equal to the input key size.
Nettle defines ARCTWO in <samp>&lt;nettle/arctwo.h&gt;</samp>.
</p>
<p>We do not recommend the use of ARCTWO; the Nettle implementation is
provided primarily for interoperability with existing applications and
standards.
</p>
<dl>
<dt><a name="index-struct-arctwo_005fctx"></a>Context struct: <strong>struct arctwo_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-ARCTWO_005fBLOCK_005fSIZE"></a>Constant: <strong>ARCTWO_BLOCK_SIZE</strong></dt>
<dd><p>The ARCTWO block-size, 8.
</p></dd></dl>

<dl>
<dt><a name="index-ARCTWO_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>ARCTWO_MIN_KEY_SIZE</strong></dt>
</dl>

<dl>
<dt><a name="index-ARCTWO_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>ARCTWO_MAX_KEY_SIZE</strong></dt>
</dl>

<dl>
<dt><a name="index-ARCTWO_005fKEY_005fSIZE"></a>Constant: <strong>ARCTWO_KEY_SIZE</strong></dt>
<dd><p>Default ARCTWO key size, 8.
</p></dd></dl>

<dl>
<dt><a name="index-arctwo_005fset_005fkey_005fekb"></a>Function: <em>void</em> <strong>arctwo_set_key_ekb</strong> <em>(struct arctwo_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>, unsigned <var>ekb</var>)</em></dt>
<dt><a name="index-arctwo_005fset_005fkey"></a>Function: <em>void</em> <strong>arctwo_set_key</strong> <em>(struct arctwo_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-arctwo_005fset_005fkey_005fgutmann"></a>Function: <em>void</em> <strong>arctwo_set_key_gutmann</strong> <em>(struct arctwo_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption
and decryption. The first function is the most general one, which lets
you provide both the variable size key, and the desired effective key
size (in bits). The maximum value for <var>ekb</var> is 1024, and for
convenience, <code>ekb = 0</code> has the same effect as <code>ekb = 1024</code>.
</p>
<p><code>arctwo_set_key(ctx, length, key)</code> is equivalent to
<code>arctwo_set_key_ekb(ctx, length, key, 8*length)</code>, and
<code>arctwo_set_key_gutmann(ctx, length, key)</code> is equivalent to
<code>arctwo_set_key_ekb(ctx, length, key, 1024)</code>
</p></dd></dl>

<dl>
<dt><a name="index-arctwo_005fencrypt"></a>Function: <em>void</em> <strong>arctwo_encrypt</strong> <em>(struct arctwo_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not
overlap in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-arctwo_005fdecrypt"></a>Function: <em>void</em> <strong>arctwo_decrypt</strong> <em>(struct arctwo_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to <code>arctwo_encrypt</code>
</p></dd></dl>

<a name="BLOWFISH"></a>
<h4 class="subsection">6.2.4 BLOWFISH</h4>

<p>BLOWFISH is a block cipher designed by Bruce Schneier. It uses a block
size of 64 bits (8 octets), and a variable key size, up to 448 bits. It
has some weak keys. Nettle defines BLOWFISH in <samp>&lt;nettle/blowfish.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-blowfish_005fctx"></a>Context struct: <strong>struct blowfish_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-BLOWFISH_005fBLOCK_005fSIZE"></a>Constant: <strong>BLOWFISH_BLOCK_SIZE</strong></dt>
<dd><p>The BLOWFISH block-size, 8.
</p></dd></dl>

<dl>
<dt><a name="index-BLOWFISH_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>BLOWFISH_MIN_KEY_SIZE</strong></dt>
<dd><p>Minimum BLOWFISH key size, 8.
</p></dd></dl>

<dl>
<dt><a name="index-BLOWFISH_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>BLOWFISH_MAX_KEY_SIZE</strong></dt>
<dd><p>Maximum BLOWFISH key size, 56.
</p></dd></dl>

<dl>
<dt><a name="index-BLOWFISH_005fKEY_005fSIZE"></a>Constant: <strong>BLOWFISH_KEY_SIZE</strong></dt>
<dd><p>Default BLOWFISH key size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-blowfish_005fset_005fkey"></a>Function: <em>int</em> <strong>blowfish_set_key</strong> <em>(struct blowfish_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. Checks for weak keys, returning 1
for good keys and 0 for weak keys. Applications that don&rsquo;t care about
weak keys can ignore the return value.
</p>
<p><code>blowfish_encrypt</code> or <code>blowfish_decrypt</code> with a weak key will
crash with an assert violation.
</p></dd></dl>

<dl>
<dt><a name="index-blowfish_005fencrypt"></a>Function: <em>void</em> <strong>blowfish_encrypt</strong> <em>(struct blowfish_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not overlap
in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-blowfish_005fdecrypt"></a>Function: <em>void</em> <strong>blowfish_decrypt</strong> <em>(struct blowfish_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to <code>blowfish_encrypt</code>
</p></dd></dl>

<a name="Camellia"></a>
<h4 class="subsection">6.2.5 Camellia</h4>

<p>Camellia is a block cipher developed by Mitsubishi and Nippon Telegraph
and Telephone Corporation, described in <cite>RFC3713</cite>. It is
recommended by some Japanese and European authorities as an alternative
to AES, and it is one of the selected algorithms in the New European
Schemes for Signatures, Integrity and Encryption (NESSIE) project. The
algorithm is patented. The implementation in Nettle is derived from the
implementation released by NTT under the GNU LGPL (v2.1 or later), and
relies on the implicit patent license of the LGPL. There is also a
statement of royalty-free licensing for Camellia at
<a href="http://www.ntt.co.jp/news/news01e/0104/010417.html">http://www.ntt.co.jp/news/news01e/0104/010417.html</a>, but this
statement has some limitations which seem problematic for free software.
</p>
<p>Camellia uses a the same block size and key sizes as AES: The block size
is 128 bits (16 octets), and the supported key sizes are 128, 192, and
256 bits. The variants with 192 and 256 bit keys are identical, except
for the key setup. Nettle defines Camellia in
<samp>&lt;nettle/camellia.h&gt;</samp>, and there is one context struct for each key
size. (Earlier versions of Nettle used a single context struct,
<code>struct camellia_ctx</code>, for all key sizes. This interface kept for
backwards compatibility).
</p>
<dl>
<dt><a name="index-struct-camellia128_005fctx"></a>Context struct: <strong>struct camellia128_ctx</strong></dt>
<dt><a name="index-struct-camellia192_005fctx"></a>Context struct: <strong>struct camellia192_ctx</strong></dt>
<dt><a name="index-struct-camellia256_005fctx"></a>Context struct: <strong>struct camellia256_ctx</strong></dt>
<dd><p>Contexts structs. Actually, <code>camellia192_ctx</code> is an alias for
<code>camellia256_ctx</code>.
</p></dd></dl>

<dl>
<dt><a name="index-struct-camellia_005fctx"></a>Context struct: <strong>struct camellia_ctx</strong></dt>
<dd><p>Alternative struct, for the old Camellia interface.
</p></dd></dl>

<dl>
<dt><a name="index-CAMELLIA_005fBLOCK_005fSIZE"></a>Constant: <strong>CAMELLIA_BLOCK_SIZE</strong></dt>
<dd><p>The CAMELLIA block-size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-CAMELLIA128_005fKEY_005fSIZE"></a>Constant: <strong>CAMELLIA128_KEY_SIZE</strong></dt>
<dt><a name="index-CAMELLIA192_005fKEY_005fSIZE"></a>Constant: <strong>CAMELLIA192_KEY_SIZE</strong></dt>
<dt><a name="index-CAMELLIA256_005fKEY_005fSIZE"></a>Constant: <strong>CAMELLIA256_KEY_SIZE</strong></dt>
<dt><a name="index-CAMELLIA_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>CAMELLIA_MIN_KEY_SIZE</strong></dt>
<dt><a name="index-CAMELLIA_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>CAMELLIA_MAX_KEY_SIZE</strong></dt>
</dl>

<dl>
<dt><a name="index-CAMELLIA_005fKEY_005fSIZE"></a>Constant: <strong>CAMELLIA_KEY_SIZE</strong></dt>
<dd><p>Default CAMELLIA key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-camellia128_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>camellia128_set_encrypt_key</strong> <em>(struct camellia128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-camellia128_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>camellia128_set_decrypt_key</strong> <em>(struct camellia128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-camellia192_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>camellia192_set_encrypt_key</strong> <em>(struct camellia192_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-camellia192_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>camellia192_set_decrypt_key</strong> <em>(struct camellia192_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-camellia256_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>camellia256_set_encrypt_key</strong> <em>(struct camellia256_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-camellia256_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>camellia256_set_decrypt_key</strong> <em>(struct camellia256_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-camellia_005fset_005fencrypt_005fkey"></a>Function: <em>void</em> <strong>camellia_set_encrypt_key</strong> <em>(struct camellia_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-camellia_005fset_005fdecrypt_005fkey"></a>Function: <em>void</em> <strong>camellia_set_decrypt_key</strong> <em>(struct camellia_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher, for encryption or decryption, respectively.
</p></dd></dl>

<dl>
<dt><a name="index-camellia128_005finvert_005fkey"></a>Function: <em>void</em> <strong>camellia128_invert_key</strong> <em>(struct camellia128_ctx *<var>dst</var>, const struct camellia128_ctx *<var>src</var>)</em></dt>
<dt><a name="index-camellia192_005finvert_005fkey"></a>Function: <em>void</em> <strong>camellia192_invert_key</strong> <em>(struct camellia192_ctx *<var>dst</var>, const struct camellia192_ctx *<var>src</var>)</em></dt>
<dt><a name="index-camellia256_005finvert_005fkey"></a>Function: <em>void</em> <strong>camellia256_invert_key</strong> <em>(struct camellia256_ctx *<var>dst</var>, const struct camellia256_ctx *<var>src</var>)</em></dt>
<dt><a name="index-camellia_005finvert_005fkey"></a>Function: <em>void</em> <strong>camellia_invert_key</strong> <em>(struct camellia_ctx *<var>dst</var>, const struct camellia_ctx *<var>src</var>)</em></dt>
<dd><p>Given a context <var>src</var> initialized for encryption, initializes the
context struct <var>dst</var> for decryption, using the same key. If the same
context struct is passed for both <code>src</code> and <code>dst</code>, it is
converted in place. These functions are mainly useful for applications
which needs to both encrypt and decrypt using the <em>same</em> key.
</p></dd></dl>

<dl>
<dt><a name="index-camellia128_005fcrypt"></a>Function: <em>void</em> <strong>camellia128_crypt</strong> <em>(struct camellia128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-camellia192_005fcrypt"></a>Function: <em>void</em> <strong>camellia192_crypt</strong> <em>(struct camellia192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-camellia256_005fcrypt"></a>Function: <em>void</em> <strong>camellia256_crypt</strong> <em>(struct camellia256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-camellia_005fcrypt"></a>Function: <em>void</em> <strong>camellia_crypt</strong> <em>(struct camellia_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>The same function is used for both encryption and decryption.
<var>length</var> must be an integral multiple of the block size. If it is
more than one block, the data is processed in ECB mode. <code>src</code> and
<code>dst</code> may be equal, but they must not overlap in any other way.
</p></dd></dl>

<a name="CAST128"></a>
<h4 class="subsection">6.2.6 CAST128</h4>

<p>CAST-128 is a block cipher, specified in <cite>RFC 2144</cite>. It uses a 64
bit (8 octets) block size, and a variable key size of up to 128 bits.
Nettle defines cast128 in <samp>&lt;nettle/cast128.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-cast128_005fctx"></a>Context struct: <strong>struct cast128_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-CAST128_005fBLOCK_005fSIZE"></a>Constant: <strong>CAST128_BLOCK_SIZE</strong></dt>
<dd><p>The CAST128 block-size, 8.
</p></dd></dl>

<dl>
<dt><a name="index-CAST128_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>CAST128_MIN_KEY_SIZE</strong></dt>
<dd><p>Minimum CAST128 key size, 5.
</p></dd></dl>

<dl>
<dt><a name="index-CAST128_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>CAST128_MAX_KEY_SIZE</strong></dt>
<dd><p>Maximum CAST128 key size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-CAST128_005fKEY_005fSIZE"></a>Constant: <strong>CAST128_KEY_SIZE</strong></dt>
<dd><p>Default CAST128 key size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-cast128_005fset_005fkey"></a>Function: <em>void</em> <strong>cast128_set_key</strong> <em>(struct cast128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. 
</p></dd></dl>

<dl>
<dt><a name="index-cast128_005fencrypt"></a>Function: <em>void</em> <strong>cast128_encrypt</strong> <em>(struct cast128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not overlap
in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-cast128_005fdecrypt"></a>Function: <em>void</em> <strong>cast128_decrypt</strong> <em>(struct cast128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to <code>cast128_encrypt</code>
</p></dd></dl>

<a name="ChaCha"></a>
<h4 class="subsection">6.2.7 ChaCha</h4>

<p>ChaCha is a variant of the stream cipher Salsa20, also designed by D. J.
Bernstein. For more information on Salsa20, see below. Nettle defines
ChaCha in <samp>&lt;nettle/chacha.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-chacha_005fctx"></a>Context struct: <strong>struct chacha_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-CHACHA_005fKEY_005fSIZE"></a>Constant: <strong>CHACHA_KEY_SIZE</strong></dt>
<dd><p>ChaCha key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-CHACHA_005fBLOCK_005fSIZE"></a>Constant: <strong>CHACHA_BLOCK_SIZE</strong></dt>
<dd><p>ChaCha block size, 64.
</p></dd></dl>

<dl>
<dt><a name="index-CHACHA_005fNONCE_005fSIZE"></a>Constant: <strong>CHACHA_NONCE_SIZE</strong></dt>
<dd><p>Size of the nonce, 8.
</p></dd></dl>

<dl>
<dt><a name="index-chacha_005fset_005fkey"></a>Function: <em>void</em> <strong>chacha_set_key</strong> <em>(struct chacha_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. Before using the cipher,
you <em>must</em> also call <code>chacha_set_nonce</code>, see below.
</p></dd></dl>

<dl>
<dt><a name="index-chacha_005fset_005fnonce"></a>Function: <em>void</em> <strong>chacha_set_nonce</strong> <em>(struct chacha_ctx *<var>ctx</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dd><p>Sets the nonce. It is always of size <code>CHACHA_NONCE_SIZE</code>, 8
octets. This function also initializes the block counter, setting it to
zero.
</p></dd></dl>

<dl>
<dt><a name="index-chacha_005fcrypt"></a>Function: <em>void</em> <strong>chacha_crypt</strong> <em>(struct chacha_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message, using ChaCha. When a
message is encrypted using a sequence of calls to <code>chacha_crypt</code>,
all but the last call <em>must</em> use a length that is a multiple of
<code>CHACHA_BLOCK_SIZE</code>.
</p></dd></dl>

<a name="DES"></a>
<h4 class="subsection">6.2.8 DES</h4>
<p>DES is the old Data Encryption Standard, specified by NIST. It uses a
block size of 64 bits (8 octets), and a key size of 56 bits. However,
the key bits are distributed over 8 octets, where the least significant
bit of each octet may be used for parity. A common way to use DES is to
generate 8 random octets in some way, then set the least significant bit
of each octet to get odd parity, and initialize DES with the resulting
key.
</p>
<p>The key size of DES is so small that keys can be found by brute force,
using specialized hardware or lots of ordinary work stations in
parallel. One shouldn&rsquo;t be using plain DES at all today, if one uses
DES at all one should be using &ldquo;triple DES&rdquo;, see DES3 below.
</p>
<p>DES also has some weak keys. Nettle defines DES in <samp>&lt;nettle/des.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-des_005fctx"></a>Context struct: <strong>struct des_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-DES_005fBLOCK_005fSIZE"></a>Constant: <strong>DES_BLOCK_SIZE</strong></dt>
<dd><p>The DES block-size, 8.
</p></dd></dl>

<dl>
<dt><a name="index-DES_005fKEY_005fSIZE"></a>Constant: <strong>DES_KEY_SIZE</strong></dt>
<dd><p>DES key size, 8.
</p></dd></dl>

<dl>
<dt><a name="index-des_005fset_005fkey"></a>Function: <em>int</em> <strong>des_set_key</strong> <em>(struct des_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. Parity bits are ignored. Checks for weak keys, returning 1
for good keys and 0 for weak keys. Applications that don&rsquo;t care about
weak keys can ignore the return value.
</p></dd></dl>

<dl>
<dt><a name="index-des_005fencrypt"></a>Function: <em>void</em> <strong>des_encrypt</strong> <em>(struct des_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not overlap
in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-des_005fdecrypt"></a>Function: <em>void</em> <strong>des_decrypt</strong> <em>(struct des_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to <code>des_encrypt</code>
</p></dd></dl>

<dl>
<dt><a name="index-des_005fcheck_005fparity"></a>Function: <em>int</em> <strong>des_check_parity</strong> <em>(size_t <var>length</var>, const uint8_t *<var>key</var>);</em></dt>
<dd><p>Checks that the given key has correct, odd, parity. Returns 1 for
correct parity, and 0 for bad parity.
</p></dd></dl>

<dl>
<dt><a name="index-des_005ffix_005fparity"></a>Function: <em>void</em> <strong>des_fix_parity</strong> <em>(size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Adjusts the parity bits to match DES&rsquo;s requirements. You need this
function if you have created a random-looking string by a key agreement
protocol, and want to use it as a DES key. <var>dst</var> and <var>src</var> may
be equal.
</p></dd></dl>

<a name="DES3"></a>
<h4 class="subsection">6.2.9 DES3</h4>
<p>The inadequate key size of DES has already been mentioned. One way to
increase the key size is to pipe together several DES boxes with
independent keys. It turns out that using two DES ciphers is not as
secure as one might think, even if the key size of the combination is a
respectable 112 bits.
</p>
<p>The standard way to increase DES&rsquo;s key size is to use three DES boxes.
The mode of operation is a little peculiar: the middle DES box is wired
in the reverse direction. To encrypt a block with DES3, you encrypt it
using the first 56 bits of the key, then <em>decrypt</em> it using the
middle 56 bits of the key, and finally encrypt it again using the last
56 bits of the key. This is known as &ldquo;ede&rdquo; triple-DES, for
&ldquo;encrypt-decrypt-encrypt&rdquo;.
</p>
<p>The &ldquo;ede&rdquo; construction provides some backward compatibility, as you get
plain single DES simply by feeding the same key to all three boxes. That
should help keeping down the gate count, and the price, of hardware
circuits implementing both plain DES and DES3.
</p>
<p>DES3 has a key size of 168 bits, but just like plain DES, useless parity
bits are inserted, so that keys are represented as 24 octets (192 bits).
As a 112 bit key is large enough to make brute force attacks
impractical, some applications uses a &ldquo;two-key&rdquo; variant of triple-DES.
In this mode, the same key bits are used for the first and the last DES
box in the pipe, while the middle box is keyed independently. The
two-key variant is believed to be secure, i.e. there are no known
attacks significantly better than brute force.
</p>
<p>Naturally, it&rsquo;s simple to implement triple-DES on top of Nettle&rsquo;s DES
functions. Nettle includes an implementation of three-key &ldquo;ede&rdquo;
triple-DES, it is defined in the same place as plain DES,
<samp>&lt;nettle/des.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-des3_005fctx"></a>Context struct: <strong>struct des3_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-DES3_005fBLOCK_005fSIZE"></a>Constant: <strong>DES3_BLOCK_SIZE</strong></dt>
<dd><p>The DES3 block-size is the same as DES_BLOCK_SIZE, 8.
</p></dd></dl>

<dl>
<dt><a name="index-DES3_005fKEY_005fSIZE"></a>Constant: <strong>DES3_KEY_SIZE</strong></dt>
<dd><p>DES key size, 24.
</p></dd></dl>

<dl>
<dt><a name="index-des3_005fset_005fkey"></a>Function: <em>int</em> <strong>des3_set_key</strong> <em>(struct des3_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. Parity bits are ignored. Checks for weak keys, returning 1
if all three keys are good keys, and 0 if one or more key is weak.
Applications that don&rsquo;t care about weak keys can ignore the return
value.
</p></dd></dl>

<p>For random-looking strings, you can use <code>des_fix_parity</code> to adjust
the parity bits before calling <code>des3_set_key</code>.
</p>
<dl>
<dt><a name="index-des3_005fencrypt"></a>Function: <em>void</em> <strong>des3_encrypt</strong> <em>(struct des3_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not overlap
in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-des3_005fdecrypt"></a>Function: <em>void</em> <strong>des3_decrypt</strong> <em>(struct des3_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to <code>des_encrypt</code>
</p></dd></dl>

<a name="Salsa20"></a>
<h4 class="subsection">6.2.10 Salsa20</h4>
<p>Salsa20 is a fairly recent stream cipher designed by D. J. Bernstein. It
is built on the observation that a cryptographic hash function can be
used for encryption: Form the hash input from the secret key and a
counter, xor the hash output and the first block of the plaintext, then
increment the counter to process the next block (similar to CTR mode, see
see <a href="#CTR">CTR</a>). Bernstein defined an encryption algorithm, Snuffle,
in this way to ridicule United States export restrictions which treated hash
functions as nice and harmless, but ciphers as dangerous munitions.
</p>
<p>Salsa20 uses the same idea, but with a new specialized hash function to
mix key, block counter, and a couple of constants. It&rsquo;s also designed
for speed; on x86_64, it is currently the fastest cipher offered by
nettle. It uses a block size of 512 bits (64 octets) and there are two
specified key sizes, 128 and 256 bits (16 and 32 octets).
</p>
<p><strong>Caution:</strong> The hash function used in Salsa20 is <em>not</em>
directly applicable for use as a general hash function. It&rsquo;s <em>not</em>
collision resistant if arbitrary inputs are allowed, and furthermore,
the input and output is of fixed size.
</p>
<p>When using Salsa20 to process a message, one specifies both a key and a
<em>nonce</em>, the latter playing a similar rôle to the initialization
vector (<acronym>IV</acronym>) used with <acronym>CBC</acronym> or <acronym>CTR</acronym> mode. One
can use the same key for several messages, provided one uses a unique
random <acronym>iv</acronym> for each message. The <acronym>iv</acronym> is 64 bits (8
octets). The block counter is initialized to zero for each message, and
is also 64 bits (8 octets). Nettle defines Salsa20 in
<samp>&lt;nettle/salsa20.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-salsa20_005fctx"></a>Context struct: <strong>struct salsa20_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SALSA20_005f128_005fKEY_005fSIZE"></a>Constant: <strong>SALSA20_128_KEY_SIZE</strong></dt>
<dt><a name="index-SALSA20_005f256_005fKEY_005fSIZE"></a>Constant: <strong>SALSA20_256_KEY_SIZE</strong></dt>
<dd><p>The two supported key sizes, 16 and 32 octets.
</p></dd></dl>

<dl>
<dt><a name="index-SALSA20_005fKEY_005fSIZE"></a>Constant: <strong>SALSA20_KEY_SIZE</strong></dt>
<dd><p>Recommended key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-SALSA20_005fBLOCK_005fSIZE"></a>Constant: <strong>SALSA20_BLOCK_SIZE</strong></dt>
<dd><p>Salsa20 block size, 64.
</p></dd></dl>

<dl>
<dt><a name="index-SALSA20_005fNONCE_005fSIZE"></a>Constant: <strong>SALSA20_NONCE_SIZE</strong></dt>
<dd><p>Size of the nonce, 8.
</p></dd></dl>

<dl>
<dt><a name="index-salsa20_005f128_005fset_005fkey"></a>Function: <em>void</em> <strong>salsa20_128_set_key</strong> <em>(struct salsa20_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-salsa20_005f256_005fset_005fkey"></a>Function: <em>void</em> <strong>salsa20_256_set_key</strong> <em>(struct salsa20_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-salsa20_005fset_005fkey"></a>Function: <em>void</em> <strong>salsa20_set_key</strong> <em>(struct salsa20_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. <code>salsa20_128_set_key</code> and <code>salsa20_128_set_key</code>
use a fix key size each, 16 and 32 octets, respectively. The function
<code>salsa20_set_key</code> is provided for backwards compatibility, and the
<var>length</var> argument must be either 16 or 32. Before using the cipher,
you <em>must</em> also call <code>salsa20_set_nonce</code>, see below.
</p></dd></dl>

<dl>
<dt><a name="index-salsa20_005fset_005fnonce"></a>Function: <em>void</em> <strong>salsa20_set_nonce</strong> <em>(struct salsa20_ctx *<var>ctx</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dd><p>Sets the nonce. It is always of size <code>SALSA20_NONCE_SIZE</code>, 8
octets. This function also initializes the block counter, setting it to
zero.
</p></dd></dl>

<dl>
<dt><a name="index-salsa20_005fcrypt"></a>Function: <em>void</em> <strong>salsa20_crypt</strong> <em>(struct salsa20_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message, using salsa20. When a
message is encrypted using a sequence of calls to <code>salsa20_crypt</code>,
all but the last call <em>must</em> use a length that is a multiple of
<code>SALSA20_BLOCK_SIZE</code>.
</p></dd></dl>

<p>The full salsa20 cipher uses 20 rounds of mixing. Variants of Salsa20
with fewer rounds are possible, and the 12-round variant is specified by
eSTREAM, see <a href="http://www.ecrypt.eu.org/stream/finallist.html">http://www.ecrypt.eu.org/stream/finallist.html</a>.
Nettle calls this variant <code>salsa20r12</code>. It uses the same context
struct and key setup as the full salsa20 cipher, but a separate function
for encryption and decryption.
</p>
<dl>
<dt><a name="index-salsa20r12_005fcrypt"></a>Function: <em>void</em> <strong>salsa20r12_crypt</strong> <em>(struct salsa20_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message, using salsa20 reduced to 12
rounds.
</p></dd></dl>

<a name="SERPENT"></a>
<h4 class="subsection">6.2.11 SERPENT</h4>
<p>SERPENT is one of the AES finalists, designed by Ross Anderson, Eli
Biham and Lars Knudsen. Thus, the interface and properties are similar
to AES&rsquo;. One peculiarity is that it is quite pointless to use it with
anything but the maximum key size, smaller keys are just padded to
larger ones. Nettle defines SERPENT in <samp>&lt;nettle/serpent.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-serpent_005fctx"></a>Context struct: <strong>struct serpent_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-SERPENT_005fBLOCK_005fSIZE"></a>Constant: <strong>SERPENT_BLOCK_SIZE</strong></dt>
<dd><p>The SERPENT block-size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-SERPENT_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>SERPENT_MIN_KEY_SIZE</strong></dt>
<dd><p>Minimum SERPENT key size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-SERPENT_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>SERPENT_MAX_KEY_SIZE</strong></dt>
<dd><p>Maximum SERPENT key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-SERPENT_005fKEY_005fSIZE"></a>Constant: <strong>SERPENT_KEY_SIZE</strong></dt>
<dd><p>Default SERPENT key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-serpent_005fset_005fkey"></a>Function: <em>void</em> <strong>serpent_set_key</strong> <em>(struct serpent_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. 
</p></dd></dl>

<dl>
<dt><a name="index-serpent_005fencrypt"></a>Function: <em>void</em> <strong>serpent_encrypt</strong> <em>(struct serpent_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not overlap
in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-serpent_005fdecrypt"></a>Function: <em>void</em> <strong>serpent_decrypt</strong> <em>(struct serpent_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to <code>serpent_encrypt</code>
</p></dd></dl>


<a name="TWOFISH"></a>
<h4 class="subsection">6.2.12 TWOFISH</h4>
<p>Another AES finalist, this one designed by Bruce Schneier and others.
Nettle defines it in <samp>&lt;nettle/twofish.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-twofish_005fctx"></a>Context struct: <strong>struct twofish_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-TWOFISH_005fBLOCK_005fSIZE"></a>Constant: <strong>TWOFISH_BLOCK_SIZE</strong></dt>
<dd><p>The TWOFISH block-size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-TWOFISH_005fMIN_005fKEY_005fSIZE"></a>Constant: <strong>TWOFISH_MIN_KEY_SIZE</strong></dt>
<dd><p>Minimum TWOFISH key size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-TWOFISH_005fMAX_005fKEY_005fSIZE"></a>Constant: <strong>TWOFISH_MAX_KEY_SIZE</strong></dt>
<dd><p>Maximum TWOFISH key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-TWOFISH_005fKEY_005fSIZE"></a>Constant: <strong>TWOFISH_KEY_SIZE</strong></dt>
<dd><p>Default TWOFISH key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-twofish_005fset_005fkey"></a>Function: <em>void</em> <strong>twofish_set_key</strong> <em>(struct twofish_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the cipher. The same function is used for both encryption and
decryption. 
</p></dd></dl>

<dl>
<dt><a name="index-twofish_005fencrypt"></a>Function: <em>void</em> <strong>twofish_encrypt</strong> <em>(struct twofish_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encryption function. <var>length</var> must be an integral multiple of the
block size. If it is more than one block, the data is processed in ECB
mode. <code>src</code> and <code>dst</code> may be equal, but they must not overlap
in any other way.
</p></dd></dl>

<dl>
<dt><a name="index-twofish_005fdecrypt"></a>Function: <em>void</em> <strong>twofish_decrypt</strong> <em>(struct twofish_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Analogous to <code>twofish_encrypt</code>
</p></dd></dl>

<a name="The-struct-nettle_005fcipher-abstraction"></a>
<h4 class="subsection">6.2.13 The <code>struct nettle_cipher</code> abstraction</h4>
<a name="index-nettle_005fcipher"></a>
<a name="index-nettle_005fciphers"></a>

<p>Nettle includes a struct including information about some of the more
regular cipher functions. It can be useful for applications that need a
simple way to handle various algorithms. Nettle defines these structs in
<samp>&lt;nettle/nettle-meta.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-nettle_005fcipher"></a>Meta struct: <strong><code>struct nettle_cipher</code></strong> <em>name context_size block_size key_size set_encrypt_key set_decrypt_key encrypt decrypt</em></dt>
<dd><p>The last four attributes are function pointers, of types
<code>nettle_set_key_func *</code> and <code>nettle_cipher_func *</code>. The first
argument to these functions is a <code>const void *</code> pointer to a context
struct, which is of size <code>context_size</code>.
</p></dd></dl>

<dl>
<dt><a name="index-nettle_005faes128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_aes128</strong></dt>
<dt><a name="index-nettle_005faes192"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_aes192</strong></dt>
<dt><a name="index-nettle_005faes256"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_aes256</strong></dt>
<dt><a name="index-nettle_005farctwo40"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_arctwo40</strong></dt>
<dt><a name="index-nettle_005farctwo64"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_arctwo64</strong></dt>
<dt><a name="index-nettle_005farctwo128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_arctwo128</strong></dt>
<dt><a name="index-nettle_005farctwo_005fgutmann128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_arctwo_gutmann128</strong></dt>
<dt><a name="index-nettle_005farcfour128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_arcfour128</strong></dt>
<dt><a name="index-nettle_005fcamellia128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_camellia128</strong></dt>
<dt><a name="index-nettle_005fcamellia192"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_camellia192</strong></dt>
<dt><a name="index-nettle_005fcamellia256"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_camellia256</strong></dt>
<dt><a name="index-nettle_005fcast128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_cast128</strong></dt>
<dt><a name="index-nettle_005fserpent128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_serpent128</strong></dt>
<dt><a name="index-nettle_005fserpent192"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_serpent192</strong></dt>
<dt><a name="index-nettle_005fserpent256"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_serpent256</strong></dt>
<dt><a name="index-nettle_005ftwofish128"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_twofish128</strong></dt>
<dt><a name="index-nettle_005ftwofish192"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_twofish192</strong></dt>
<dt><a name="index-nettle_005ftwofish256"></a>Constant Struct: <em>struct nettle_cipher</em> <strong>nettle_twofish256</strong></dt>
<dd><p>Nettle includes such structs for all the <em>regular</em> ciphers, i.e.
ones without weak keys or other oddities.
</p></dd></dl>

<p>Nettle also exports a list of all these ciphers without weak keys or
other oddities.
</p>
<dl>
<dt><a name="index-nettle_005fciphers-1"></a>Constant Array: <em>struct nettle_cipher **</em> <strong>nettle_ciphers</strong></dt>
<dd><p>This list can be used to dynamically enumerate or search the supported
algorithms. NULL-terminated.
</p></dd></dl>

<hr>
<a name="Cipher-modes"></a>
<div class="header">
<p>
Next: <a href="#Authenticated-encryption" accesskey="n" rel="next">Authenticated encryption</a>, Previous: <a href="#Cipher-functions" accesskey="p" rel="prev">Cipher functions</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Cipher-modes-1"></a>
<h3 class="section">6.3 Cipher modes</h3>

<p>Cipher modes of operation specifies the procedure to use when encrypting
a message that is larger than the cipher&rsquo;s block size. As explained in
See <a href="#Cipher-functions">Cipher functions</a>, splitting the message into blocks and
processing them independently with the block cipher (Electronic Code
Book mode, <acronym>ECB</acronym>), leaks information.
</p>
<p>Besides <acronym>ECB</acronym>, Nettle provides a two other modes of operation:
Cipher Block Chaining (<acronym>CBC</acronym>), Counter mode (<acronym>CTR</acronym>), and
a couple of <acronym>AEAD</acronym> modes (see <a href="#Authenticated-encryption">Authenticated encryption</a>).
<acronym>CBC</acronym> is widely used, but there are a few subtle issues of
information leakage, see, e.g.,
<a href="http://www.kb.cert.org/vuls/id/958563"><acronym>SSH</acronym> <acronym>CBC</acronym>
vulnerability</a>. Today, <acronym>CTR</acronym> is usually preferred over <acronym>CBC</acronym>.
</p>
<p>Modes like <acronym>CBC</acronym> and <acronym>CTR</acronym> provide <em>no</em> message
authentication, and should always be used together with a <acronym>MAC</acronym>
(see <a href="#Keyed-hash-functions">Keyed hash functions</a>) or signature to authenticate the message.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#CBC" accesskey="1">CBC</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#CTR" accesskey="2">CTR</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<hr>
<a name="CBC"></a>
<div class="header">
<p>
Next: <a href="#CTR" accesskey="n" rel="next">CTR</a>, Previous: <a href="#Cipher-modes" accesskey="p" rel="prev">Cipher modes</a>, Up: <a href="#Cipher-modes" accesskey="u" rel="up">Cipher modes</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Cipher-Block-Chaining"></a>
<h4 class="subsection">6.3.1 Cipher Block Chaining</h4>

<a name="index-Cipher-Block-Chaining"></a>
<a name="index-CBC-Mode"></a>

<p>When using <acronym>CBC</acronym> mode, plaintext blocks are not encrypted
independently of each other, like in Electronic Cook Book mode. Instead,
when encrypting a block in <acronym>CBC</acronym> mode, the previous ciphertext
block is XORed with the plaintext before it is fed to the block cipher.
When encrypting the first block, a random block called an <em>IV</em>, or
Initialization Vector, is used as the &ldquo;previous ciphertext block&rdquo;. The
IV should be chosen randomly, but it need not be kept secret, and can
even be transmitted in the clear together with the encrypted data.
</p>
<p>In symbols, if <code>E_k</code> is the encryption function of a block cipher,
and <code>IV</code> is the initialization vector, then <code>n</code> plaintext blocks
<code>M_1</code>,&hellip; <code>M_n</code> are transformed into <code>n</code> ciphertext blocks
<code>C_1</code>,&hellip; <code>C_n</code> as follows:
</p>
<div class="example">
<pre class="example">C_1 = E_k(IV  XOR M_1)
C_2 = E_k(C_1 XOR M_2)

&hellip;

C_n = E_k(C_(n-1) XOR M_n)
</pre></div>

<p>Nettle&rsquo;s includes two functions for applying a block cipher in Cipher
Block Chaining (<acronym>CBC</acronym>) mode, one for encryption and one for
decryption. These functions uses <code>void *</code> to pass cipher contexts
around.
</p>
<dl>
<dt><a name="index-cbc_005fencrypt"></a>Function: <em>void</em> <strong>cbc_encrypt</strong> <em>(const void *<var>ctx</var>, nettle_cipher_func *<var>f</var>, size_t <var>block_size</var>, uint8_t *<var>iv</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-cbc_005fdecrypt"></a>Function: <em>void</em> <strong>cbc_decrypt</strong> <em>(const void *<var>ctx</var>, nettle_cipher_func *<var>f</var>, size_t <var>block_size</var>, uint8_t *<var>iv</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd>
<p>Applies the encryption or decryption function <var>f</var> in <acronym>CBC</acronym>
mode. The final ciphertext block processed is copied into <var>iv</var>
before returning, so that a large message can be processed by a sequence of
calls to <code>cbc_encrypt</code>. The function <var>f</var> is of type
</p>
<p><code>void f (void *<var>ctx</var>, size_t <var>length</var>, uint8_t <var>dst</var>,
const uint8_t *<var>src</var>)</code>,
</p>
<p>and the <code>cbc_encrypt</code> and <code>cbc_decrypt</code> functions pass their
argument <var>ctx</var> on to <var>f</var>.
</p></dd></dl>

<p>There are also some macros to help use these functions correctly.
</p>
<dl>
<dt><a name="index-CBC_005fCTX"></a>Macro: <strong>CBC_CTX</strong> <em>(<var>context_type</var>, <var>block_size</var>)</em></dt>
<dd><p>Expands to
</p><div class="example">
<pre class="example">{
   context_type ctx;
   uint8_t iv[block_size];
}
</pre></div>
</dd></dl>

<p>It can be used to define a <acronym>CBC</acronym> context struct, either directly,
</p>
<div class="example">
<pre class="example">struct CBC_CTX(struct aes_ctx, AES_BLOCK_SIZE) ctx;
</pre></div>

<p>or to give it a struct tag,
</p>
<div class="example">
<pre class="example">struct aes_cbc_ctx CBC_CTX (struct aes_ctx, AES_BLOCK_SIZE);
</pre></div>

<dl>
<dt><a name="index-CBC_005fSET_005fIV"></a>Macro: <strong>CBC_SET_IV</strong> <em>(<var>ctx</var>, <var>iv</var>)</em></dt>
<dd><p>First argument is a pointer to a context struct as defined by <code>CBC_CTX</code>,
and the second is a pointer to an Initialization Vector (IV) that is
copied into that context.
</p></dd></dl>

<dl>
<dt><a name="index-CBC_005fENCRYPT"></a>Macro: <strong>CBC_ENCRYPT</strong> <em>(<var>ctx</var>, <var>f</var>, <var>length</var>, <var>dst</var>, <var>src</var>)</em></dt>
<dt><a name="index-CBC_005fDECRYPT"></a>Macro: <strong>CBC_DECRYPT</strong> <em>(<var>ctx</var>, <var>f</var>, <var>length</var>, <var>dst</var>, <var>src</var>)</em></dt>
<dd><p>A simpler way to invoke <code>cbc_encrypt</code> and <code>cbc_decrypt</code>. The
first argument is a pointer to a context struct as defined by
<code>CBC_CTX</code>, and the second argument is an encryption or decryption
function following Nettle&rsquo;s conventions. The last three arguments define
the source and destination area for the operation.
</p></dd></dl>

<p>These macros use some tricks to make the compiler display a warning if
the types of <var>f</var> and <var>ctx</var> don&rsquo;t match, e.g. if you try to use
an <code>struct aes_ctx</code> context with the <code>des_encrypt</code> function.
</p>
<hr>
<a name="CTR"></a>
<div class="header">
<p>
Previous: <a href="#CBC" accesskey="p" rel="prev">CBC</a>, Up: <a href="#Cipher-modes" accesskey="u" rel="up">Cipher modes</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Counter-mode"></a>
<h4 class="subsection">6.3.2 Counter mode</h4>

<a name="index-Counter-Mode"></a>
<a name="index-CTR-Mode"></a>

<p>Counter mode (<acronym>CTR</acronym>) uses the block cipher as a keyed
pseudo-random generator. The output of the generator is XORed with the
data to be encrypted. It can be understood as a way to transform a block
cipher to a stream cipher.
</p>
<p>The message is divided into <code>n</code> blocks <code>M_1</code>,&hellip;
<code>M_n</code>, where <code>M_n</code> is of size <code>m</code> which may be smaller
than the block size. Except for the last block, all the message blocks
must be of size equal to the cipher&rsquo;s block size.
</p>
<p>If <code>E_k</code> is the encryption function of a block cipher, <code>IC</code> is
the initial counter, then the <code>n</code> plaintext blocks are
transformed into <code>n</code> ciphertext blocks <code>C_1</code>,&hellip;
<code>C_n</code> as follows:
</p>
<div class="example">
<pre class="example">C_1 = E_k(IC) XOR M_1
C_2 = E_k(IC + 1) XOR M_2

&hellip;

C_(n-1) = E_k(IC + n - 2) XOR M_(n-1)
C_n = E_k(IC + n - 1) [1..m] XOR M_n
</pre></div>

<p>The <acronym>IC</acronym> is the initial value for the counter, it plays a
similar rôle as the <acronym>IV</acronym> for <acronym>CBC</acronym>. When adding,
<code>IC + x</code>, <acronym>IC</acronym> is interpreted as an integer, in network
byte order. For the last block, <code>E_k(IC + n - 1) [1..m]</code> means that
the cipher output is truncated to <code>m</code> bytes.
</p>
<dl>
<dt><a name="index-ctr_005fcrypt"></a>Function: <em>void</em> <strong>ctr_crypt</strong> <em>(const void *<var>ctx</var>, nettle_cipher_func *<var>f</var>, size_t <var>block_size</var>, uint8_t *<var>ctr</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd>
<p>Applies the encryption function <var>f</var> in <acronym>CTR</acronym> mode. Note that
for <acronym>CTR</acronym> mode, encryption and decryption is the same operation,
and hence <var>f</var> should always be the encryption function for the
underlying block cipher.
</p>
<p>When a message is encrypted using a sequence of calls to
<code>ctr_crypt</code>, all but the last call <em>must</em> use a length that is
a multiple of the block size.
</p></dd></dl>

<p>Like for <acronym>CBC</acronym>, there are also a couple of helper macros.
</p>
<dl>
<dt><a name="index-CTR_005fCTX"></a>Macro: <strong>CTR_CTX</strong> <em>(<var>context_type</var>, <var>block_size</var>)</em></dt>
<dd><p>Expands to
</p><div class="example">
<pre class="example">{
   context_type ctx;
   uint8_t ctr[block_size];
}
</pre></div>
</dd></dl>

<dl>
<dt><a name="index-CTR_005fSET_005fCOUNTER"></a>Macro: <strong>CTR_SET_COUNTER</strong> <em>(<var>ctx</var>, <var>iv</var>)</em></dt>
<dd><p>First argument is a pointer to a context struct as defined by
<code>CTR_CTX</code>, and the second is a pointer to an initial counter that
is copied into that context.
</p></dd></dl>

<dl>
<dt><a name="index-CTR_005fCRYPT"></a>Macro: <strong>CTR_CRYPT</strong> <em>(<var>ctx</var>, <var>f</var>, <var>length</var>, <var>dst</var>, <var>src</var>)</em></dt>
<dd><p>A simpler way to invoke <code>ctr_crypt</code>. The first argument is a
pointer to a context struct as defined by <code>CTR_CTX</code>, and the second
argument is an encryption function following Nettle&rsquo;s conventions. The
last three arguments define the source and destination area for the
operation.
</p></dd></dl>

<hr>
<a name="Authenticated-encryption"></a>
<div class="header">
<p>
Next: <a href="#Keyed-hash-functions" accesskey="n" rel="next">Keyed hash functions</a>, Previous: <a href="#Cipher-modes" accesskey="p" rel="prev">Cipher modes</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>

<a name="Authenticated-encryption-with-associated-data"></a>
<h3 class="section">6.4 Authenticated encryption with associated data</h3>
<a name="index-AEAD"></a>
<a name="index-Authenticated-encryption"></a>

<p>Since there are some subtle design choices to be made when combining a
block cipher mode with out authentication with a <acronym>MAC</acronym>. In
recent years, several constructions that combine encryption and
authentication have been defined. These constructions typically also
have an additional input, the &ldquo;associated data&rdquo;, which is
authenticated but not included with the message. A simple example is an
implicit message number which is available at both sender and receiver,
and which needs authentication in order to detect deletions or replay of
messages. This family of building blocks are therefore called
<acronym>AEAD</acronym>, Authenticated encryption with associated data.
</p>
<p>The aim is to provide building blocks that it is easier for designers of
protocols and applications to use correctly. There is also some
potential for improved performance, if encryption and authentication can
be done in a single step, although that potential is not realized for
the constructions currently supported by Nettle.
</p>
<p>For encryption, the inputs are:
</p>
<ul>
<li> The key, which can be used for many messages.
</li><li> A nonce, which must be unique for each message using the same key.
</li><li> Additional associated data to be authenticated, but not included in the
message.
</li><li> The cleartext message to be encrypted.
</li></ul>

<p>The outputs are:
</p>
<ul>
<li> The ciphertext, of the same size as the cleartext.
</li><li> A digest or &ldquo;authentication tag&rdquo;.
</li></ul>

<p>Decryption works the same, but with cleartext and ciphertext
interchanged. All currently supported <acronym>AEAD</acronym> algorithms always
use the encryption function of the underlying block cipher, for both
encryption and decryption.
</p>
<p>Usually, the authentication tag should be appended at the end of the
ciphertext, producing an encrypted message which is slightly longer than
the cleartext. However, Nettle&rsquo;s low level <acronym>AEAD</acronym> functions
produce the authentication tag as a separate output for both encryption
and decryption.
</p>
<p>Both associated data and the message data (cleartext or ciphertext) can
be processed incrementally. In general, all associated data must be
processed before the message data, and all calls but the last one must
use a length that is a multiple of the block size, although some
<acronym>AEAD</acronym> may implement more liberal conventions. The <acronym>CCM</acronym>
mode is a bit special in that it requires the message lengths up front,
other <acronym>AEAD</acronym> constructions don&rsquo;t have this restriction.
</p>
<p>The supported <acronym>AEAD</acronym> constructions are Galois/Counter mode
(<acronym>GCM</acronym>), <acronym>EAX</acronym>, ChaCha-Poly1305, and Counter with
<acronym>CBC</acronym>-<acronym>MAC</acronym> (<acronym>CCM</acronym>). There are some weaknesses
in <acronym>GCM</acronym> authentication, see
<a href="http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/comments/CWC-GCM/Ferguson2.pdf">http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/comments/CWC-GCM/Ferguson2.pdf</a>.
<acronym>CCM</acronym> and <acronym>EAX</acronym> use the same building blocks, but the
<acronym>EAX</acronym> design is cleaner and avoids a couple of inconveniences of
<acronym>CCM</acronym>. Therefore, <acronym>EAX</acronym> seems like a good conservative
choice. The more recent ChaCha-Poly1305 may also be an attractive but
more adventurous alternative, in particular if performance is important.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#EAX" accesskey="1">EAX</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#GCM" accesskey="2">GCM</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#CCM" accesskey="3">CCM</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#ChaCha_002dPoly1305" accesskey="4">ChaCha-Poly1305</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#nettle_005faead-abstraction" accesskey="5">nettle_aead abstraction</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<hr>
<a name="EAX"></a>
<div class="header">
<p>
Next: <a href="#GCM" accesskey="n" rel="next">GCM</a>, Previous: <a href="#Authenticated-encryption" accesskey="p" rel="prev">Authenticated encryption</a>, Up: <a href="#Authenticated-encryption" accesskey="u" rel="up">Authenticated encryption</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="EAX-1"></a>
<h4 class="subsection">6.4.1 EAX</h4>

<p>The <acronym>EAX</acronym> mode is an <acronym>AEAD</acronym> mode whichcombines
<acronym>CTR</acronym> mode encryption, See <a href="#CTR">CTR</a>, with a message authentication
based on <acronym>CBC</acronym>, See <a href="#CBC">CBC</a>. The implementation in Nettle is
restricted to ciphers with a block size of 128 bits (16 octets).
<acronym>EAX</acronym> was defined as a reaction to the <acronym>CCM</acronym> mode,
See <a href="#CCM">CCM</a>, which uses the same primitives but has some undesirable and
inelegant properties.
</p>
<p><acronym>EAX</acronym> supports arbitrary nonce size; it&rsquo;s even possible to use
an empty nonce in case only a single message is encrypted for each key. 
</p>
<p>Nettle&rsquo;s support for <acronym>EAX</acronym> consists of a low-level general
interface, some convenience macros, and specific functions for
<acronym>EAX</acronym> using <acronym>AES</acronym>-128 as the underlying cipher. These
interfaces are defined in <samp>&lt;nettle/eax.h&gt;</samp>
</p>
<a name="General-EAX-interface"></a>
<h4 class="subsubsection">6.4.1.1 General <acronym>EAX</acronym> interface</h4>

<dl>
<dt><a name="index-struct-eax_005fkey"></a>Context struct: <strong>struct eax_key</strong></dt>
<dd><p><acronym>EAX</acronym> state which depends only on the key, but not on the nonce
or the message.
</p></dd></dl>

<dl>
<dt><a name="index-struct-eax_005fctx"></a>Context struct: <strong>struct eax_ctx</strong></dt>
<dd><p>Holds state corresponding to a particular message.
</p></dd></dl>

<dl>
<dt><a name="index-EAX_005fBLOCK_005fSIZE"></a>Constant: <strong>EAX_BLOCK_SIZE</strong></dt>
<dd><p><acronym>EAX</acronym>&rsquo;s block size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-EAX_005fDIGEST_005fSIZE"></a>Constant: <strong>EAX_DIGEST_SIZE</strong></dt>
<dd><p>Size of the <acronym>EAX</acronym> digest, also 16.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005fset_005fkey"></a>Function: <em>void</em> <strong>eax_set_key</strong> <em>(struct eax_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>)</em></dt>
<dd><p>Initializes <var>key</var>. <var>cipher</var> gives a context struct for the
underlying cipher, which must have been previously initialized for
encryption, and <var>f</var> is the encryption function.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005fset_005fnonce"></a>Function: <em>void</em> <strong>eax_set_nonce</strong> <em>(struct eax_ctx *<var>eax</var>, const struct eax_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>nonce_length</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dd><p>Initializes <var>ctx</var> for processing a new message, using the given
nonce.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005fupdate"></a>Function: <em>void</em> <strong>eax_update</strong> <em>(struct eax_ctx *<var>eax</var>, const struct eax_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>data_length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process associated data for authentication. All but the last call for
each message <em>must</em> use a length that is a multiple of the block
size. Unlike many other <acronym>AEAD</acronym> constructions, for <acronym>EAX</acronym>
it&rsquo;s not necessary to complete the processing of all associated data
before encrypting or decrypting the message data.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005fencrypt"></a>Function: <em>void</em> <strong>eax_encrypt</strong> <em>(struct eax_ctx *<var>eax</var>, const struct eax_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-eax_005fdecrypt"></a>Function: <em>void</em> <strong>eax_decrypt</strong> <em>(struct eax_ctx *<var>eax</var>, const struct eax_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message. <var>cipher</var> is the context
struct for the underlying cipher and <var>f</var> is the encryption function.
All but the last call for each message <em>must</em> use a length that is
a multiple of the block size.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005fdigest"></a>Function: <em>void</em> <strong>eax_digest</strong> <em>(struct eax_ctx *<var>eax</var>, const struct eax_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>digest</var>);</em></dt>
<dd><p>Extracts the message digest (also known &ldquo;authentication tag&rdquo;). This is
the final operation when processing a message. If <var>length</var> is
smaller than <code>EAX_DIGEST_SIZE</code>, only the first <var>length</var> octets
of the digest are written.
</p></dd></dl>


<a name="EAX-helper-macros"></a>
<h4 class="subsubsection">6.4.1.2 <acronym>EAX</acronym> helper macros</h4>

<p>The following macros are defined.
</p>
<dl>
<dt><a name="index-EAX_005fCTX"></a>Macro: <strong>EAX_CTX</strong> <em>(<var>context_type</var>)</em></dt>
<dd><p>This defines an all-in-one context struct, including the context of the
underlying cipher and all <acronym>EAX</acronym> state. It expands
to
</p><div class="example">
<pre class="example">{
   struct eax_key key;
   struct eax_ctx eax;
   context_type cipher;
}
</pre></div>
</dd></dl>

<p>For all these macros, <var>ctx</var>, is a context struct as defined by
<code>EAX_CTX</code>, and <var>encrypt</var> is the encryption function of the
underlying cipher.
</p>
<dl>
<dt><a name="index-EAX_005fSET_005fKEY"></a>Macro: <strong>EAX_SET_KEY</strong> <em>(<var>ctx</var>, <var>set_key</var>, <var>encrypt</var>, <var>key</var>)</em></dt>
<dd><p><var>set_key</var> is the function for setting the encryption key for the
underlying cipher, and <var>key</var> is the key.
</p></dd></dl>

<dl>
<dt><a name="index-EAX_005fSET_005fNONCE"></a>Macro: <strong>EAX_SET_NONCE</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>nonce</var>)</em></dt>
<dd><p>Sets the nonce to be used for the message.
</p></dd></dl>

<dl>
<dt><a name="index-EAX_005fUPDATE"></a>Macro: <strong>EAX_UPDATE</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>data</var>)</em></dt>
<dd><p>Process associated data for authentication.
</p></dd></dl>

<dl>
<dt><a name="index-EAX_005fENCRYPT"></a>Macro: <strong>EAX_ENCRYPT</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>dst</var>, <var>src</var>)</em></dt>
<dt><a name="index-EAX_005fDECRYPT"></a>Macro: <strong>EAX_DECRYPT</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>dst</var>, <var>src</var>)</em></dt>
<dd><p>Process message data for encryption or decryption.
</p></dd></dl>

<dl>
<dt><a name="index-EAX_005fDIGEST"></a>Macro: <strong>EAX_DIGEST</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>digest</var>)</em></dt>
<dd><p>Extract te authentication tag for the message.
</p></dd></dl>


<a name="EAX_002dAES128-interface"></a>
<h4 class="subsubsection">6.4.1.3 <acronym>EAX</acronym>-<acronym>AES</acronym>128 interface</h4>

<p>The following functions implement <acronym>EAX</acronym> using <acronym>AES</acronym>-128
as the underlying cipher.
</p>
<dl>
<dt><a name="index-struct-eax_005faes128_005fctx"></a>Context struct: <strong>struct eax_aes128_ctx</strong></dt>
<dd><p>The context struct, defined using <code>EAX_CTX</code>.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005faes128_005fset_005fkey"></a>Function: <em>void</em> <strong>eax_aes128_set_key</strong> <em>(struct eax_aes128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes <var>ctx</var> using the given key.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005faes128_005fset_005fnonce"></a>Function: <em>void</em> <strong>eax_aes128_set_nonce</strong> <em>(struct eax_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dd><p>Initializes the per-message state, using the given nonce.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005faes128_005fupdate"></a>Function: <em>void</em> <strong>eax_aes128_update</strong> <em>(struct eax_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process associated data for authentication. All but the last call for
each message <em>must</em> use a length that is a multiple of the block
size.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005faes128_005fencrypt"></a>Function: <em>void</em> <strong>eax_aes128_encrypt</strong> <em>(struct eax_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-eax_005faes128_005fdecrypt"></a>Function: <em>void</em> <strong>eax_aes128_decrypt</strong> <em>(struct eax_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message. All but the last call for
each message <em>must</em> use a length that is a multiple of the block
size.
</p></dd></dl>

<dl>
<dt><a name="index-eax_005faes128_005fdigest"></a>Function: <em>void</em> <strong>eax_aes128_digest</strong> <em>(struct eax_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>);</em></dt>
<dd><p>Extracts the message digest (also known &ldquo;authentication tag&rdquo;). This is
the final operation when processing a message. If <var>length</var> is
smaller than <code>EAX_DIGEST_SIZE</code>, only the first <var>length</var> octets
of the digest are written.
</p></dd></dl>

<hr>
<a name="GCM"></a>
<div class="header">
<p>
Next: <a href="#CCM" accesskey="n" rel="next">CCM</a>, Previous: <a href="#EAX" accesskey="p" rel="prev">EAX</a>, Up: <a href="#Authenticated-encryption" accesskey="u" rel="up">Authenticated encryption</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Galois-counter-mode"></a>
<h4 class="subsection">6.4.2 Galois counter mode</h4>

<a name="index-Galois-Counter-Mode"></a>
<a name="index-GCM"></a>

<p>Galois counter mode is an <acronym>AEAD</acronym> constructions combining counter
mode with message authentication based on universal hashing. The main
objective of the design is to provide high performance for hardware
implementations, where other popular <acronym>MAC</acronym> algorithms
(see <a href="#Keyed-hash-functions">Keyed hash functions</a>) become a bottleneck for high-speed
hardware implementations. It was proposed by David A. McGrew and John
Viega in 2005, and recommended by NIST in 2007,
<a href="http://csrc.nist.gov/publications/nistpubs/800-38D/SP-800-38D.pdf">NIST Special Publication 800-38D</a>. It is constructed on top of a block
cipher which must have a block size of 128 bits.
</p>
<p>The authentication in <acronym>GCM</acronym> has some known weaknesses, see
<a href="http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/comments/CWC-GCM/Ferguson2.pdf">http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/comments/CWC-GCM/Ferguson2.pdf</a>.
In particular, don&rsquo;t use <acronym>GCM</acronym> with short authentication tags.
</p>
<p>Nettle&rsquo;s support for <acronym>GCM</acronym> consists of a low-level general
interface, some convenience macros, and specific functions for
<acronym>GCM</acronym> using <acronym>AES</acronym> or Camellia as the underlying cipher.
These interfaces are defined in <samp>&lt;nettle/gcm.h&gt;</samp>
</p>
<a name="General-GCM-interface"></a>
<h4 class="subsubsection">6.4.2.1 General <acronym>GCM</acronym> interface</h4>

<dl>
<dt><a name="index-struct-gcm_005fkey"></a>Context struct: <strong>struct gcm_key</strong></dt>
<dd><p>Message independent hash sub-key, and related tables.
</p></dd></dl>

<dl>
<dt><a name="index-struct-gcm_005fctx"></a>Context struct: <strong>struct gcm_ctx</strong></dt>
<dd><p>Holds state corresponding to a particular message.
</p></dd></dl>

<dl>
<dt><a name="index-GCM_005fBLOCK_005fSIZE"></a>Constant: <strong>GCM_BLOCK_SIZE</strong></dt>
<dd><p><acronym>GCM</acronym>&rsquo;s block size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-GCM_005fDIGEST_005fSIZE"></a>Constant: <strong>GCM_DIGEST_SIZE</strong></dt>
<dd><p>Size of the <acronym>GCM</acronym> digest, also 16.
</p></dd></dl>

<dl>
<dt><a name="index-GCM_005fIV_005fSIZE"></a>Constant: <strong>GCM_IV_SIZE</strong></dt>
<dd><p>Recommended size of the <acronym>IV</acronym>, 12. Arbitrary sizes are allowed.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fset_005fkey"></a>Function: <em>void</em> <strong>gcm_set_key</strong> <em>(struct gcm_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>)</em></dt>
<dd><p>Initializes <var>key</var>. <var>cipher</var> gives a context struct for the
underlying cipher, which must have been previously initialized for
encryption, and <var>f</var> is the encryption function.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fset_005fiv"></a>Function: <em>void</em> <strong>gcm_set_iv</strong> <em>(struct gcm_ctx *<var>ctx</var>, const struct gcm_key *<var>key</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dd><p>Initializes <var>ctx</var> using the given <acronym>IV</acronym>. The <var>key</var>
argument is actually needed only if <var>length</var> differs from
<code>GCM_IV_SIZE</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fupdate"></a>Function: <em>void</em> <strong>gcm_update</strong> <em>(struct gcm_ctx *<var>ctx</var>, const struct gcm_key *<var>key</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Provides associated data to be authenticated. If used, must be called
before <code>gcm_encrypt</code> or <code>gcm_decrypt</code>. All but the last call
for each message <em>must</em> use a length that is a multiple of the
block size.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fencrypt"></a>Function: <em>void</em> <strong>gcm_encrypt</strong> <em>(struct gcm_ctx *<var>ctx</var>, const struct gcm_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005fdecrypt"></a>Function: <em>void</em> <strong>gcm_decrypt</strong> <em>(struct gcm_ctx *<var>ctx</var>, const struct gcm_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message. <var>cipher</var> is the context
struct for the underlying cipher and <var>f</var> is the encryption function.
All but the last call for each message <em>must</em> use a length that is
a multiple of the block size.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fdigest"></a>Function: <em>void</em> <strong>gcm_digest</strong> <em>(struct gcm_ctx *<var>ctx</var>, const struct gcm_key *<var>key</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the message digest (also known &ldquo;authentication tag&rdquo;). This is
the final operation when processing a message. It&rsquo;s strongly recommended
that <var>length</var> is <code>GCM_DIGEST_SIZE</code>, but if you provide a smaller
value, only the first <var>length</var> octets of the digest are written.
</p></dd></dl>

<p>To encrypt a message using <acronym>GCM</acronym>, first initialize a context for
the underlying block cipher with a key to use for encryption. Then call
the above functions in the following order: <code>gcm_set_key</code>,
<code>gcm_set_iv</code>, <code>gcm_update</code>, <code>gcm_encrypt</code>,
<code>gcm_digest</code>. The decryption procedure is analogous, just calling
<code>gcm_decrypt</code> instead of <code>gcm_encrypt</code> (note that
<acronym>GCM</acronym> decryption still uses the encryption function of the
underlying block cipher). To process a new message, using the same key,
call <code>gcm_set_iv</code> with a new <acronym>iv</acronym>.
</p>
<a name="GCM-helper-macros"></a>
<h4 class="subsubsection">6.4.2.2 <acronym>GCM</acronym> helper macros</h4>

<p>The following macros are defined.
</p>
<dl>
<dt><a name="index-GCM_005fCTX"></a>Macro: <strong>GCM_CTX</strong> <em>(<var>context_type</var>)</em></dt>
<dd><p>This defines an all-in-one context struct, including the context of the
underlying cipher, the hash sub-key, and the per-message state. It expands
to
</p><div class="example">
<pre class="example">{
   struct gcm_key key; 
   struct gcm_ctx gcm;
   context_type cipher;
}
</pre></div>
</dd></dl>

<p>Example use:
</p><div class="example">
<pre class="example">struct gcm_aes128_ctx GCM_CTX(struct aes128_ctx);
</pre></div>

<p>The following macros operate on context structs of this form.
</p>
<dl>
<dt><a name="index-GCM_005fSET_005fKEY"></a>Macro: <strong>GCM_SET_KEY</strong> <em>(<var>ctx</var>, <var>set_key</var>, <var>encrypt</var>, <var>key</var>)</em></dt>
<dd><p>First argument, <var>ctx</var>, is a context struct as defined
by <code>GCM_CTX</code>. <var>set_key</var> and <var>encrypt</var> are functions for
setting the encryption key and for encrypting data using the underlying
cipher.
</p></dd></dl>

<dl>
<dt><a name="index-GCM_005fSET_005fIV"></a>Macro: <strong>GCM_SET_IV</strong> <em>(<var>ctx</var>, <var>length</var>, <var>data</var>)</em></dt>
<dd><p>First argument is a context struct as defined by
<code>GCM_CTX</code>. <var>length</var> and <var>data</var> give the initialization
vector (<acronym>IV</acronym>).
</p></dd></dl>

<dl>
<dt><a name="index-GCM_005fUPDATE"></a>Macro: <strong>GCM_UPDATE</strong> <em>(<var>ctx</var>, <var>length</var>, <var>data</var>)</em></dt>
<dd><p>Simpler way to call <code>gcm_update</code>. First argument is a context
struct as defined by <code>GCM_CTX</code>
</p></dd></dl>

<dl>
<dt><a name="index-GCM_005fENCRYPT"></a>Macro: <strong>GCM_ENCRYPT</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>dst</var>, <var>src</var>)</em></dt>
<dt><a name="index-GCM_005fDECRYPT"></a>Macro: <strong>GCM_DECRYPT</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>dst</var>, <var>src</var>)</em></dt>
<dt><a name="index-GCM_005fDIGEST"></a>Macro: <strong>GCM_DIGEST</strong> <em>(<var>ctx</var>, <var>encrypt</var>, <var>length</var>, <var>digest</var>)</em></dt>
<dd><p>Simpler way to call <code>gcm_encrypt</code>, <code>gcm_decrypt</code> or
<code>gcm_digest</code>. First argument is a context struct as defined by
<code>GCM_CTX</code>. Second argument, <var>encrypt</var>, is the encryption
function of the underlying cipher.
</p></dd></dl>

<a name="GCM_002dAES-interface"></a>
<h4 class="subsubsection">6.4.2.3 <acronym>GCM</acronym>-<acronym>AES</acronym> interface</h4>

<p>The following functions implement the common case of <acronym>GCM</acronym> using
<acronym>AES</acronym> as the underlying cipher. The variants with a specific
<acronym>AES</acronym> flavor are recommended, while the fucntinos using
<code>struct gcm_aes_ctx</code> are kept for compatibility with older versiosn
of Nettle.
</p>
<dl>
<dt><a name="index-struct-gcm_005faes128_005fctx"></a>Context struct: <strong>struct gcm_aes128_ctx</strong></dt>
<dt><a name="index-struct-gcm_005faes192_005fctx"></a>Context struct: <strong>struct gcm_aes192_ctx</strong></dt>
<dt><a name="index-struct-gcm_005faes256_005fctx"></a>Context struct: <strong>struct gcm_aes256_ctx</strong></dt>
<dd><p>Context structs, defined using <code>GCM_CTX</code>.
</p></dd></dl>

<dl>
<dt><a name="index-struct-gcm_005faes_005fctx"></a>Context struct: <strong>struct gcm_aes_ctx</strong></dt>
<dd><p>Alternative context struct, usign the old <acronym>AES</acronym> interface.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005faes128_005fset_005fkey"></a>Function: <em>void</em> <strong>gcm_aes128_set_key</strong> <em>(struct gcm_aes128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-gcm_005faes192_005fset_005fkey"></a>Function: <em>void</em> <strong>gcm_aes192_set_key</strong> <em>(struct gcm_aes192_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-gcm_005faes256_005fset_005fkey"></a>Function: <em>void</em> <strong>gcm_aes256_set_key</strong> <em>(struct gcm_aes256_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes <var>ctx</var> using the given key.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005faes_005fset_005fkey"></a>Function: <em>void</em> <strong>gcm_aes_set_key</strong> <em>(struct gcm_aes_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Corresponding function, using the old <acronym>AES</acronym> interface. All valid
<acronym>AES</acronym> key sizes can be used.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005faes128_005fset_005fiv"></a>Function: <em>void</em> <strong>gcm_aes128_set_iv</strong> <em>(struct gcm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dt><a name="index-gcm_005faes192_005fset_005fiv"></a>Function: <em>void</em> <strong>gcm_aes192_set_iv</strong> <em>(struct gcm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dt><a name="index-gcm_005faes256_005fset_005fiv"></a>Function: <em>void</em> <strong>gcm_aes256_set_iv</strong> <em>(struct gcm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dt><a name="index-gcm_005faes_005fset_005fiv"></a>Function: <em>void</em> <strong>gcm_aes_set_iv</strong> <em>(struct gcm_aes_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dd><p>Initializes the per-message state, using the given <acronym>IV</acronym>.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005faes128_005fupdate"></a>Function: <em>void</em> <strong>gcm_aes128_update</strong> <em>(struct gcm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-gcm_005faes192_005fupdate"></a>Function: <em>void</em> <strong>gcm_aes192_update</strong> <em>(struct gcm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-gcm_005faes256_005fupdate"></a>Function: <em>void</em> <strong>gcm_aes256_update</strong> <em>(struct gcm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-gcm_005faes_005fupdate"></a>Function: <em>void</em> <strong>gcm_aes_update</strong> <em>(struct gcm_aes_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Provides associated data to be authenticated. If used, must be called
before <code>gcm_aes_encrypt</code> or <code>gcm_aes_decrypt</code>. All but the
last call for each message <em>must</em> use a length that is a multiple
of the block size.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005faes128_005fencrypt"></a>Function: <em>void</em> <strong>gcm_aes128_encrypt</strong> <em>(struct gcm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005faes192_005fencrypt"></a>Function: <em>void</em> <strong>gcm_aes192_encrypt</strong> <em>(struct gcm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005faes256_005fencrypt"></a>Function: <em>void</em> <strong>gcm_aes256_encrypt</strong> <em>(struct gcm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005faes_005fencrypt"></a>Function: <em>void</em> <strong>gcm_aes_encrypt</strong> <em>(struct gcm_aes_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005faes128_005fdecrypt"></a>Function: <em>void</em> <strong>gcm_aes128_decrypt</strong> <em>(struct gcm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005faes192_005fdecrypt"></a>Function: <em>void</em> <strong>gcm_aes192_decrypt</strong> <em>(struct gcm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005faes256_005fdecrypt"></a>Function: <em>void</em> <strong>gcm_aes256_decrypt</strong> <em>(struct gcm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005faes_005fdecrypt"></a>Function: <em>void</em> <strong>gcm_aes_decrypt</strong> <em>(struct gcm_aes_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message. All but the last call for
each message <em>must</em> use a length that is a multiple of the block
size.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005faes128_005fdigest"></a>Function: <em>void</em> <strong>gcm_aes128_digest</strong> <em>(struct gcm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-gcm_005faes192_005fdigest"></a>Function: <em>void</em> <strong>gcm_aes192_digest</strong> <em>(struct gcm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-gcm_005faes256_005fdigest"></a>Function: <em>void</em> <strong>gcm_aes256_digest</strong> <em>(struct gcm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-gcm_005faes_005fdigest"></a>Function: <em>void</em> <strong>gcm_aes_digest</strong> <em>(struct gcm_aes_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the message digest (also known &ldquo;authentication tag&rdquo;). This is
the final operation when processing a message. It&rsquo;s strongly recommended
that <var>length</var> is <code>GCM_DIGEST_SIZE</code>, but if you provide a smaller
value, only the first <var>length</var> octets of the digest are written.
</p></dd></dl>

<a name="GCM_002dCamellia-interface"></a>
<h4 class="subsubsection">6.4.2.4 <acronym>GCM</acronym>-Camellia interface</h4>

<p>The following functions implement the case of <acronym>GCM</acronym> using
Camellia as the underlying cipher.
</p>
<dl>
<dt><a name="index-struct-gcm_005fcamellia128_005fctx"></a>Context struct: <strong>struct gcm_camellia128_ctx</strong></dt>
<dt><a name="index-struct-gcm_005fcamellia256_005fctx"></a>Context struct: <strong>struct gcm_camellia256_ctx</strong></dt>
<dd><p>Context structs, defined using <code>GCM_CTX</code>.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fcamellia128_005fset_005fkey"></a>Function: <em>void</em> <strong>gcm_camellia128_set_key</strong> <em>(struct gcm_camellia128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia256_005fset_005fkey"></a>Function: <em>void</em> <strong>gcm_camellia256_set_key</strong> <em>(struct gcm_camellia256_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes <var>ctx</var> using the given key.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fcamellia128_005fset_005fiv"></a>Function: <em>void</em> <strong>gcm_camellia128_set_iv</strong> <em>(struct gcm_camellia128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia256_005fset_005fiv"></a>Function: <em>void</em> <strong>gcm_camellia256_set_iv</strong> <em>(struct gcm_camellia256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>iv</var>)</em></dt>
<dd><p>Initializes the per-message state, using the given <acronym>IV</acronym>.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fcamellia128_005fupdate"></a>Function: <em>void</em> <strong>gcm_camellia128_update</strong> <em>(struct gcm_camellia128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia256_005fupdate"></a>Function: <em>void</em> <strong>gcm_camellia256_update</strong> <em>(struct gcm_camellia256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Provides associated data to be authenticated. If used, must be called
before <code>gcm_camellia_encrypt</code> or <code>gcm_camellia_decrypt</code>. All but the
last call for each message <em>must</em> use a length that is a multiple
of the block size.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fcamellia128_005fencrypt"></a>Function: <em>void</em> <strong>gcm_camellia128_encrypt</strong> <em>(struct gcm_camellia128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia256_005fencrypt"></a>Function: <em>void</em> <strong>gcm_camellia256_encrypt</strong> <em>(struct gcm_camellia256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia128_005fdecrypt"></a>Function: <em>void</em> <strong>gcm_camellia128_decrypt</strong> <em>(struct gcm_camellia128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia256_005fdecrypt"></a>Function: <em>void</em> <strong>gcm_camellia256_decrypt</strong> <em>(struct gcm_camellia256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message. All but the last call for
each message <em>must</em> use a length that is a multiple of the block
size.
</p></dd></dl>

<dl>
<dt><a name="index-gcm_005fcamellia128_005fdigest"></a>Function: <em>void</em> <strong>gcm_camellia128_digest</strong> <em>(struct gcm_camellia128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia192_005fdigest"></a>Function: <em>void</em> <strong>gcm_camellia192_digest</strong> <em>(struct gcm_camellia192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia256_005fdigest"></a>Function: <em>void</em> <strong>gcm_camellia256_digest</strong> <em>(struct gcm_camellia256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-gcm_005fcamellia_005fdigest"></a>Function: <em>void</em> <strong>gcm_camellia_digest</strong> <em>(struct gcm_camellia_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the message digest (also known &ldquo;authentication tag&rdquo;). This is
the final operation when processing a message. It&rsquo;s strongly recommended
that <var>length</var> is <code>GCM_DIGEST_SIZE</code>, but if you provide a smaller
value, only the first <var>length</var> octets of the digest are written.
</p></dd></dl>

<hr>
<a name="CCM"></a>
<div class="header">
<p>
Next: <a href="#ChaCha_002dPoly1305" accesskey="n" rel="next">ChaCha-Poly1305</a>, Previous: <a href="#GCM" accesskey="p" rel="prev">GCM</a>, Up: <a href="#Authenticated-encryption" accesskey="u" rel="up">Authenticated encryption</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Counter-with-CBC_002dMAC-mode"></a>
<h4 class="subsection">6.4.3 Counter with CBC-MAC mode</h4>

<a name="index-Counter-with-CBC_002dMAC-Mode"></a>
<a name="index-CCM-Mode"></a>

<p><acronym>CCM</acronym> mode is a combination of counter mode with message
authentication based on cipher block chaining, the same building blocks
as <acronym>EAX</acronym>, see <a href="#EAX">EAX</a>. It is constructed on top of a block cipher
which must have a block size of 128 bits. <acronym>CCM</acronym> mode is
recommended by NIST in
<a href="http://csrc.nist.gov/publications/nistpubs/800-38C/SP800-38C_updated-July20_2007.pdf">NIST Special Publication 800-38C</a>. Nettle&rsquo;s support for CCM consists of
a low-level general interface, a message encryption and authentication
interface, and specific functions for CCM using AES as the underlying
block cipher. These interfaces are defined in <samp>&lt;nettle/ccm.h&gt;</samp>.
</p>
<p>In <acronym>CCM</acronym>, the length of the message must be known before
processing. The maximum message size depends on the size of the nonce,
since the message size is encoded in a field which must fit in a single
block, together with the nonce and a flag byte. E.g., with a nonce size
of 12 octets, there are three octets left for encoding the message
length, the maximum message length is <em>2^24 - 1</em> octets.
</p>
<p><acronym>CCM</acronym> mode encryption operates as follows:
</p><ul>
<li> The nonce and message length are concatenated to create
<code>B_0 = flags | nonce | mlength</code>

</li><li> The authenticated data and plaintext is formatted into the string
<code>B = L(adata) | adata | padding | plaintext | padding</code> with
<code>padding</code> being the shortest string of zero bytes such that the
length of the string is a multiple of the block size, and
<code>L(adata)</code> is an encoding of the length of <code>adata</code>.

</li><li> The string <code>B</code> is separated into blocks <code>B_1</code> ...
<code>B_n</code>
</li><li> The authentication tag <code>T</code> is calculated as
<code>T=0, for i=0 to n, do T = E_k(B_i XOR T)</code>

</li><li> An initial counter is then initialized from the nonce to create
<code>IC = flags | nonce | padding</code>, where <code>padding</code> is the
shortest string of zero bytes such that <code>IC</code> is exactly one block
in length.

</li><li> The authentication tag is encrypted using using <acronym>CTR</acronym> mode:
<code>MAC = E_k(IC) XOR T</code>

</li><li> The plaintext is then encrypted using <acronym>CTR</acronym> mode with an
initial counter of <code>IC+1</code>.
</li></ul>

<p><acronym>CCM</acronym> mode decryption operates similarly, except that the
ciphertext and <acronym>MAC</acronym> are first decrypted using CTR mode to
retreive the plaintext and authentication tag. The authentication tag
can then be recalucated from the authenticated data and plantext, and
compared to the value in the message to check for authenticity.
</p>
<a name="General-CCM-interface"></a>
<h4 class="subsubsection">6.4.3.1 General <acronym>CCM</acronym> interface</h4>

<p>For all of the functions in the <acronym>CCM</acronym> interface, <var>cipher</var> is
the context struct for the underlying cipher and <var>f</var> is the
encryption function. The cipher&rsquo;s encryption key must be set before
calling any of the <acronym>CCM</acronym> functions. The cipher&rsquo;s decryption
function and key are never used.
</p>
<dl>
<dt><a name="index-struct-ccm_005fctx"></a>Context struct: <strong>struct ccm_ctx</strong></dt>
<dd><p>Holds state corresponding to a particular message.
</p></dd></dl>

<dl>
<dt><a name="index-CCM_005fBLOCK_005fSIZE"></a>Constant: <strong>CCM_BLOCK_SIZE</strong></dt>
<dd><p><acronym>CCM</acronym>&rsquo;s block size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-CCM_005fDIGEST_005fSIZE"></a>Constant: <strong>CCM_DIGEST_SIZE</strong></dt>
<dd><p>Size of the <acronym>CCM</acronym> digest, 16.
</p></dd></dl>

<dl>
<dt><a name="index-CCM_005fMIN_005fNONCE_005fSIZE"></a>Constant: <strong>CCM_MIN_NONCE_SIZE</strong></dt>
<dt><a name="index-CCM_005fMAX_005fNONCE_005fSIZE"></a>Constant: <strong>CCM_MAX_NONCE_SIZE</strong></dt>
<dd><p>The the minimum and maximum sizes for an <acronym>CCM</acronym> nonce, 7 and 14,
respectively.
</p></dd></dl>

<dl>
<dt><a name="index-CCM_005fMAX_005fMSG_005fSIZE"></a>Macro: <strong>CCM_MAX_MSG_SIZE</strong> <em>(<var>nonce_size</var>)</em></dt>
<dd><p>The largest allowed plaintext length, when using <acronym>CCM</acronym> with a
nonce of the given size.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005fset_005fnonce"></a>Function: <em>void</em> <strong>ccm_set_nonce</strong> <em>(struct ccm_ctx *<var>ctx</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>noncelen</var>, const uint8_t *<var>nonce</var>, size_t <var>authlen</var>, size_t <var>msglen</var>, size_t <var>taglen</var>)</em></dt>
<dd><p>Initializes <var>ctx</var> using the given nonce and the sizes of the
authenticated data, message, and <acronym>MAC</acronym> to be processed.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005fupdate"></a>Function: <em>void</em> <strong>ccm_update</strong> <em>(struct ccm_ctx *<var>ctx</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Provides associated data to be authenticated. Must be called after
<code>ccm_set_nonce</code>, and before <code>ccm_encrypt</code>, <code>ccm_decrypt</code>, or
<code>ccm_digest</code>.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005fencrypt"></a>Function: <em>void</em> <strong>ccm_encrypt</strong> <em>(struct ccm_ctx *<var>ctx</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005fdecrypt"></a>Function: <em>void</em> <strong>ccm_decrypt</strong> <em>(struct ccm_ctx *<var>ctx</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the message data. Must be called after
<code>ccm_set_nonce</code> and before <code>ccm_digest</code>. All but the last call
for each message <em>must</em> use a length that is a multiple of the
block size.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005fdigest"></a>Function: <em>void</em> <strong>ccm_digest</strong> <em>(struct ccm_ctx *<var>ctx</var>, const void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the message digest (also known &ldquo;authentication tag&rdquo;). This is
the final operation when processing a message. <var>length</var> is usually
equal to the <var>taglen</var> parameter supplied to <code>ccm_set_nonce</code>,
but if you provide a smaller value, only the first <var>length</var> octets
of the digest are written.
</p></dd></dl>

<p>To encrypt a message using the general <acronym>CCM</acronym> interface, set the
message nonce and length using <code>ccm_set_nonce</code> and then call
<code>ccm_update</code> to generate the digest of any authenticated data.
After all of the authenticated data has been digested use
<code>ccm_encrypt</code> to encrypt the plaintext. Finally, use
<code>ccm_digest</code> to return the encrypted <acronym>MAC</acronym>.
</p>
<p>To decrypt a message, use <code>ccm_set_nonce</code> and <code>ccm_update</code> the
same as you would for encryption, and then call <code>ccm_decrypt</code> to
decrypt the ciphertext. After decrypting the ciphertext
<code>ccm_digest</code> will return the encrypted <acronym>MAC</acronym> which should
be identical to the <acronym>MAC</acronym> in the received message.
</p>
<a name="CCM-message-interface"></a>
<h4 class="subsubsection">6.4.3.2 <acronym>CCM</acronym> message interface</h4>

<p>The <acronym>CCM</acronym> message fuctions provides a simple interface that will
perform authentication and message encryption in a single function call.
The length of the cleartext is given by <var>mlength</var> and the length of
the ciphertext is given by <var>clength</var>, always exactly <var>tlength</var>
bytes longer than the corresponding plaintext. The length argument
passed to a function is always the size for the result, <var>clength</var>
for the encryption functions, and <var>mlength</var> for the decryption
functions.
</p>
<dl>
<dt><a name="index-ccm_005fencrypt_005fmessage"></a>Function: <em>void</em> <strong>ccm_encrypt_message</strong> <em>(void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>clength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Computes the message digest from the <var>adata</var> and <var>src</var>
parameters, encrypts the plaintext from <var>src</var>, appends the encrypted
<acronym>MAC</acronym> to ciphertext and outputs it to <var>dst</var>.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005fdecrypt_005fmessage"></a>Function: <em>int</em> <strong>ccm_decrypt_message</strong> <em>(void *<var>cipher</var>, nettle_cipher_func *<var>f</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>mlength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Decrypts the ciphertext from <var>src</var>, outputs the plaintext to
<var>dst</var>, recalculates the <acronym>MAC</acronym> from <var>adata</var> and the
plaintext, and compares it to the final <var>tlength</var> bytes of
<var>src</var>. If the values of the received and calculated <acronym>MAC</acronym>s
are equal, this will return 1 indicating a valid and authenticated
message. Otherwise, this function will return zero.
</p></dd></dl>

<a name="CCM_002dAES-interface"></a>
<h4 class="subsubsection">6.4.3.3 <acronym>CCM</acronym>-<acronym>AES</acronym> interface</h4>

<p>The <acronym>AES</acronym> <acronym>CCM</acronym> functions provide an API for using
<acronym>CCM</acronym> mode with the <acronym>AES</acronym> block ciphers. The parameters
all have the same meaning as the general and message interfaces, except
that the <var>cipher</var>, <var>f</var>, and <var>ctx</var> parameters are replaced
with an <acronym>AES</acronym> context structure, and a set-key function must be
called before using any of the other functions in this interface.
</p>
<dl>
<dt><a name="index-struct-ccm_005faes128_005fctx"></a>Context struct: <strong>struct ccm_aes128_ctx</strong></dt>
<dd><p>Holds state corresponding to a particular message encrypted using the
AES-128 block cipher.
</p></dd></dl>

<dl>
<dt><a name="index-struct-ccm_005faes192_005fctx"></a>Context struct: <strong>struct ccm_aes192_ctx</strong></dt>
<dd><p>Holds state corresponding to a particular message encrypted using the
AES-192 block cipher.
</p></dd></dl>

<dl>
<dt><a name="index-struct-ccm_005faes256_005fctx"></a>Context struct: <strong>struct ccm_aes256_ctx</strong></dt>
<dd><p>Holds state corresponding to a particular message encrypted using the
AES-256 block cipher.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005faes128_005fset_005fkey"></a>Function: <em>void</em> <strong>ccm_aes128_set_key</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fset_005fkey"></a>Function: <em>void</em> <strong>ccm_aes192_set_key</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-ccm_005faes256_005fset_005fkey"></a>Function: <em>void</em> <strong>ccm_aes256_set_key</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes the encryption key for the AES block cipher. One of these
functions must be called before any of the other functions in the
<acronym>AES</acronym> <acronym>CCM</acronym> interface.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005faes128_005fset_005fnonce"></a>Function: <em>void</em> <strong>ccm_aes128_set_nonce</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, size_t <var>noncelen</var>, const uint8_t *<var>nonce</var>, size_t <var>authlen</var>, size_t <var>msglen</var>, size_t <var>taglen</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fset_005fnonce"></a>Function: <em>void</em> <strong>ccm_aes192_set_nonce</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, size_t <var>noncelen</var>, const uint8_t *<var>nonce</var>, size_t <var>authlen</var>, size_t <var>msglen</var>, size_t <var>taglen</var>)</em></dt>
<dt><a name="index-ccm_005faes256_005fset_005fnonce"></a>Function: <em>void</em> <strong>ccm_aes256_set_nonce</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, size_t <var>noncelen</var>, const uint8_t *<var>nonce</var>, size_t <var>authlen</var>, size_t <var>msglen</var>, size_t <var>taglen</var>)</em></dt>
<dd><p>These are identical to <code>ccm_set_nonce</code>, except that <var>cipher</var>,
<var>f</var>, and <var>ctx</var> are replaced with a context structure.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005faes128_005fupdate"></a>Function: <em>void</em> <strong>ccm_aes128_update</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fupdate"></a>Function: <em>void</em> <strong>ccm_aes192_update</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-ccm_005faes256_005fupdate"></a>Function: <em>void</em> <strong>ccm_aes256_update</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>These are identical to <code>ccm_set_update</code>, except that <var>cipher</var>,
<var>f</var>, and <var>ctx</var> are replaced with a context structure.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005faes128_005fencrypt"></a>Function: <em>void</em> <strong>ccm_aes128_encrypt</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fencrypt"></a>Function: <em>void</em> <strong>ccm_aes192_encrypt</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes256_005fencrypt"></a>Function: <em>void</em> <strong>ccm_aes256_encrypt</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes128_005fdecrypt"></a>Function: <em>void</em> <strong>ccm_aes128_decrypt</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fdecrypt"></a>Function: <em>void</em> <strong>ccm_aes192_decrypt</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes256_005fdecrypt"></a>Function: <em>void</em> <strong>ccm_aes256_decrypt</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>These are identical to <code>ccm_set_encrypt</code> and <code>ccm_set_decrypt</code>, except
that <var>cipher</var>, <var>f</var>, and <var>ctx</var> are replaced with a context structure.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005faes128_005fdigest"></a>Function: <em>void</em> <strong>ccm_aes128_digest</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fdigest"></a>Function: <em>void</em> <strong>ccm_aes192_digest</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-ccm_005faes256_005fdigest"></a>Function: <em>void</em> <strong>ccm_aes256_digest</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>These are identical to <code>ccm_set_digest</code>, except that <var>cipher</var>,
<var>f</var>, and <var>ctx</var> are replaced with a context structure.
</p></dd></dl>

<dl>
<dt><a name="index-ccm_005faes128_005fencrypt_005fmessage"></a>Function: <em>void</em> <strong>ccm_aes128_encrypt_message</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>clength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fencrypt_005fmessage"></a>Function: <em>void</em> <strong>ccm_aes192_encrypt_message</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>clength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes256_005fencrypt_005fmessage"></a>Function: <em>void</em> <strong>ccm_aes256_encrypt_message</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>clength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes128_005fdecrypt_005fmessage"></a>Function: <em>int</em> <strong>ccm_aes128_decrypt_message</strong> <em>(struct ccm_aes128_ctx *<var>ctx</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>mlength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fdecrypt_005fmessage"></a>Function: <em>int</em> <strong>ccm_aes192_decrypt_message</strong> <em>(struct ccm_aes192_ctx *<var>ctx</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>mlength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-ccm_005faes192_005fdecrypt_005fmessage-1"></a>Function: <em>int</em> <strong>ccm_aes192_decrypt_message</strong> <em>(struct ccm_aes256_ctx *<var>ctx</var>, size_t <var>nlength</var>, const uint8_t *<var>nonce</var>, size_t <var>alength</var>, const uint8_t *<var>adata</var>, size_t <var>tlength</var>, size_t <var>mlength</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>These are identical to <code>ccm_encrypt_message</code> and <code>ccm_decrypt_message</code>
except that <var>cipher</var> and <var>f</var> are replaced with a context structure.
</p></dd></dl>

<hr>
<a name="ChaCha_002dPoly1305"></a>
<div class="header">
<p>
Next: <a href="#nettle_005faead-abstraction" accesskey="n" rel="next">nettle_aead abstraction</a>, Previous: <a href="#CCM" accesskey="p" rel="prev">CCM</a>, Up: <a href="#Authenticated-encryption" accesskey="u" rel="up">Authenticated encryption</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="ChaCha_002dPoly1305-1"></a>
<h4 class="subsection">6.4.4 ChaCha-Poly1305</h4>

<p>ChaCha-Poly1305 is a combination of the ChaCha stream cipher and the
poly1305 message authentication code (see <a href="#Poly1305">Poly1305</a>). It originates
from the NaCl cryptographic library by D. J. Bernstein et al, which
defines a similar construction but with Salsa20 instead of ChaCha. 
</p>
<p>Nettle&rsquo;s implementation ChaCha-Poly1305 should be considered
<strong>experimental</strong>. At the time of this writing, there is no
authoritative specification for ChaCha-Poly1305, and a couple of
different incompatible variants. Nettle implements it using the original
definition of ChaCha, with 64 bits (8 octets) each for the nonce and the
block counter. Some protocols prefer to use nonces of 12 bytes, and it&rsquo;s
a small change to ChaCha to use the upper 32 bits of the block counter
as a nonce, instead limiting message size to <em>2^32</em> blocks or 256
GBytes, but that variant is currently not supported.
</p>
<p>For ChaCha-Poly1305, the ChaCha cipher is initialized with a key, of 256
bits, and a per-message nonce. The first block of the key stream
(counter all zero) is set aside for the authentication subkeys. Of this
64-octet block, the first 16 octets specify the poly1305 evaluation
point, and the next 16 bytes specify the value to add in for the final
digest. The final 32 bytes of this block are unused. Note that unlike
poly1305-aes, the evaluation point depends on the nonce. This is
preferable, because it leaks less information in case the attacker for
some reason is lucky enough to forge a valid authentication tag, and
observe (from the receiver&rsquo;s behaviour) that the forgery succeeded.
</p>
<p>The ChaCha key stream, starting with counter value 1, is then used to
encrypt the message. For authentication, poly1305 is applied to the
concatenation of the associated data, the cryptotext, and the lengths of
the associated data and the message, each a 64-bit number (eight octets,
little-endian). Nettle defines ChaCha-Poly1305 in
<samp>&lt;nettle/chacha-poly1305.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-CHACHA_005fPOLY1305_005fBLOCK_005fSIZE"></a>Constant: <strong>CHACHA_POLY1305_BLOCK_SIZE</strong></dt>
<dd><p>Same as the ChaCha block size, 64.
</p></dd></dl>

<dl>
<dt><a name="index-CHACHA_005fPOLY1305_005fKEY_005fSIZE"></a>Constant: <strong>CHACHA_POLY1305_KEY_SIZE</strong></dt>
<dd><p>ChaCha-Poly1305 key size, 32.
</p></dd></dl>

<dl>
<dt><a name="index-CHACHA_005fPOLY1305_005fNONCE_005fSIZE"></a>Constant: <strong>CHACHA_POLY1305_NONCE_SIZE</strong></dt>
<dd><p>Same as the ChaCha nonce size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-CHACHA_005fPOLY1305_005fDIGEST_005fSIZE"></a>Constant: <strong>CHACHA_POLY1305_DIGEST_SIZE</strong></dt>
<dd><p>Digest size, 16.
</p></dd></dl>

<dl>
<dt><a name="index-struct-chacha_005fpoly1305_005fctx"></a>Context struct: <strong>struct chacha_poly1305_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-chacha_005fpoly1305_005fset_005fkey"></a>Function: <em>void</em> <strong>chacha_poly1305_set_key</strong> <em>(struct chacha_poly1305_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes <var>ctx</var> using the given key. Before using the context, you
<em>must</em> also call <code>chacha_poly1305_set_nonce</code>, see below.
</p></dd></dl>

<dl>
<dt><a name="index-chacha_005fpoly1305_005fset_005fnonce"></a>Function: <em>void</em> <strong>chacha_poly1305_set_nonce</strong> <em>(struct chacha_poly1305_ctx *<var>ctx</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dd><p>Initializes the per-message state, using the given nonce.
</p></dd></dl>

<dl>
<dt><a name="index-chacha_005fpoly1305_005fupdate"></a>Function: <em>void</em> <strong>chacha_poly1305_update</strong> <em>(struct chacha_poly1305_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process associated data for authentication.
</p></dd></dl>

<dl>
<dt><a name="index-chacha_005fpoly1305_005fencrypt"></a>Function: <em>void</em> <strong>chacha_poly1305_encrypt</strong> <em>(struct chacha_poly1305_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dt><a name="index-chacha_005fpoly1305_005fdecrypt"></a>Function: <em>void</em> <strong>chacha_poly1305_decrypt</strong> <em>(struct chacha_poly1305_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Encrypts or decrypts the data of a message. All but the last call for
each message <em>must</em> use a length that is a multiple of the block
size.
</p></dd></dl>

<dl>
<dt><a name="index-chacha_005fpoly1305_005fdigest"></a>Function: <em>void</em> <strong>chacha_poly1305_digest</strong> <em>(struct chacha_poly1305_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the message digest (also known &ldquo;authentication tag&rdquo;). This is
the final operation when processing a message. If <var>length</var> is
smaller than <code>CHACHA_POLY1305_DIGEST_SIZE</code>, only the first
<var>length</var> octets of the digest are written.
</p></dd></dl>

<hr>
<a name="nettle_005faead-abstraction"></a>
<div class="header">
<p>
Previous: <a href="#ChaCha_002dPoly1305" accesskey="p" rel="prev">ChaCha-Poly1305</a>, Up: <a href="#Authenticated-encryption" accesskey="u" rel="up">Authenticated encryption</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="The-struct-nettle_005faead-abstraction"></a>
<h4 class="subsection">6.4.5 The <code>struct nettle_aead</code> abstraction</h4>
<a name="index-nettle_005faead"></a>
<a name="index-nettle_005faeads"></a>

<p>Nettle includes a struct including information about the supported hash
functions. It is defined in <samp>&lt;nettle/nettle-meta.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-nettle_005faead"></a>Meta struct: <strong><code>struct nettle_aead</code></strong> <em>name context_size block_size key_size nonce_size digest_size set_encrypt_key set_decrypt_key set_nonce update encrypt decrypt digest</em></dt>
<dd><p>The last seven attributes are function pointers.
</p></dd></dl>

<dl>
<dt><a name="index-nettle_005fgcm_005faes128"></a>Constant Struct: <em>struct nettle_aead</em> <strong>nettle_gcm_aes128</strong></dt>
<dt><a name="index-nettle_005fgcm_005faes192"></a>Constant Struct: <em>struct nettle_aead</em> <strong>nettle_gcm_aes192</strong></dt>
<dt><a name="index-nettle_005fgcm_005faes256"></a>Constant Struct: <em>struct nettle_aead</em> <strong>nettle_gcm_aes256</strong></dt>
<dt><a name="index-nettle_005fgcm_005fcamellia128"></a>Constant Struct: <em>struct nettle_aead</em> <strong>nettle_gcm_camellia128</strong></dt>
<dt><a name="index-nettle_005fgcm_005fcamellia256"></a>Constant Struct: <em>struct nettle_aead</em> <strong>nettle_gcm_camellia256</strong></dt>
<dt><a name="index-nettle_005feax_005faes128"></a>Constant Struct: <em>struct nettle_aead</em> <strong>nettle_eax_aes128</strong></dt>
<dt><a name="index-nettle_005fchacha_005fpoly1305"></a>Constant Struct: <em>struct nettle_aead</em> <strong>nettle_chacha_poly1305</strong></dt>
<dd><p>These are most of the <acronym>AEAD</acronym> constructions that Nettle
implements. Note that <acronym>CCM</acronym> is missing; it requirement that the
message size is specified in advance makes it incompatible with the
<code>nettle_aead</code> abstraction.
</p></dd></dl>

<p>Nettle also exports a list of all these constructions.
</p>
<dl>
<dt><a name="index-nettle_005faeads-1"></a>Constant Array: <em>struct nettle_aead **</em> <strong>nettle_aeads</strong></dt>
<dd><p>This list can be used to dynamically enumerate or search the supported
algorithms. NULL-terminated.
</p></dd></dl>

<hr>
<a name="Keyed-hash-functions"></a>
<div class="header">
<p>
Next: <a href="#Key-derivation-functions" accesskey="n" rel="next">Key derivation functions</a>, Previous: <a href="#Authenticated-encryption" accesskey="p" rel="prev">Authenticated encryption</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Keyed-Hash-Functions"></a>
<h3 class="section">6.5 Keyed Hash Functions</h3>

<a name="index-Keyed-Hash-Function"></a>
<a name="index-Message-Authentication-Code"></a>
<a name="index-MAC"></a>

<p>A <em>keyed hash function</em>, or <em>Message Authentication Code</em>
(<acronym>MAC</acronym>) is a function that takes a key and a message, and
produces fixed size <acronym>MAC</acronym>. It should be hard to compute a
message and a matching <acronym>MAC</acronym> without knowledge of the key. It
should also be hard to compute the key given only messages and
corresponding <acronym>MAC</acronym>s.
</p>
<p>Keyed hash functions are useful primarily for message authentication,
when Alice and Bob shares a secret: The sender, Alice, computes the
<acronym>MAC</acronym> and attaches it to the message. The receiver, Bob, also computes
the <acronym>MAC</acronym> of the message, using the same key, and compares that
to Alice&rsquo;s value. If they match, Bob can be assured that
the message has not been modified on its way from Alice.
</p>
<p>However, unlike digital signatures, this assurance is not transferable.
Bob can&rsquo;t show the message and the <acronym>MAC</acronym> to a third party and
prove that Alice sent that message. Not even if he gives away the key to
the third party. The reason is that the <em>same</em> key is used on both
sides, and anyone knowing the key can create a correct <acronym>MAC</acronym> for
any message. If Bob believes that only he and Alice knows the key, and
he knows that he didn&rsquo;t attach a <acronym>MAC</acronym> to a particular message,
he knows it must be Alice who did it. However, the third party can&rsquo;t
distinguish between a <acronym>MAC</acronym> created by Alice and one created by
Bob.
</p>
<p>Keyed hash functions are typically a lot faster than digital signatures
as well.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#HMAC" accesskey="1">HMAC</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#UMAC" accesskey="2">UMAC</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Poly1305" accesskey="3">Poly1305</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<hr>
<a name="HMAC"></a>
<div class="header">
<p>
Next: <a href="#UMAC" accesskey="n" rel="next">UMAC</a>, Previous: <a href="#Keyed-hash-functions" accesskey="p" rel="prev">Keyed hash functions</a>, Up: <a href="#Keyed-hash-functions" accesskey="u" rel="up">Keyed hash functions</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>

<a name="HMAC-1"></a>
<h4 class="subsection">6.5.1 <acronym>HMAC</acronym></h4>
<a name="index-HMAC"></a>

<p>One can build keyed hash functions from ordinary hash functions. Older
constructions simply concatenate secret key and message and hashes that, but
such constructions have weaknesses. A better construction is
<acronym>HMAC</acronym>, described in <cite>RFC 2104</cite>.
</p>
<p>For an underlying hash function <code>H</code>, with digest size <code>l</code> and
internal block size <code>b</code>, <acronym>HMAC-H</acronym> is constructed as
follows: From a given key <code>k</code>, two distinct subkeys <code>k_i</code> and
<code>k_o</code> are constructed, both of length <code>b</code>. The
<acronym>HMAC-H</acronym> of a message <code>m</code> is then computed as <code>H(k_o |
H(k_i | m))</code>, where <code>|</code> denotes string concatenation.
</p>
<p><acronym>HMAC</acronym> keys can be of any length, but it is recommended to use
keys of length <code>l</code>, the digest size of the underlying hash function
<code>H</code>. Keys that are longer than <code>b</code> are shortened to length
<code>l</code> by hashing with <code>H</code>, so arbitrarily long keys aren&rsquo;t
very useful. 
</p>
<p>Nettle&rsquo;s <acronym>HMAC</acronym> functions are defined in <samp>&lt;nettle/hmac.h&gt;</samp>.
There are abstract functions that use a pointer to a <code>struct
nettle_hash</code> to represent the underlying hash function and <code>void *</code>
pointers that point to three different context structs for that hash
function. There are also concrete functions for <acronym>HMAC-MD5</acronym>,
<acronym>HMAC-RIPEMD160</acronym> <acronym>HMAC-SHA1</acronym>, <acronym>HMAC-SHA256</acronym>, and
<acronym>HMAC-SHA512</acronym>. First, the abstract functions:
</p>
<dl>
<dt><a name="index-hmac_005fset_005fkey"></a>Function: <em>void</em> <strong>hmac_set_key</strong> <em>(void *<var>outer</var>, void *<var>inner</var>, void *<var>state</var>, const struct nettle_hash *<var>H</var>, size_t <var>length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes the three context structs from the key. The <var>outer</var> and
<var>inner</var> contexts corresponds to the subkeys <code>k_o</code> and
<code>k_i</code>. <var>state</var> is used for hashing the message, and is
initialized as a copy of the <var>inner</var> context.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fupdate"></a>Function: <em>void</em> <strong>hmac_update</strong> <em>(void *<var>state</var>, const struct nettle_hash *<var>H</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>This function is called zero or more times to process the message.
Actually, <code>hmac_update(state, H, length, data)</code> is equivalent to
<code>H-&gt;update(state, length, data)</code>, so if you wish you can use the
ordinary update function of the underlying hash function instead.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fdigest"></a>Function: <em>void</em> <strong>hmac_digest</strong> <em>(const void *<var>outer</var>, const void *<var>inner</var>, void *<var>state</var>, const struct nettle_hash *<var>H</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the <acronym>MAC</acronym> of the message, writing it to <var>digest</var>.
<var>outer</var> and <var>inner</var> are not modified. <var>length</var> is usually
equal to <code>H-&gt;digest_size</code>, but if you provide a smaller value,
only the first <var>length</var> octets of the <acronym>MAC</acronym> are written.
</p>
<p>This function also resets the <var>state</var> context so that you can start
over processing a new message (with the same key).
</p></dd></dl>

<p>Like for <acronym>CBC</acronym>, there are some macros to help use these
functions correctly.
</p>
<dl>
<dt><a name="index-HMAC_005fCTX"></a>Macro: <strong>HMAC_CTX</strong> <em>(<var>type</var>)</em></dt>
<dd><p>Expands to
</p><div class="example">
<pre class="example">{
   type outer;
   type inner;
   type state;
}
</pre></div>
</dd></dl>

<p>It can be used to define a <acronym>HMAC</acronym> context struct, either
directly,
</p>
<div class="example">
<pre class="example">struct HMAC_CTX(struct md5_ctx) ctx;
</pre></div>

<p>or to give it a struct tag,
</p>
<div class="example">
<pre class="example">struct hmac_md5_ctx HMAC_CTX (struct md5_ctx);
</pre></div>

<dl>
<dt><a name="index-HMAC_005fSET_005fKEY"></a>Macro: <strong>HMAC_SET_KEY</strong> <em>(<var>ctx</var>, <var>H</var>, <var>length</var>, <var>key</var>)</em></dt>
<dd><p><var>ctx</var> is a pointer to a context struct as defined by
<code>HMAC_CTX</code>, <var>H</var> is a pointer to a <code>const struct
nettle_hash</code> describing the underlying hash function (so it must match
the type of the components of <var>ctx</var>). The last two arguments specify
the secret key.
</p></dd></dl>

<dl>
<dt><a name="index-HMAC_005fDIGEST"></a>Macro: <strong>HMAC_DIGEST</strong> <em>(<var>ctx</var>, <var>H</var>, <var>length</var>, <var>digest</var>)</em></dt>
<dd><p><var>ctx</var> is a pointer to a context struct as defined by
<code>HMAC_CTX</code>, <var>H</var> is a pointer to a <code>const struct
nettle_hash</code> describing the underlying hash function. The last two
arguments specify where the digest is written.
</p></dd></dl>

<p>Note that there is no <code>HMAC_UPDATE</code> macro; simply call
<code>hmac_update</code> function directly, or the update function of the
underlying hash function.
</p>
<a name="Concrete-HMAC-functions"></a>
<h4 class="subsection">6.5.2 Concrete <acronym>HMAC</acronym> functions</h4>
<p>Now we come to the specialized <acronym>HMAC</acronym> functions, which are
easier to use than the general <acronym>HMAC</acronym> functions.
</p>
<a name="HMAC_002dMD5"></a>
<h4 class="subsubsection">6.5.2.1 <acronym>HMAC-MD5</acronym></h4>

<dl>
<dt><a name="index-struct-hmac_005fmd5_005fctx"></a>Context struct: <strong>struct hmac_md5_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-hmac_005fmd5_005fset_005fkey"></a>Function: <em>void</em> <strong>hmac_md5_set_key</strong> <em>(struct hmac_md5_ctx *<var>ctx</var>, size_t <var>key_length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes the context with the key.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fmd5_005fupdate"></a>Function: <em>void</em> <strong>hmac_md5_update</strong> <em>(struct hmac_md5_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process some more data.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fmd5_005fdigest"></a>Function: <em>void</em> <strong>hmac_md5_digest</strong> <em>(struct hmac_md5_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the <acronym>MAC</acronym>, writing it to <var>digest</var>. <var>length</var> may be smaller than
<code>MD5_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the <acronym>MAC</acronym> are written.
</p>
<p>This function also resets the context for processing new messages, with
the same key.
</p></dd></dl>

<a name="HMAC_002dRIPEMD160"></a>
<h4 class="subsubsection">6.5.2.2 <acronym>HMAC-RIPEMD160</acronym></h4>

<dl>
<dt><a name="index-struct-hmac_005fripemd160_005fctx"></a>Context struct: <strong>struct hmac_ripemd160_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-hmac_005fripemd160_005fset_005fkey"></a>Function: <em>void</em> <strong>hmac_ripemd160_set_key</strong> <em>(struct hmac_ripemd160_ctx *<var>ctx</var>, size_t <var>key_length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes the context with the key.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fripemd160_005fupdate"></a>Function: <em>void</em> <strong>hmac_ripemd160_update</strong> <em>(struct hmac_ripemd160_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process some more data.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fripemd160_005fdigest"></a>Function: <em>void</em> <strong>hmac_ripemd160_digest</strong> <em>(struct hmac_ripemd160_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the <acronym>MAC</acronym>, writing it to <var>digest</var>. <var>length</var> may be smaller than
<code>RIPEMD160_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the <acronym>MAC</acronym> are written.
</p>
<p>This function also resets the context for processing new messages, with
the same key.
</p></dd></dl>

<a name="HMAC_002dSHA1"></a>
<h4 class="subsubsection">6.5.2.3 <acronym>HMAC-SHA1</acronym></h4>

<dl>
<dt><a name="index-struct-hmac_005fsha1_005fctx"></a>Context struct: <strong>struct hmac_sha1_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-hmac_005fsha1_005fset_005fkey"></a>Function: <em>void</em> <strong>hmac_sha1_set_key</strong> <em>(struct hmac_sha1_ctx *<var>ctx</var>, size_t <var>key_length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes the context with the key.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fsha1_005fupdate"></a>Function: <em>void</em> <strong>hmac_sha1_update</strong> <em>(struct hmac_sha1_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process some more data.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fsha1_005fdigest"></a>Function: <em>void</em> <strong>hmac_sha1_digest</strong> <em>(struct hmac_sha1_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the <acronym>MAC</acronym>, writing it to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA1_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the <acronym>MAC</acronym> are written.
</p>
<p>This function also resets the context for processing new messages, with
the same key.
</p></dd></dl>


<a name="HMAC_002dSHA256"></a>
<h4 class="subsubsection">6.5.2.4 <acronym>HMAC-SHA256</acronym></h4>

<dl>
<dt><a name="index-struct-hmac_005fsha256_005fctx"></a>Context struct: <strong>struct hmac_sha256_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-hmac_005fsha256_005fset_005fkey"></a>Function: <em>void</em> <strong>hmac_sha256_set_key</strong> <em>(struct hmac_sha256_ctx *<var>ctx</var>, size_t <var>key_length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes the context with the key.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fsha256_005fupdate"></a>Function: <em>void</em> <strong>hmac_sha256_update</strong> <em>(struct hmac_sha256_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process some more data.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fsha256_005fdigest"></a>Function: <em>void</em> <strong>hmac_sha256_digest</strong> <em>(struct hmac_sha256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the <acronym>MAC</acronym>, writing it to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA256_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the <acronym>MAC</acronym> are written.
</p>
<p>This function also resets the context for processing new messages, with
the same key.
</p></dd></dl>


<a name="HMAC_002dSHA512"></a>
<h4 class="subsubsection">6.5.2.5 <acronym>HMAC-SHA512</acronym></h4>

<dl>
<dt><a name="index-struct-hmac_005fsha512_005fctx"></a>Context struct: <strong>struct hmac_sha512_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-hmac_005fsha512_005fset_005fkey"></a>Function: <em>void</em> <strong>hmac_sha512_set_key</strong> <em>(struct hmac_sha512_ctx *<var>ctx</var>, size_t <var>key_length</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initializes the context with the key.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fsha512_005fupdate"></a>Function: <em>void</em> <strong>hmac_sha512_update</strong> <em>(struct hmac_sha512_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process some more data.
</p></dd></dl>

<dl>
<dt><a name="index-hmac_005fsha512_005fdigest"></a>Function: <em>void</em> <strong>hmac_sha512_digest</strong> <em>(struct hmac_sha512_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the <acronym>MAC</acronym>, writing it to <var>digest</var>. <var>length</var> may be smaller than
<code>SHA512_DIGEST_SIZE</code>, in which case only the first <var>length</var>
octets of the <acronym>MAC</acronym> are written.
</p>
<p>This function also resets the context for processing new messages, with
the same key.
</p></dd></dl>

<hr>
<a name="UMAC"></a>
<div class="header">
<p>
Next: <a href="#Poly1305" accesskey="n" rel="next">Poly1305</a>, Previous: <a href="#HMAC" accesskey="p" rel="prev">HMAC</a>, Up: <a href="#Keyed-hash-functions" accesskey="u" rel="up">Keyed hash functions</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>

<a name="UMAC-1"></a>
<h4 class="subsection">6.5.3 <acronym>UMAC</acronym></h4>
<a name="index-UMAC"></a>

<p><acronym>UMAC</acronym> is a message authentication code based on universal
hashing, and designed for high performance on modern processors (in
contrast to GCM, See <a href="#GCM">GCM</a>, which is designed primarily for hardware
performance). On processors with good integer multiplication
performance, it can be 10 times faster than SHA256 and SHA512.
<acronym>UMAC</acronym> is specified in <cite>RFC 4418</cite>.
</p>
<p>The secret key is always 128 bits (16 octets). The key is used as an
encryption key for the <acronym>AES</acronym> block cipher. This cipher is used
in counter mode to generate various internal subkeys needed in
<acronym>UMAC</acronym>. Messages are of arbitrary size, and for each message,
<acronym>UMAC</acronym> also needs a unique nonce. Nonce values must not be
reused for two messages with the same key, but they need not be kept
secret.
</p>
<p>The nonce must be at least one octet, and at most 16; nonces shorter
than 16 octets are zero-padded. Nettle&rsquo;s implementation of
<acronym>UMAC</acronym> increments the nonce automatically for each message, so
explicitly setting the nonce for each message is optional. This
auto-increment uses network byte order and it takes the length of the
nonce into account. E.g., if the initial nonce is &ldquo;abc&rdquo; (3 octets),
this value is zero-padded to 16 octets for the first message. For the
next message, the nonce is incremented to &ldquo;abd&rdquo;, and this incremented
value is zero-padded to 16 octets.
</p>
<p><acronym>UMAC</acronym> is defined in four variants, for different output sizes:
32 bits (4 octets), 64 bits (8 octets), 96 bits (12 octets) and 128 bits
(16 octets), corresponding to different trade-offs between speed and
security. Using a shorter output size sometimes (but not always!) gives
the same result as using a longer output size and truncating the result.
So it is important to use the right variant. For consistency with other
hash and <acronym>MAC</acronym> functions, Nettle&rsquo;s <code>_digest</code> functions for
<acronym>UMAC</acronym> accept a length parameter so that the output can be
truncated to any desired size, but it is recommended to stick to the
specified output size and select the <acronym>umac</acronym> variant
corresponding to the desired size.
</p>
<p>The internal block size of <acronym>UMAC</acronym> is 1024 octets, and it also
generates more than 1024 bytes of subkeys. This makes the size of the
context struct quite a bit larger than other hash functions and
<acronym>MAC</acronym> algorithms in Nettle.
</p>
<p>Nettle defines <acronym>UMAC</acronym> in <samp>&lt;nettle/umac.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-umac32_005fctx"></a>Context struct: <strong>struct umac32_ctx</strong></dt>
<dt><a name="index-struct-umac64_005fctx"></a>Context struct: <strong>struct umac64_ctx</strong></dt>
<dt><a name="index-struct-umac96_005fctx"></a>Context struct: <strong>struct umac96_ctx</strong></dt>
<dt><a name="index-struct-umac128_005fctx"></a>Context struct: <strong>struct umac128_ctx</strong></dt>
<dd><p>Each <acronym>UMAC</acronym> variant uses its own context struct.
</p></dd></dl>

<dl>
<dt><a name="index-UMAC_005fKEY_005fSIZE"></a>Constant: <strong>UMAC_KEY_SIZE</strong></dt>
<dd><p>The UMAC key size, 16.
</p></dd></dl>
<dl>
<dt><a name="index-UMAC_005fMIN_005fNONCE_005fSIZE"></a>Constant: <strong>UMAC_MIN_NONCE_SIZE</strong></dt>
<dt><a name="index-UMAC_005fMAX_005fNONCE_005fSIZE"></a>Constant: <strong>UMAC_MAX_NONCE_SIZE</strong></dt>
<dd><p>The the minimum and maximum sizes for an UMAC nonce, 1 and 16,
respectively.
</p></dd></dl>
<dl>
<dt><a name="index-UMAC32_005fDIGEST_005fSIZE"></a>Constant: <strong>UMAC32_DIGEST_SIZE</strong></dt>
<dd><p>The size of an UMAC32 digest, 4.
</p></dd></dl>
<dl>
<dt><a name="index-UMAC64_005fDIGEST_005fSIZE"></a>Constant: <strong>UMAC64_DIGEST_SIZE</strong></dt>
<dd><p>The size of an UMAC64 digest, 8.
</p></dd></dl>
<dl>
<dt><a name="index-UMAC96_005fDIGEST_005fSIZE"></a>Constant: <strong>UMAC96_DIGEST_SIZE</strong></dt>
<dd><p>The size of an UMAC96 digest, 12.
</p></dd></dl>
<dl>
<dt><a name="index-UMAC128_005fDIGEST_005fSIZE"></a>Constant: <strong>UMAC128_DIGEST_SIZE</strong></dt>
<dd><p>The size of an UMAC128 digest, 16.
</p></dd></dl>
<dl>
<dt><a name="index-UMAC_005fBLOCK_005fSIZE"></a>Constant: <strong>UMAC_BLOCK_SIZE</strong></dt>
<dd><p>The internal block size of UMAC.
</p></dd></dl>

<dl>
<dt><a name="index-umac32_005fset_005fkey"></a>Function: <em>void</em> <strong>umac32_set_key</strong> <em>(struct umac32_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-umac64_005fset_005fkey"></a>Function: <em>void</em> <strong>umac64_set_key</strong> <em>(struct umac64_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-umac96_005fset_005fkey"></a>Function: <em>void</em> <strong>umac96_set_key</strong> <em>(struct umac96_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dt><a name="index-umac128_005fset_005fkey"></a>Function: <em>void</em> <strong>umac128_set_key</strong> <em>(struct umac128_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>These functions initialize the <acronym>UMAC</acronym> context struct. They also
initialize the nonce to zero (with length 16, for auto-increment).
</p></dd></dl>

<dl>
<dt><a name="index-umac32_005fset_005fnonce"></a>Function: <em>void</em> <strong>umac32_set_nonce</strong> <em>(struct umac32_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dt><a name="index-umac64_005fset_005fnonce"></a>Function: <em>void</em> <strong>umac64_set_nonce</strong> <em>(struct umac64_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dt><a name="index-umac96_005fset_005fnonce"></a>Function: <em>void</em> <strong>umac96_set_nonce</strong> <em>(struct umac96_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dt><a name="index-umac128_005fset_005fnonce"></a>Function: <em>void</em> <strong>umac128_set_nonce</strong> <em>(struct umac128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dd><p>Sets the nonce to be used for the next message. In general, nonces
should be set before processing of the message. This is not strictly
required for <acronym>UMAC</acronym> (the nonce only affects the final processing
generating the digest), but it is nevertheless recommended that this
function is called <em>before</em> the first <code>_update</code> call for the
message.
</p></dd></dl>

<dl>
<dt><a name="index-umac32_005fupdate"></a>Function: <em>void</em> <strong>umac32_update</strong> <em>(struct umac32_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-umac64_005fupdate"></a>Function: <em>void</em> <strong>umac64_update</strong> <em>(struct umac64_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-umac96_005fupdate"></a>Function: <em>void</em> <strong>umac96_update</strong> <em>(struct umac96_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dt><a name="index-umac128_005fupdate"></a>Function: <em>void</em> <strong>umac128_update</strong> <em>(struct umac128_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>These functions are called zero or more times to process the message.
</p></dd></dl>

<dl>
<dt><a name="index-umac32_005fdigest"></a>Function: <em>void</em> <strong>umac32_digest</strong> <em>(struct umac32_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-umac64_005fdigest"></a>Function: <em>void</em> <strong>umac64_digest</strong> <em>(struct umac64_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-umac96_005fdigest"></a>Function: <em>void</em> <strong>umac96_digest</strong> <em>(struct umac96_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dt><a name="index-umac128_005fdigest"></a>Function: <em>void</em> <strong>umac128_digest</strong> <em>(struct umac128_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the <acronym>MAC</acronym> of the message, writing it to <var>digest</var>.
<var>length</var> is usually equal to the specified output size, but if you
provide a smaller value, only the first <var>length</var> octets of the
<acronym>MAC</acronym> are written. These functions reset the context for
processing of a new message with the same key. The nonce is incremented
as described above, the new value is used unless you call the
<code>_set_nonce</code> function explicitly for each message.
</p></dd></dl>

<hr>
<a name="Poly1305"></a>
<div class="header">
<p>
Previous: <a href="#UMAC" accesskey="p" rel="prev">UMAC</a>, Up: <a href="#Keyed-hash-functions" accesskey="u" rel="up">Keyed hash functions</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Poly1305-1"></a>
<h4 class="subsection">6.5.4 Poly1305</h4>

<p>Poly1305-<acronym>AES</acronym> is a message authentication code designed by D. J.
Bernstein. It treats the message as a polynomial modulo the prime number
<em>2^130 - 5</em>.
</p>
<p>The key, 256 bits, consists of two parts, where the first half is an
<acronym>AES</acronym>-128 key, and the second half specifies the point where the
polynomial is evaluated. Of the latter half, 22 bits are set to zero, to
enable high-performance implementation, leaving 106 bits for specifying
an evaluation point <code>r</code>. For each message, one must also provide a
128-bit nonce. The nonce is encrypted using the <acronym>AES</acronym> key, and
that&rsquo;s the only thing <acronym>AES</acronym> is used for.
</p>
<p>The message is split into 128-bit chunks (with final chunk possibly
being shorter), each read as a little-endian integer. Each chunk has a
one-bit appended at the high end. The resulting integers are treated as
polynomial coefficients modulo <em>2^130 - 5</em>, and the polynomial is
evaluated at the point <code>r</code>. Finally, this value is reduced modulo
<em>2^128</em>, and added (also modulo <em>2^128</em>) to the encrypted
nonce, to produce an 128-bit authenticator for the message. See
<a href="http://cr.yp.to/mac/poly1305-20050329.pdf">http://cr.yp.to/mac/poly1305-20050329.pdf</a> for further details.
</p>
<p>Clearly, variants using a different cipher than <acronym>AES</acronym> could be
defined. Another variant is the ChaCha-Poly1305 <acronym>AEAD</acronym>
construction (see <a href="#ChaCha_002dPoly1305">ChaCha-Poly1305</a>). Nettle defines
Poly1305-<acronym>AES</acronym> in <samp>nettle/poly1305.h</samp>.
</p>
<dl>
<dt><a name="index-POLY1305_005fAES_005fKEY_005fSIZE"></a>Constant: <strong>POLY1305_AES_KEY_SIZE</strong></dt>
<dd><p>Key size, 32 octets.
</p></dd></dl>

<dl>
<dt><a name="index-POLY1305_005fAES_005fDIGEST_005fSIZE"></a>Constant: <strong>POLY1305_AES_DIGEST_SIZE</strong></dt>
<dd><p>Size of the digest or &ldquo;authenticator&rdquo;, 16 octets.
</p></dd></dl>

<dl>
<dt><a name="index-POLY1305_005fAES_005fNONCE_005fSIZE"></a>Constant: <strong>POLY1305_AES_NONCE_SIZE</strong></dt>
<dd><p>Nonce size, 16 octets.
</p></dd></dl>

<dl>
<dt><a name="index-struct-poly1305_005faes_005fctx"></a>Context struct: <strong>struct poly1305_aes_ctx</strong></dt>
<dd><p>The poly1305-aes context struct.
</p></dd></dl>

<dl>
<dt><a name="index-poly1305_005faes_005fset_005fkey"></a>Function: <em>void</em> <strong>poly1305_aes_set_key</strong> <em>(struct poly1305_aes_ctx *<var>ctx</var>, const uint8_t *<var>key</var>)</em></dt>
<dd><p>Initialize the context struct. Also sets the nonce to zero.
</p></dd></dl>

<dl>
<dt><a name="index-poly1305_005faes_005fset_005fnonce"></a>Function: <em>void</em> <strong>poly1305_aes_set_nonce</strong> <em>(struct poly1305_aes_ctx *<var>ctx</var>, const uint8_t *<var>nonce</var>)</em></dt>
<dd><p>Sets the nonce. Calling this function is optional, since the nonce is
incremented automatically for each message.
</p></dd></dl>

<dl>
<dt><a name="index-poly1305_005faes_005fupdate"></a>Function: <em>void</em> <strong>poly1305_aes_update</strong> <em>(struct poly1305_aes_ctx *<var>ctx</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Process more data.
</p></dd></dl>

<dl>
<dt><a name="index-poly1305_005faes_005fdigest"></a>Function: <em>void</em> <strong>poly1305_aes_digest</strong> <em>(struct poly1305_aes_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>digest</var>)</em></dt>
<dd><p>Extracts the digest. If <var>length</var> is smaller than
<code>POLY1305_AES_DIGEST_SIZE</code>, only the first <var>length</var> octets are
written. Also increments the nonce, and prepares the context for
processing a new message.
</p></dd></dl>


<hr>
<a name="Key-derivation-functions"></a>
<div class="header">
<p>
Next: <a href="#Public_002dkey-algorithms" accesskey="n" rel="next">Public-key algorithms</a>, Previous: <a href="#Keyed-hash-functions" accesskey="p" rel="prev">Keyed hash functions</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Key-derivation-Functions"></a>
<h3 class="section">6.6 Key derivation Functions</h3>

<a name="index-Key-Derivation-Function"></a>
<a name="index-Password-Based-Key-Derivation-Function"></a>
<a name="index-PKCS-_00235"></a>
<a name="index-KDF"></a>
<a name="index-PBKDF"></a>

<p>A <em>key derivation function</em> (<acronym>KDF</acronym>) is a function that from
a given symmetric key derives other symmetric keys.  A sub-class of KDFs
is the <em>password-based key derivation functions</em> (<acronym>PBKDFs</acronym>),
which take as input a password or passphrase, and its purpose is
typically to strengthen it and protect against certain pre-computation
attacks by using salting and expensive computation.
</p>
<a name="PBKDF2"></a>
<h4 class="subsection">6.6.1 <acronym>PBKDF2</acronym></h4>
<p>The most well known PBKDF is the <code>PKCS #5 PBKDF2</code> described in
<cite>RFC 2898</cite> which uses a pseudo-random function such as
<acronym>HMAC-SHA1</acronym>.
</p>
<p>Nettle&rsquo;s <acronym>PBKDF2</acronym> functions are defined in
<samp>&lt;nettle/pbkdf2.h&gt;</samp>.  There is an abstract function that operate on
any PRF implemented via the <code>nettle_hash_update_func</code>,
<code>nettle_hash_digest_func</code> interfaces.  There is also helper macros
and concrete functions PBKDF2-HMAC-SHA1 and PBKDF2-HMAC-SHA256.  First,
the abstract function:
</p>
<dl>
<dt><a name="index-pbkdf2"></a>Function: <em>void</em> <strong>pbkdf2</strong> <em>(void *mac_ctx, nettle_hash_update_func *update, nettle_hash_digest_func *digest, size_t digest_size, unsigned iterations, size_t salt_length, const uint8_t *salt, size_t length, uint8_t *dst)</em></dt>
<dd><p>Derive symmetric key from a password according to PKCS #5 PBKDF2.  The
PRF is assumed to have been initialized and this function will call the
<var>update</var> and <var>digest</var> functions passing the <var>mac_ctx</var>
context parameter as an argument in order to compute digest of size
<var>digest_size</var>.  Inputs are the salt <var>salt</var> of length
<var>salt_length</var>, the iteration counter <var>iterations</var> (&gt; 0), and the
desired derived output length <var>length</var>.  The output buffer is
<var>dst</var> which must have room for at least <var>length</var> octets.
</p></dd></dl>

<p>Like for CBC and HMAC, there is a macro to help use the function
correctly.
</p>
<dl>
<dt><a name="index-PBKDF2"></a>Macro: <strong>PBKDF2</strong> <em>(<var>ctx</var>, <var>update</var>, <var>digest</var>, <var>digest_size</var>, <var>iterations</var>, <var>salt_length</var>, <var>salt</var>, <var>length</var>, <var>dst</var>)</em></dt>
<dd><p><var>ctx</var> is a pointer to a context struct passed to the <var>update</var>
and <var>digest</var> functions (of the types <code>nettle_hash_update_func</code>
and <code>nettle_hash_digest_func</code> respectively) to implement the
underlying PRF with digest size of <var>digest_size</var>.  Inputs are the
salt <var>salt</var> of length <var>salt_length</var>, the iteration counter
<var>iterations</var> (&gt; 0), and the desired derived output length
<var>length</var>.  The output buffer is <var>dst</var> which must have room for
at least <var>length</var> octets.
</p></dd></dl>

<a name="Concrete-PBKDF2-functions"></a>
<h4 class="subsection">6.6.2 Concrete <acronym>PBKDF2</acronym> functions</h4>
<p>Now we come to the specialized <acronym>PBKDF2</acronym> functions, which are
easier to use than the general <acronym>PBKDF2</acronym> function.
</p>
<a name="PBKDF2_002dHMAC_002dSHA1"></a>
<h4 class="subsubsection">6.6.2.1 <acronym>PBKDF2-HMAC-SHA1</acronym></h4>

<dl>
<dt><a name="index-pbkdf2_005fhmac_005fsha1"></a>Function: <em>void</em> <strong>pbkdf2_hmac_sha1</strong> <em>(size_t <var>key_length</var>, const uint8_t *<var>key</var>, unsigned <var>iterations</var>, size_t <var>salt_length</var>, const uint8_t *<var>salt</var>, size_t <var>length</var>, uint8_t *<var>dst</var>)</em></dt>
<dd><p>PBKDF2 with HMAC-SHA1.  Derive <var>length</var> bytes of key into buffer
<var>dst</var> using the password <var>key</var> of length <var>key_length</var> and
salt <var>salt</var> of length <var>salt_length</var>, with iteration counter
<var>iterations</var> (&gt; 0).  The output buffer is <var>dst</var> which must have
room for at least <var>length</var> octets.
</p></dd></dl>

<a name="PBKDF2_002dHMAC_002dSHA256"></a>
<h4 class="subsubsection">6.6.2.2 <acronym>PBKDF2-HMAC-SHA256</acronym></h4>

<dl>
<dt><a name="index-pbkdf2_005fhmac_005fsha256"></a>Function: <em>void</em> <strong>pbkdf2_hmac_sha256</strong> <em>(size_t <var>key_length</var>, const uint8_t *<var>key</var>, unsigned <var>iterations</var>, size_t <var>salt_length</var>, const uint8_t *<var>salt</var>, size_t <var>length</var>, uint8_t *<var>dst</var>)</em></dt>
<dd><p>PBKDF2 with HMAC-SHA256.  Derive <var>length</var> bytes of key into buffer
<var>dst</var> using the password <var>key</var> of length <var>key_length</var> and
salt <var>salt</var> of length <var>salt_length</var>, with iteration counter
<var>iterations</var> (&gt; 0).  The output buffer is <var>dst</var> which must have
room for at least <var>length</var> octets.
</p></dd></dl>

<hr>
<a name="Public_002dkey-algorithms"></a>
<div class="header">
<p>
Next: <a href="#Randomness" accesskey="n" rel="next">Randomness</a>, Previous: <a href="#Key-derivation-functions" accesskey="p" rel="prev">Key derivation functions</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Public_002dkey-algorithms-1"></a>
<h3 class="section">6.7 Public-key algorithms</h3>

<p>Nettle uses <acronym>GMP</acronym>, the GNU bignum library, for all calculations
with large numbers. In order to use the public-key features of Nettle,
you must install <acronym>GMP</acronym>, at least version 3.0, before compiling
Nettle, and you need to link your programs with <code>-lhogweed -lnettle
-lgmp</code>.
</p>
<p>The concept of <em>Public-key</em> encryption and digital signatures was
discovered by Whitfield Diffie and Martin E. Hellman and described in a
paper 1976. In traditional, &ldquo;symmetric&rdquo;, cryptography, sender and
receiver share the same keys, and these keys must be distributed in a
secure way. And if there are many users or entities that need to
communicate, each <em>pair</em> needs a shared secret key known by nobody
else.
</p>
<a name="index-Public-Key-Cryptography"></a>
<a name="index-One_002dway-function"></a>

<p>Public-key cryptography uses trapdoor one-way functions. A
<em>one-way function</em> is a function <code>F</code> such that it is easy to
compute the value <code>F(x)</code> for any <code>x</code>, but given a value
<code>y</code>, it is hard to compute a corresponding <code>x</code> such that
<code>y = F(x)</code>. Two examples are cryptographic hash functions, and
exponentiation in certain groups.
</p>
<p>A <em>trapdoor one-way function</em> is a function <code>F</code> that is
one-way, unless one knows some secret information about <code>F</code>. If one
knows the secret, it is easy to compute both <code>F</code> and it&rsquo;s inverse.
If this sounds strange, look at the <acronym>RSA</acronym> example below.
</p>
<p>Two important uses for one-way functions with trapdoors are public-key
encryption, and digital signatures. The public-key encryption functions
in Nettle are not yet documented; the rest of this chapter is about
digital signatures.
</p>
<p>To use a digital signature algorithm, one must first create a
<em>key-pair</em>: A public key and a corresponding private key. The private
key is used to sign messages, while the public key is used for verifying
that that signatures and messages match. Some care must be taken when
distributing the public key; it need not be kept secret, but if a bad
guy is able to replace it (in transit, or in some user&rsquo;s list of known
public keys), bad things may happen.
</p>
<p>There are two operations one can do with the keys. The signature
operation takes a message and a private key, and creates a signature for
the message. A signature is some string of bits, usually at most a few
thousand bits or a few hundred octets. Unlike paper-and-ink signatures,
the digital signature depends on the message, so one can&rsquo;t cut it out of
context and glue it to a different message.
</p>
<p>The verification operation takes a public key, a message, and a string
that is claimed to be a signature on the message, and returns true or
false. If it returns true, that means that the three input values
matched, and the verifier can be sure that someone went through with the
signature operation on that very message, and that the &ldquo;someone&rdquo; also
knows the private key corresponding to the public key.
</p>
<p>The desired properties of a digital signature algorithm are as follows:
Given the public key and pairs of messages and valid signatures on them,
it should be hard to compute the private key, and it should also be hard
to create a new message and signature that is accepted by the
verification operation.
</p>
<p>Besides signing meaningful messages, digital signatures can be used for
authorization. A server can be configured with a public key, such that
any client that connects to the service is given a random nonce message.
If the server gets a reply with a correct signature matching the nonce
message and the configured public key, the client is granted access. So
the configuration of the server can be understood as &ldquo;grant access to
whoever knows the private key corresponding to this particular public
key, and to no others&rdquo;.
</p>

<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#RSA" accesskey="1">RSA</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">The RSA public key algorithm.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#DSA" accesskey="2">DSA</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">The DSA digital signature algorithm.
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Elliptic-curves" accesskey="3">Elliptic curves</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">Elliptic curves and ECDSA
</td></tr>
</table>

<hr>
<a name="RSA"></a>
<div class="header">
<p>
Next: <a href="#DSA" accesskey="n" rel="next">DSA</a>, Previous: <a href="#Public_002dkey-algorithms" accesskey="p" rel="prev">Public-key algorithms</a>, Up: <a href="#Public_002dkey-algorithms" accesskey="u" rel="up">Public-key algorithms</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="RSA-1"></a>
<h4 class="subsection">6.7.1 <acronym>RSA</acronym></h4>

<p>The <acronym>RSA</acronym> algorithm was the first practical digital signature
algorithm that was constructed. It was described 1978 in a paper by
Ronald Rivest, Adi Shamir and L.M. Adleman, and the technique was also
patented in the <acronym>USA</acronym> in 1983. The patent expired on September 20, 2000, and since
that day, <acronym>RSA</acronym> can be used freely, even in the <acronym>USA</acronym>.
</p>
<p>It&rsquo;s remarkably simple to describe the trapdoor function behind
<acronym>RSA</acronym>. The &ldquo;one-way&rdquo;-function used is
</p>
<div class="example">
<pre class="example">F(x) = x^e mod n
</pre></div>

<p>I.e. raise x to the <code>e</code>&rsquo;th power, while discarding all multiples of
<code>n</code>. The pair of numbers <code>n</code> and <code>e</code> is the public key.
<code>e</code> can be quite small, even <code>e = 3</code> has been used, although
slightly larger numbers are recommended. <code>n</code> should be about 2000
bits or larger.
</p>
<p>If <code>n</code> is large enough, and properly chosen, the inverse of F,
the computation of <code>e</code>&rsquo;th roots modulo <code>n</code>, is very difficult.
But, where&rsquo;s the trapdoor?
</p>
<p>Let&rsquo;s first look at how <acronym>RSA</acronym> key-pairs are generated. First
<code>n</code> is chosen as the product of two large prime numbers <code>p</code>
and <code>q</code> of roughly the same size (so if <code>n</code> is 2000 bits,
<code>p</code> and <code>q</code> are about 1000 bits each). One also computes the
number <code>phi = (p-1)(q-1)</code>, in mathematical speak, <code>phi</code> is the
order of the multiplicative group of integers modulo n.
</p>
<p>Next, <code>e</code> is chosen. It must have no factors in common with <code>phi</code> (in
particular, it must be odd), but can otherwise be chosen more or less
randomly. <code>e = 65537</code> is a popular choice, because it makes raising
to the <code>e</code>&rsquo;th power particularly efficient, and being prime, it
usually has no factors common with <code>phi</code>.
</p>
<p>Finally, a number <code>d</code>, <code>d &lt; n</code> is computed such that <code>e d
mod phi = 1</code>. It can be shown that such a number exists (this is why
<code>e</code> and <code>phi</code> must have no common factors), and that for all x,
</p>
<div class="example">
<pre class="example">(x^e)^d mod n = x^(ed) mod n = (x^d)^e mod n = x
</pre></div>

<p>Using Euclid&rsquo;s algorithm, <code>d</code> can be computed quite easily from
<code>phi</code> and <code>e</code>. But it is still hard to get <code>d</code> without
knowing <code>phi</code>, which depends on the factorization of <code>n</code>.
</p>
<p>So <code>d</code> is the trapdoor, if we know <code>d</code> and <code>y = F(x)</code>, we can
recover x as <code>y^d mod n</code>. <code>d</code> is also the private half of
the <acronym>RSA</acronym> key-pair.
</p>
<p>The most common signature operation for <acronym>RSA</acronym> is defined in
<cite>PKCS#1</cite>, a specification by RSA Laboratories. The message to be
signed is first hashed using a cryptographic hash function, e.g.
<acronym>MD5</acronym> or <acronym>SHA1</acronym>. Next, some padding, the <acronym>ASN.1</acronym>
&ldquo;Algorithm Identifier&rdquo; for the hash function, and the message digest
itself, are concatenated and converted to a number <code>x</code>. The
signature is computed from <code>x</code> and the private key as <code>s = x^d
mod n</code><a name="DOCF1" href="#FOOT1"><sup>1</sup></a>. The signature, <code>s</code> is a
number of about the same size of <code>n</code>, and it usually encoded as a
sequence of octets, most significant octet first.
</p>
<p>The verification operation is straight-forward, <code>x</code> is computed
from the message in the same way as above. Then <code>s^e mod n</code> is
computed, the operation returns true if and only if the result equals
<code>x</code>.
</p>
<p>The <acronym>RSA</acronym> algorithm can also be used for encryption. RSA encryption uses
the public key <code>(n,e)</code> to compute the ciphertext <code>m^e mod n</code>.
The <cite>PKCS#1</cite> padding scheme will use at least 8 random and non-zero
octets, using <var>m</var> of the form <code>[00 02 padding 00 plaintext]</code>.
It is required that <code>m &lt; n</code>, and therefor the plaintext must be
smaller than the octet size of the modulo <code>n</code>, with some margin.
</p>
<p>To decrypt the message, one needs the private key to compute <code>m =
c^e mod n</code> followed by checking and removing the padding.
</p>
<a name="Nettle_0027s-RSA-support"></a>
<h4 class="subsubsection">6.7.1.1 Nettle&rsquo;s <acronym>RSA</acronym> support</h4>

<p>Nettle represents <acronym>RSA</acronym> keys using two structures that contain
large numbers (of type <code>mpz_t</code>).
</p>
<dl>
<dt><a name="index-rsa_005fpublic_005fkey"></a>Context struct: <strong>rsa_public_key</strong> <em>size n e</em></dt>
<dd><p><code>size</code> is the size, in octets, of the modulo, and is used internally.
<code>n</code> and <code>e</code> is the public key.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fprivate_005fkey"></a>Context struct: <strong>rsa_private_key</strong> <em>size d p q a b c</em></dt>
<dd><p><code>size</code> is the size, in octets, of the modulo, and is used internally.
<code>d</code> is the secret exponent, but it is not actually used when
signing. Instead, the factors <code>p</code> and <code>q</code>, and the parameters
<code>a</code>, <code>b</code> and <code>c</code> are used. They are computed from <code>p</code>,
<code>q</code> and <code>e</code> such that <code>a e mod (p - 1) = 1, b e mod (q -
1) = 1, c q mod p = 1</code>.
</p></dd></dl>

<p>Before use, these structs must be initialized by calling one of
</p>
<dl>
<dt><a name="index-rsa_005fpublic_005fkey_005finit"></a>Function: <em>void</em> <strong>rsa_public_key_init</strong> <em>(struct rsa_public_key *<var>pub</var>)</em></dt>
<dt><a name="index-rsa_005fprivate_005fkey_005finit"></a>Function: <em>void</em> <strong>rsa_private_key_init</strong> <em>(struct rsa_private_key *<var>key</var>)</em></dt>
<dd><p>Calls <code>mpz_init</code> on all numbers in the key struct.
</p></dd></dl>

<p>and when finished with them, the space for the numbers must be
deallocated by calling one of
</p>
<dl>
<dt><a name="index-rsa_005fpublic_005fkey_005fclear"></a>Function: <em>void</em> <strong>rsa_public_key_clear</strong> <em>(struct rsa_public_key *<var>pub</var>)</em></dt>
<dt><a name="index-rsa_005fprivate_005fkey_005fclear"></a>Function: <em>void</em> <strong>rsa_private_key_clear</strong> <em>(struct rsa_private_key *<var>key</var>)</em></dt>
<dd><p>Calls <code>mpz_clear</code> on all numbers in the key struct.
</p></dd></dl>

<p>In general, Nettle&rsquo;s <acronym>RSA</acronym> functions deviates from Nettle&rsquo;s &ldquo;no
memory allocation&rdquo;-policy. Space for all the numbers, both in the key structs
above, and temporaries, are allocated dynamically. For information on how
to customize allocation, see
See <a href="http://www.gmplib.org/manual/Custom-Allocation.html#Custom-Allocation">GMP Allocation</a> in <cite>GMP Manual</cite>.
</p>
<p>When you have assigned values to the attributes of a key, you must call
</p>
<dl>
<dt><a name="index-rsa_005fpublic_005fkey_005fprepare"></a>Function: <em>int</em> <strong>rsa_public_key_prepare</strong> <em>(struct rsa_public_key *<var>pub</var>)</em></dt>
<dt><a name="index-rsa_005fprivate_005fkey_005fprepare"></a>Function: <em>int</em> <strong>rsa_private_key_prepare</strong> <em>(struct rsa_private_key *<var>key</var>)</em></dt>
<dd><p>Computes the octet size of the key (stored in the <code>size</code> attribute,
and may also do other basic sanity checks. Returns one if successful, or
zero if the key can&rsquo;t be used, for instance if the modulo is smaller
than the minimum size needed for <acronym>RSA</acronym> operations specified by PKCS#1.
</p></dd></dl>

<p>For each operation using the private key, there are two variants, e.g.,
<code>rsa_sha256_sign</code> and <code>rsa_sha256_sign_tr</code>. The former
function is older, and it should be avoided, because it provides no
defenses against side-channel attacks. The latter function use
randomized <acronym>RSA</acronym> blinding, which defends against timing attacks
using chosen-ciphertext, and it also checks the correctness of the
private key computation using the public key, which defends against
software or hardware errors which could leak the private key.
</p>
<p>Before signing or verifying a message, you first hash it with the
appropriate hash function. You pass the hash function&rsquo;s context struct
to the <acronym>RSA</acronym> signature function, and it will extract the message
digest and do the rest of the work. There are also alternative functions
that take the hash digest as argument.
</p>
<p>There is currently no support for using SHA224 or SHA384 with
<acronym>RSA</acronym> signatures, since there&rsquo;s no gain in either computation
time nor message size compared to using SHA256 and SHA512, respectively.
</p>
<p>Creating an <acronym>RSA</acronym> signature is done with one of the following
functions:
</p>
<dl>
<dt><a name="index-rsa_005fmd5_005fsign_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_md5_sign_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, struct md5_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha1_005fsign_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_sha1_sign_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, struct sha1_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha256_005fsign_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_sha256_sign_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, struct sha256_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha512_005fsign_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_sha512_sign_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, struct sha512_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dd><p>The signature is stored in <var>signature</var> (which must have been
<code>mpz_init</code>&rsquo;ed earlier). The hash context is reset so that it can be
used for new messages. The <var>random_ctx</var> and <var>random</var> pointers
are used to generate the <acronym>RSA</acronym> blinding. Returns one on success,
or zero on failure. Signing fails if an error in the computation was
detected, or if the key is too small for the given hash size, e.g., it&rsquo;s
not possible to create a signature using SHA512 and a 512-bit
<acronym>RSA</acronym> key.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fmd5_005fsign_005fdigest_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_md5_sign_digest_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha1_005fsign_005fdigest_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_sha1_sign_digest_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha256_005fsign_005fdigest_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_sha256_sign_digest_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha512_005fsign_005fdigest_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_sha512_sign_digest_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>)</em></dt>
<dd><p>Creates a signature from the given hash digest. <var>digest</var> should
point to a digest of size <code>MD5_DIGEST_SIZE</code>,
<code>SHA1_DIGEST_SIZE</code>, <code>SHA256_DIGEST_SIZE</code>, or
<code>SHA512_DIGEST_SIZE</code>respectively. The signature is stored in
<var>signature</var> (which must have been <code>mpz_init</code>:ed earlier).
Returns one on success, or zero on failure.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fpkcs1_005fsign_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_pkcs1_sign_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, size_t <var>length</var>, const uint8_t *<var>digest_info</var>, mpz_t <var>signature</var>)</em></dt>
<dd><p>Similar to the above <code>_sign_digest_tr</code> functions, but the input is not the
plain hash digest, but a PKCS#1 &ldquo;DigestInfo&rdquo;, an ASN.1 DER-encoding
of the digest together with an object identifier for the used hash
algorithm.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fmd5_005fsign"></a>Function: <em>int</em> <strong>rsa_md5_sign</strong> <em>(const struct rsa_private_key *<var>key</var>, struct md5_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha1_005fsign"></a>Function: <em>int</em> <strong>rsa_sha1_sign</strong> <em>(const struct rsa_private_key *<var>key</var>, struct sha1_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha256_005fsign"></a>Function: <em>int</em> <strong>rsa_sha256_sign</strong> <em>(const struct rsa_private_key *<var>key</var>, struct sha256_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha512_005fsign"></a>Function: <em>int</em> <strong>rsa_sha512_sign</strong> <em>(const struct rsa_private_key *<var>key</var>, struct sha512_ctx *<var>hash</var>, mpz_t <var>signature</var>)</em></dt>
<dd><p>The signature is stored in <var>signature</var> (which must have been
<code>mpz_init</code>&rsquo;ed earlier). The hash context is reset so that it can be
used for new messages. Returns one on success, or zero on failure.
Signing fails if the key is too small for the given hash size, e.g.,
it&rsquo;s not possible to create a signature using SHA512 and a 512-bit
<acronym>RSA</acronym> key.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fmd5_005fsign_005fdigest"></a>Function: <em>int</em> <strong>rsa_md5_sign_digest</strong> <em>(const struct rsa_private_key *<var>key</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha1_005fsign_005fdigest"></a>Function: <em>int</em> <strong>rsa_sha1_sign_digest</strong> <em>(const struct rsa_private_key *<var>key</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>);</em></dt>
<dt><a name="index-rsa_005fsha256_005fsign_005fdigest"></a>Function: <em>int</em> <strong>rsa_sha256_sign_digest</strong> <em>(const struct rsa_private_key *<var>key</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>);</em></dt>
<dt><a name="index-rsa_005fsha512_005fsign_005fdigest"></a>Function: <em>int</em> <strong>rsa_sha512_sign_digest</strong> <em>(const struct rsa_private_key *<var>key</var>, const uint8_t *<var>digest</var>, mpz_t <var>signature</var>);</em></dt>
<dd><p>Creates a signature from the given hash digest; otherwise analoguous to
the above signing functions. <var>digest</var> should point to a digest of
size <code>MD5_DIGEST_SIZE</code>, <code>SHA1_DIGEST_SIZE</code>,
<code>SHA256_DIGEST_SIZE</code>, or <code>SHA512_DIGEST_SIZE</code>, respectively.
The signature is stored in <var>signature</var> (which must have been
<code>mpz_init</code>:ed earlier). Returns one on success, or zero on failure.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fpkcs1_005fsign_0028const"></a>Function: <em>int</em> <strong>rsa_pkcs1_sign(const</strong> <em>struct rsa_private_key *<var>key</var>, size_t <var>length</var>, const uint8_t *<var>digest_info</var>, mpz_t <var>s</var>)</em></dt>
<dd><p>Similar to the above _sign_digest functions, but the input is not the
plain hash digest, but a PKCS#1 &ldquo;DigestInfo&rdquo;, an ASN.1 DER-encoding
of the digest together with an object identifier for the used hash
algorithm.
</p></dd></dl>

<p>Verifying an RSA signature is done with one of the following functions:
</p>
<dl>
<dt><a name="index-rsa_005fmd5_005fverify"></a>Function: <em>int</em> <strong>rsa_md5_verify</strong> <em>(const struct rsa_public_key *<var>key</var>, struct md5_ctx *<var>hash</var>, const mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha1_005fverify"></a>Function: <em>int</em> <strong>rsa_sha1_verify</strong> <em>(const struct rsa_public_key *<var>key</var>, struct sha1_ctx *<var>hash</var>, const mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha256_005fverify"></a>Function: <em>int</em> <strong>rsa_sha256_verify</strong> <em>(const struct rsa_public_key *<var>key</var>, struct sha256_ctx *<var>hash</var>, const mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha512_005fverify"></a>Function: <em>int</em> <strong>rsa_sha512_verify</strong> <em>(const struct rsa_public_key *<var>key</var>, struct sha512_ctx *<var>hash</var>, const mpz_t <var>signature</var>)</em></dt>
<dd><p>Returns 1 if the signature is valid, or 0 if it isn&rsquo;t. In either case,
the hash context is reset so that it can be used for new messages.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fmd5_005fverify_005fdigest"></a>Function: <em>int</em> <strong>rsa_md5_verify_digest</strong> <em>(const struct rsa_public_key *<var>key</var>, const uint8_t *<var>digest</var>, const mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha1_005fverify_005fdigest"></a>Function: <em>int</em> <strong>rsa_sha1_verify_digest</strong> <em>(const struct rsa_public_key *<var>key</var>, const uint8_t *<var>digest</var>, const mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha256_005fverify_005fdigest"></a>Function: <em>int</em> <strong>rsa_sha256_verify_digest</strong> <em>(const struct rsa_public_key *<var>key</var>, const uint8_t *<var>digest</var>, const mpz_t <var>signature</var>)</em></dt>
<dt><a name="index-rsa_005fsha512_005fverify_005fdigest"></a>Function: <em>int</em> <strong>rsa_sha512_verify_digest</strong> <em>(const struct rsa_public_key *<var>key</var>, const uint8_t *<var>digest</var>, const mpz_t <var>signature</var>)</em></dt>
<dd><p>Returns 1 if the signature is valid, or 0 if it isn&rsquo;t. <var>digest</var>
should point to a digest of size <code>MD5_DIGEST_SIZE</code>,
<code>SHA1_DIGEST_SIZE</code>, <code>SHA256_DIGEST_SIZE</code>, or
<code>SHA512_DIGEST_SIZE</code> respectively.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fpkcs1_005fverify_0028const"></a>Function: <em>int</em> <strong>rsa_pkcs1_verify(const</strong> <em>struct rsa_public_key *<var>key</var>, size_t <var>length</var>, const uint8_t *<var>digest_info</var>, const mpz_t <var>signature</var>)</em></dt>
<dd><p>Similar to the above _verify_digest functions, but the input is not the
plain hash digest, but a PKCS#1 &ldquo;DigestInfo&rdquo;, and ASN.1 DER-encoding
of the digest together with an object identifier for the used hash
algorithm.
</p></dd></dl>

<p>The following function is used to encrypt a clear text message using RSA.
</p><dl>
<dt><a name="index-rsa_005fencrypt"></a>Function: <em>int</em> <strong>rsa_encrypt</strong> <em>(const struct rsa_public_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, size_t <var>length</var>, const uint8_t *<var>cleartext</var>, mpz_t <var>ciphertext</var>)</em></dt>
<dd><p>Returns 1 on success, 0 on failure. If the message is too long then this
will lead to a failure.
</p></dd></dl>
<p>The following function is used to decrypt a cipher text message using RSA.
</p><dl>
<dt><a name="index-rsa_005fdecrypt"></a>Function: <em>int</em> <strong>rsa_decrypt</strong> <em>(const struct rsa_private_key *<var>key</var>, size_t *<var>length</var>, uint8_t *<var>cleartext</var>, const mpz_t <var>ciphertext</var>)</em></dt>
<dd><p>Returns 1 on success, 0 on failure. Causes of failure include decryption
failing or the resulting message being to large. The message buffer
pointed to by <var>cleartext</var> must be of size *<var>length</var>. After
decryption, *<var>length</var> will be updated with the size of the
message.
</p></dd></dl>
<p>There is also a timing resistant version of decryption that utilizes
randomized RSA blinding.
</p><dl>
<dt><a name="index-rsa_005fdecrypt_005ftr"></a>Function: <em>int</em> <strong>rsa_decrypt_tr</strong> <em>(const struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, size_t *<var>length</var>, uint8_t *<var>message</var>, const mpz_t <var>ciphertext</var>)</em></dt>
<dd><p>Returns 1 on success, 0 on failure.
</p></dd></dl>

<p>If you need to use the <acronym>RSA</acronym> trapdoor, the private key, in a way
that isn&rsquo;t supported by the above functions Nettle also includes a
function that computes <code>x^d mod n</code> and nothing more, using the
<acronym>CRT</acronym> optimization.
</p>
<dl>
<dt><a name="index-rsa_005fcompute_005froot_005ftr_0028const"></a>Function: <em>int</em> <strong>rsa_compute_root_tr(const</strong> <em>struct rsa_public_key *<var>pub</var>, const struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, mpz_t <var>x</var>, const mpz_t <var>m</var>)</em></dt>
<dd><p>Computes <code>x = m^d</code>. Returns one on success, or zero if a failure in
the computation was detected.
</p></dd></dl>

<dl>
<dt><a name="index-rsa_005fcompute_005froot"></a>Function: <em>void</em> <strong>rsa_compute_root</strong> <em>(struct rsa_private_key *<var>key</var>, mpz_t <var>x</var>, const mpz_t <var>m</var>)</em></dt>
<dd><p>Computes <code>x = m^d</code>.
</p></dd></dl>

<p>At last, how do you create new keys?
</p>
<dl>
<dt><a name="index-rsa_005fgenerate_005fkeypair"></a>Function: <em>int</em> <strong>rsa_generate_keypair</strong> <em>(struct rsa_public_key *<var>pub</var>, struct rsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func <var>random</var>, void *<var>progress_ctx</var>, nettle_progress_func <var>progress</var>, unsigned <var>n_size</var>, unsigned <var>e_size</var>);</em></dt>
<dd><p>There are lots of parameters. <var>pub</var> and <var>key</var> is where the
resulting key pair is stored. The structs should be initialized, but you
don&rsquo;t need to call <code>rsa_public_key_prepare</code> or
<code>rsa_private_key_prepare</code> after key generation.
</p>
<p><var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. For advice, see
See <a href="#Randomness">Randomness</a>.
</p>
<p><var>progress</var> and <var>progress_ctx</var> can be used to get callbacks
during the key generation process, in order to uphold an illusion of
progress. <var>progress</var> can be NULL, in that case there are no
callbacks.
</p>
<p><var>size_n</var> is the desired size of the modulo, in bits. If <var>size_e</var>
is non-zero, it is the desired size of the public exponent and a random
exponent of that size is selected. But if <var>e_size</var> is zero, it is
assumed that the caller has already chosen a value for <code>e</code>, and
stored it in <var>pub</var>.
Returns one on success, and zero on failure. The function can fail for
example if if <var>n_size</var> is too small, or if <var>e_size</var> is zero and
<code>pub-&gt;e</code> is an even number.
</p></dd></dl>

<hr>
<a name="DSA"></a>
<div class="header">
<p>
Next: <a href="#Elliptic-curves" accesskey="n" rel="next">Elliptic curves</a>, Previous: <a href="#RSA" accesskey="p" rel="prev">RSA</a>, Up: <a href="#Public_002dkey-algorithms" accesskey="u" rel="up">Public-key algorithms</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="DSA-1"></a>
<h4 class="subsection">6.7.2 <acronym>DSA</acronym></h4>

<p>The <acronym>DSA</acronym> digital signature algorithm is more complex than
<acronym>RSA</acronym>. It was specified during the early 1990s, and in 1994 NIST
published <acronym>FIPS</acronym> 186 which is the authoritative specification.
Sometimes <acronym>DSA</acronym> is referred to using the acronym <acronym>DSS</acronym>,
for Digital Signature Standard. The most recent revision of the
specification, FIPS186-3, was issued in 2009, and it adds support for
larger hash functions than <acronym>sha1</acronym>.
</p>
<p>For <acronym>DSA</acronym>, the underlying mathematical problem is the
computation of discrete logarithms. The public key consists of a large
prime <code>p</code>, a small prime <code>q</code> which is a factor of <code>p-1</code>,
a number <code>g</code> which generates a subgroup of order <code>q</code> modulo
<code>p</code>, and an element <code>y</code> in that subgroup.
</p>
<p>In the original <acronym>DSA</acronym>, the size of <code>q</code> is fixed to 160
bits, to match with the <acronym>SHA1</acronym> hash algorithm. The size of
<code>p</code> is in principle unlimited, but the
standard specifies only nine specific sizes: <code>512 + l*64</code>, where
<code>l</code> is between 0 and 8. Thus, the maximum size of <code>p</code> is 1024
bits, and sizes less than 1024 bits are considered obsolete and not
secure.
</p>
<p>The subgroup requirement means that if you compute 
</p>
<div class="example">
<pre class="example">g^t mod p
</pre></div>

<p>for all possible integers <code>t</code>, you will get precisely <code>q</code>
distinct values.
</p>
<p>The private key is a secret exponent <code>x</code>, such that
</p>
<div class="example">
<pre class="example">g^x = y mod p
</pre></div>

<p>In mathematical speak, <code>x</code> is the <em>discrete logarithm</em> of
<code>y</code> mod <code>p</code>, with respect to the generator <code>g</code>. The size
of <code>x</code> will also be about the same size as <code>q</code>. The security of the
<acronym>DSA</acronym> algorithm relies on the difficulty of the discrete
logarithm problem. Current algorithms to compute discrete logarithms in
this setting, and hence crack <acronym>DSA</acronym>, are of two types. The first
type works directly in the (multiplicative) group of integers mod
<code>p</code>. The best known algorithm of this type is the Number Field
Sieve, and it&rsquo;s complexity is similar to the complexity of factoring
numbers of the same size as <code>p</code>. The other type works in the
smaller <code>q</code>-sized subgroup generated by <code>g</code>, which has a more
difficult group structure. One good algorithm is Pollard-rho, which has
complexity <code>sqrt(q)</code>.
</p>
<p>The important point is that security depends on the size of <em>both</em>
<code>p</code> and <code>q</code>, and they should be chosen so that the difficulty
of both discrete logarithm methods are comparable. Today, the security
margin of the original <acronym>DSA</acronym> may be uncomfortably small. Using a
<code>p</code> of 1024 bits implies that cracking using the number field sieve
is expected to take about the same time as factoring a 1024-bit
<acronym>RSA</acronym> modulo, and using a <code>q</code> of size 160 bits implies
that cracking using Pollard-rho will take roughly <code>2^80</code> group
operations. With the size of <code>q</code> fixed, tied to the <acronym>SHA1</acronym>
digest size, it may be tempting to increase the size of <code>p</code> to,
say, 4096 bits. This will provide excellent resistance against attacks
like the number field sieve which works in the large group. But it will
do very little to defend against Pollard-rho attacking the small
subgroup; the attacker is slowed down at most by a single factor of 10
due to the more expensive group operation. And the attacker will surely
choose the latter attack.
</p>
<p>The signature generation algorithm is randomized; in order to create a
<acronym>DSA</acronym> signature, you need a good source for random numbers
(see <a href="#Randomness">Randomness</a>). Let us describe the common case of a 160-bit
<code>q</code>.
</p>
<p>To create a signature, one starts with the hash digest of the message,
<code>h</code>, which is a 160 bit number, and a random number <code>k,
0&lt;k&lt;q</code>, also 160 bits. Next, one computes 
</p>
<div class="example">
<pre class="example">r = (g^k mod p) mod q
s = k^-1 (h + x r) mod q
</pre></div>

<p>The signature is the pair <code>(r, s)</code>, two 160 bit numbers. Note the
two different mod operations when computing <code>r</code>, and the use of the
secret exponent <code>x</code>.
</p>
<p>To verify a signature, one first checks that <code>0 &lt; r,s &lt; q</code>, and
then one computes backwards,
</p>
<div class="example">
<pre class="example">w = s^-1 mod q
v = (g^(w h) y^(w r) mod p) mod q
</pre></div>

<p>The signature is valid if <code>v = r</code>. This works out because <code>w =
s^-1 mod q = k (h + x r)^-1 mod q</code>, so that
</p>
<div class="example">
<pre class="example">g^(w h) y^(w r) = g^(w h) (g^x)^(w r) = g^(w (h + x r)) = g^k 
</pre></div>

<p>When reducing mod <code>q</code> this yields <code>r</code>. Note that when
verifying a signature, we don&rsquo;t know either <code>k</code> or <code>x</code>: those
numbers are secret.
</p>
<p>If you can choose between <acronym>RSA</acronym> and <acronym>DSA</acronym>, which one is
best? Both are believed to be secure. <acronym>DSA</acronym> gained popularity in
the late 1990s, as a patent free alternative to <acronym>RSA</acronym>. Now that
the <acronym>RSA</acronym> patents have expired, there&rsquo;s no compelling reason to
want to use <acronym>DSA</acronym>. Today, the original <acronym>DSA</acronym> key size
does not provide a large security margin, and it should probably be
phased out together with <acronym>RSA</acronym> keys of 1024 bits. Using the
revised <acronym>DSA</acronym> algorithm with a larger hash function, in
particular, <acronym>SHA256</acronym>, a 256-bit <code>q</code>, and <code>p</code> of size
2048 bits or more, should provide for a more comfortable security
margin, but these variants are not yet in wide use.
</p>
<p><acronym>DSA</acronym> signatures are smaller than <acronym>RSA</acronym> signatures,
which is important for some specialized applications.
</p>
<p>From a practical point of view, <acronym>DSA</acronym>&rsquo;s need for a good
randomness source is a serious disadvantage. If you ever use the same
<code>k</code> (and <code>r</code>) for two different message, you leak your private
key.
</p>
<a name="Nettle_0027s-DSA-support"></a>
<h4 class="subsubsection">6.7.2.1 Nettle&rsquo;s <acronym>DSA</acronym> support</h4>

<p>Like for <acronym>RSA</acronym>, Nettle represents <acronym>DSA</acronym> keys using two
structures, containing values of type <code>mpz_t</code>. For information on
how to customize allocation, see See <a href="http://www.gmplib.org/manual/Custom-Allocation.html#Custom-Allocation">GMP
Allocation</a> in <cite>GMP Manual</cite>. Nettle&rsquo;s <acronym>DSA</acronym> interface is defined
in <samp>&lt;nettle/dsa.h&gt;</samp>.
</p>
<p>A <acronym>DSA</acronym> group is represented using the following struct.
</p>
<dl>
<dt><a name="index-dsa_005fparams"></a>Context struct: <strong>dsa_params</strong> <em>p q g</em></dt>
<dd><p>Parameters of the <acronym>DSA</acronym> group.
</p></dd></dl>

<dl>
<dt><a name="index-dsa_005fparams_005finit"></a>Function: <em>void</em> <strong>dsa_params_init</strong> <em>(struct dsa_params *<var>params</var>)</em></dt>
<dd><p>Calls <code>mpz_init</code> on all numbers in the struct.
</p></dd></dl>

<dl>
<dt><a name="index-dsa_005fparams_005fclear"></a>Function: <em>void</em> <strong>dsa_params_clear</strong> <em>(struct dsa_params *<var>params</var>params)</em></dt>
<dd><p>Calls <code>mpz_clear</code> on all numbers in the struct.
</p></dd></dl>

<dl>
<dt><a name="index-dsa_005fgenerate_005fparams"></a>Function: <em>int</em> <strong>dsa_generate_params</strong> <em>(struct dsa_params *<var>params</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, void *<var>progress_ctx</var>, nettle_progress_func *<var>progress</var>, unsigned <var>p_bits</var>, unsigned <var>q_bits</var>)</em></dt>
<dd><p>Generates paramaters of a new group. The <var>params</var> struct should be
initialized before you call this function.
</p>
<p><var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. For advice, see
See <a href="#Randomness">Randomness</a>.
</p>
<p><var>progress</var> and <var>progress_ctx</var> can be used to get callbacks
during the key generation process, in order to uphold an illusion of
progress. <var>progress</var> can be NULL, in that case there are no
callbacks.
</p>
<p><var>p_bits</var> and <var>q_bits</var> are the desired sizes of <code>p</code> and
<code>q</code>. To generate keys that conform to the original <acronym>DSA</acronym>
standard, you must use <code>q_bits = 160</code> and select <var>p_bits</var> of
the form <code>p_bits = 512 + l*64</code>, for <code>0 &lt;= l &lt;= 8</code>, where the
smaller sizes are no longer recommended, so you should most likely stick
to <code>p_bits = 1024</code>. Non-standard sizes are possible, in particular
<code>p_bits</code> larger than 1024, although <acronym>DSA</acronym> implementations
can not in general be expected to support such keys. Also note that
using very large <var>p_bits</var>, with <var>q_bits</var> fixed at 160, doesn&rsquo;t
make much sense, because the security is also limited by the size of the
smaller prime. To generate <acronym>DSA</acronym> keys for use with
<acronym>SHA256</acronym>, use <code>q_bits = 256</code> and, e.g., <code>p_bits =
2048</code>.
</p>
<p>Returns one on success, and zero on failure. The function will fail if
<var>q_bits</var> is too small, or too close to <var>p_bits</var>.
</p></dd></dl>

<p>Signatures are represented using the structure below.
</p>
<dl>
<dt><a name="index-dsa_005fsignature"></a>Context struct: <strong>dsa_signature</strong> <em>r s</em></dt>
</dl>

<dl>
<dt><a name="index-dsa_005fsignature_005finit"></a>Function: <em>void</em> <strong>dsa_signature_init</strong> <em>(struct dsa_signature *<var>signature</var>)</em></dt>
<dt><a name="index-dsa_005fsignature_005fclear"></a>Function: <em>void</em> <strong>dsa_signature_clear</strong> <em>(struct dsa_signature *<var>signature</var>)</em></dt>
<dd><p>You must call <code>dsa_signature_init</code> before creating or using a
signature, and call <code>dsa_signature_clear</code> when you are finished
with it.
</p></dd></dl>

<p>Keys are represented as bignums, of type <code>mpz_t</code>. A public keys
represent a group element, and is of the same size as <code>p</code>, while a
private key is an exponent, of the same size as <code>q</code>.
</p>
<dl>
<dt><a name="index-dsa_005fsign"></a>Function: <em>int</em> <strong>dsa_sign</strong> <em>(const struct dsa_params *<var>params</var>, const mpz_t <var>x</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, size_t <var>digest_size</var>, const uint8_t *<var>digest</var>, struct dsa_signature *<var>signature</var>)</em></dt>
<dd><p>Creates a signature from the given hash digest, using the private key
<var>x</var>. <var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. For advice, see
See <a href="#Randomness">Randomness</a>. Returns one on success, or zero on failure. Signing
can fail only if the key is invalid, so that inversion modulo <code>q</code>
fails.
</p></dd></dl>

<dl>
<dt><a name="index-dsa_005fverify"></a>Function: <em>int</em> <strong>dsa_verify</strong> <em>(const struct dsa_params *<var>params</var>, const mpz_t <var>y</var>, size_t <var>digest_size</var>, const uint8_t *<var>digest</var>, const struct dsa_signature *<var>signature</var>)</em></dt>
<dd><p>Verifies a signature, using the public key y. Returns 1 if the signature
is valid, otherwise 0.
</p></dd></dl>

<p>To generate a keypair, first generate a <acronym>DSA</acronym> group using
<code>dsa_generate_params</code>. A keypair in this group is then created
using
</p>
<dl>
<dt><a name="index-dsa_005fgenerate_005fkeypair"></a>Function: <em>void</em> <strong>dsa_generate_keypair</strong> <em>(const struct dsa_params *<var>params</var>, mpz_t <var>pub</var>, mpz_t <var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>)</em></dt>
<dd><p>Generates a new keypair, using the group <var>params</var>. The public key is
stored in <var>pub</var>, and the private key in <var>key</var>. Both variables
must be initialized using <code>mpz_init</code> before this call.
</p>
<p><var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. For advice, see
See <a href="#Randomness">Randomness</a>.
</p></dd></dl>

<a name="Old_002c-deprecated_002c-DSA-interface"></a>
<h4 class="subsubsection">6.7.2.2 Old, deprecated, <acronym>DSA</acronym> interface</h4>

<p>Versions before nettle-3.0 used a different interface for <acronym>DSA</acronym>
signatures, where the group parameters and the public key was packed
together as <code>struct dsa_public_key</code>. Most of this interface is kept
for backwards compatibility, and declared in <samp>nettle/dsa-compat.h</samp>.
Below is the old documentation. The old and new interface use distinct
names and don&rsquo;t confict, with one exception: The key generation
function. The <samp>nettle/dsa-compat.h</samp> redefines
<code>dsa_generate_keypair</code> as an alias for
<code>dsa_compat_generate_keypair</code>, compatible with the old interface
and documented below.
</p>
<p>The old <acronym>DSA</acronym> functions are very similar to the corresponding
<acronym>RSA</acronym> functions, but there are a few differences pointed out
below. For a start, there are no functions corresponding to
<code>rsa_public_key_prepare</code> and <code>rsa_private_key_prepare</code>.
</p>
<dl>
<dt><a name="index-dsa_005fpublic_005fkey"></a>Context struct: <strong>dsa_public_key</strong> <em>p q g y</em></dt>
<dd><p>The public parameters described above.
</p></dd></dl>

<dl>
<dt><a name="index-dsa_005fprivate_005fkey"></a>Context struct: <strong>dsa_private_key</strong> <em>x</em></dt>
<dd><p>The private key <code>x</code>.
</p></dd></dl>

<p>Before use, these structs must be initialized by calling one of
</p>
<dl>
<dt><a name="index-dsa_005fpublic_005fkey_005finit"></a>Function: <em>void</em> <strong>dsa_public_key_init</strong> <em>(struct dsa_public_key *<var>pub</var>)</em></dt>
<dt><a name="index-dsa_005fprivate_005fkey_005finit"></a>Function: <em>void</em> <strong>dsa_private_key_init</strong> <em>(struct dsa_private_key *<var>key</var>)</em></dt>
<dd><p>Calls <code>mpz_init</code> on all numbers in the key struct.
</p></dd></dl>

<p>When finished with them, the space for the numbers must be
deallocated by calling one of
</p>
<dl>
<dt><a name="index-dsa_005fpublic_005fkey_005fclear"></a>Function: <em>void</em> <strong>dsa_public_key_clear</strong> <em>(struct dsa_public_key *<var>pub</var>)</em></dt>
<dt><a name="index-dsa_005fprivate_005fkey_005fclear"></a>Function: <em>void</em> <strong>dsa_private_key_clear</strong> <em>(struct dsa_private_key *<var>key</var>)</em></dt>
<dd><p>Calls <code>mpz_clear</code> on all numbers in the key struct.
</p></dd></dl>

<p>Signatures are represented using <code>struct dsa_signature</code>, described
earlier.
</p>
<p>For signing, you need to provide both the public and the private key
(unlike <acronym>RSA</acronym>, where the private key struct includes all
information needed for signing), and a source for random numbers.
Signatures can use the <acronym>SHA1</acronym> or the <acronym>SHA256</acronym> hash
function, although the implementation of <acronym>DSA</acronym> with
<acronym>SHA256</acronym> should be considered somewhat experimental due to lack
of official test vectors and interoperability testing.
</p>
<dl>
<dt><a name="index-dsa_005fsha1_005fsign"></a>Function: <em>int</em> <strong>dsa_sha1_sign</strong> <em>(const struct dsa_public_key *<var>pub</var>, const struct dsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func <var>random</var>, struct sha1_ctx *<var>hash</var>, struct dsa_signature *<var>signature</var>)</em></dt>
<dt><a name="index-dsa_005fsha1_005fsign_005fdigest"></a>Function: <em>int</em> <strong>dsa_sha1_sign_digest</strong> <em>(const struct dsa_public_key *<var>pub</var>, const struct dsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func <var>random</var>, const uint8_t *<var>digest</var>, struct dsa_signature *<var>signature</var>)</em></dt>
<dt><a name="index-dsa_005fsha256_005fsign"></a>Function: <em>int</em> <strong>dsa_sha256_sign</strong> <em>(const struct dsa_public_key *<var>pub</var>, const struct dsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func <var>random</var>, struct sha256_ctx *<var>hash</var>, struct dsa_signature *<var>signature</var>)</em></dt>
<dt><a name="index-dsa_005fsha256_005fsign_005fdigest"></a>Function: <em>int</em> <strong>dsa_sha256_sign_digest</strong> <em>(const struct dsa_public_key *<var>pub</var>, const struct dsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func <var>random</var>, const uint8_t *<var>digest</var>, struct dsa_signature *<var>signature</var>)</em></dt>
<dd><p>Creates a signature from the given hash context or digest.
<var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. For advice, see
See <a href="#Randomness">Randomness</a>. Returns one on success, or zero on failure.
Signing fails if the key size and the hash size don&rsquo;t match.
</p></dd></dl>

<p>Verifying signatures is a little easier, since no randomness generator is
needed. The functions are
</p>
<dl>
<dt><a name="index-dsa_005fsha1_005fverify"></a>Function: <em>int</em> <strong>dsa_sha1_verify</strong> <em>(const struct dsa_public_key *<var>key</var>, struct sha1_ctx *<var>hash</var>, const struct dsa_signature *<var>signature</var>)</em></dt>
<dt><a name="index-dsa_005fsha1_005fverify_005fdigest"></a>Function: <em>int</em> <strong>dsa_sha1_verify_digest</strong> <em>(const struct dsa_public_key *<var>key</var>, const uint8_t *<var>digest</var>, const struct dsa_signature *<var>signature</var>)</em></dt>
<dt><a name="index-dsa_005fsha256_005fverify"></a>Function: <em>int</em> <strong>dsa_sha256_verify</strong> <em>(const struct dsa_public_key *<var>key</var>, struct sha256_ctx *<var>hash</var>, const struct dsa_signature *<var>signature</var>)</em></dt>
<dt><a name="index-dsa_005fsha256_005fverify_005fdigest"></a>Function: <em>int</em> <strong>dsa_sha256_verify_digest</strong> <em>(const struct dsa_public_key *<var>key</var>, const uint8_t *<var>digest</var>, const struct dsa_signature *<var>signature</var>)</em></dt>
<dd><p>Verifies a signature. Returns 1 if the signature is valid, otherwise 0.
</p></dd></dl>

<p>Key generation uses mostly the same parameters as the corresponding
<acronym>RSA</acronym> function.
</p>
<dl>
<dt><a name="index-dsa_005fcompat_005fgenerate_005fkeypair"></a>Function: <em>int</em> <strong>dsa_compat_generate_keypair</strong> <em>(struct dsa_public_key *<var>pub</var>, struct dsa_private_key *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func <var>random</var>, void *<var>progress_ctx</var>, nettle_progress_func <var>progress</var>, unsigned <var>p_bits</var>, unsigned <var>q_bits</var>)</em></dt>
<dd><p><var>pub</var> and <var>key</var> is where the resulting key pair is stored. The
structs should be initialized before you call this function. 
</p>
<p><var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. For advice, see
See <a href="#Randomness">Randomness</a>.
</p>
<p><var>progress</var> and <var>progress_ctx</var> can be used to get callbacks
during the key generation process, in order to uphold an illusion of
progress. <var>progress</var> can be NULL, in that case there are no
callbacks.
</p>
<p><var>p_bits</var> and <var>q_bits</var> are the desired sizes of <code>p</code> and
<code>q</code>. See <code>dsa_generate_keypair</code> for details.
</p></dd></dl>

<hr>
<a name="Elliptic-curves"></a>
<div class="header">
<p>
Previous: <a href="#DSA" accesskey="p" rel="prev">DSA</a>, Up: <a href="#Public_002dkey-algorithms" accesskey="u" rel="up">Public-key algorithms</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Elliptic-curves-1"></a>
<h4 class="subsection">6.7.3 <acronym>Elliptic curves</acronym></h4>

<p>For cryptographic purposes, an elliptic curve is a mathematical group of
points, and computing logarithms in this group is computationally
difficult problem. Nettle uses additive notation for elliptic curve
groups. If <em>P</em> and <em>Q</em> are two points, and <em>k</em> is an
integer, the point sum, <em>P + Q</em>, and the multiple <em>k P</em> can be
computed efficiently, but given only two points <em>P</em> and <em>Q</em>,
finding an integer <em>k</em> such that <em>Q = k P</em> is the elliptic
curve discrete logarithm problem.
</p>
<p>Nettle supports standard curves which are all of the form <em>y^2 =
x^3 - 3 x + b (mod p)</em>, i.e., the points have coordinates <em>(x,y)</em>,
both considered as integers modulo a specified prime <em>p</em>. Curves
are represented as a <code>struct ecc_curve</code>. It also supports
curve25519, which uses a different form of curve. Supported curves are
declared in <samp>&lt;nettle/ecc-curve.h&gt;</samp>, e.g., <code>nettle_secp_256r1</code>
for a standardized curve using the 256-bit prime <em>p = 2^{256} -
2^{224} + 2^{192} + 2^{96} - 1</em>. The contents of these structs is not
visible to nettle users. The &ldquo;bitsize of the curve&rdquo; is used as a
shorthand for the bitsize of the curve&rsquo;s prime <em>p</em>, e.g., 256 bits
for <code>nettle_secp_256r1</code>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="#Side_002dchannel-silence" accesskey="1">Side-channel silence</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#ECDSA" accesskey="2">ECDSA</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="#Curve-25519" accesskey="3">Curve 25519</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<hr>
<a name="Side_002dchannel-silence"></a>
<div class="header">
<p>
Next: <a href="#ECDSA" accesskey="n" rel="next">ECDSA</a>, Up: <a href="#Elliptic-curves" accesskey="u" rel="up">Elliptic curves</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Side_002dchannel-silence-1"></a>
<h4 class="subsubsection">6.7.3.1 Side-channel silence</h4>
<a name="index-Side_002dchannel-attack"></a>

<p>Nettle&rsquo;s implementation of the elliptic curve operations is intended to
be side-channel silent. The side-channel attacks considered are:
</p>
<ul>
<li> Timing attacks
If the timing of operations depends on secret values, an attacker
interacting with your system can measure the response time, and infer
information about your secrets, e.g., a private signature key.

</li><li> Attacks using memory caches
Assume you have some secret data on a multi-user system, and that this
data is properly protected so that other users get no direct access to
it. If you have a process operating on the secret data, and this process
does memory accesses depending on the data, e.g, an internal lookup
table in some cryptographic algorithm, an attacker running a separate
process on the same system may use behavior of internal CPU caches to
get information about your secrets. This type of attack can even cross
virtual machine boundaries.
</li></ul>

<p>Nettle&rsquo;s ECC implementation is designed to be <em>side-channel silent</em>,
and not leak any information to these attacks. Timing and memory
accesses depend only on the size of the input data and its location in
memory, not on the actual data bits. This implies a performance penalty
in several of the building blocks.
</p>
<hr>
<a name="ECDSA"></a>
<div class="header">
<p>
Next: <a href="#Curve-25519" accesskey="n" rel="next">Curve 25519</a>, Previous: <a href="#Side_002dchannel-silence" accesskey="p" rel="prev">Side-channel silence</a>, Up: <a href="#Elliptic-curves" accesskey="u" rel="up">Elliptic curves</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="ECDSA-1"></a>
<h4 class="subsubsection">6.7.3.2 ECDSA</h4>

<p>ECDSA is a variant of the DSA digital signature scheme (see <a href="#DSA">DSA</a>),
which works over an elliptic curve group rather than over a (subgroup
of) integers modulo <em>p</em>. Like DSA, creating a signature requires a unique
random nonce (repeating the nonce with two different messages reveals
the private key, and any leak or bias in the generation of the nonce
also leaks information about the key).
</p>
<p>Unlike DSA, signatures are in general not tied to any particular hash
function or even hash size. Any hash function can be used, and the hash
value is truncated or padded as needed to get a size matching the curve
being used. It is recommended to use a strong cryptographic hash
function with digest size close to the bit size of the curve, e.g.,
SHA256 is a reasonable choice when using ECDSA signature over the curve
secp256r1. A protocol or application using ECDSA has to specify which
curve and which hash function to use, or provide some mechanism for
negotiating.
</p>
<p>Nettle defines ECDSA in <samp>&lt;nettle/ecdsa.h&gt;</samp>. We first need
to define the data types used to represent public and private keys.
</p>
<dl>
<dt><a name="index-struct-ecc_005fpoint"></a>struct: <strong>struct ecc_point</strong></dt>
<dd><p>Represents a point on an elliptic curve. In particular, it is used to
represent an ECDSA public key.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fpoint_005finit"></a>Function: <em>void</em> <strong>ecc_point_init</strong> <em>(struct ecc_point *<var>p</var>, const struct ecc_curve *<var>ecc</var>)</em></dt>
<dd><p>Initializes <var>p</var> to represent points on the given curve <var>ecc</var>.
Allocates storage for the coordinates, using the same allocation
functions as GMP.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fpoint_005fclear"></a>Function: <em>void</em> <strong>ecc_point_clear</strong> <em>(struct ecc_point *<var>p</var>)</em></dt>
<dd><p>Deallocate storage.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fpoint_005fset"></a>Function: <em>int</em> <strong>ecc_point_set</strong> <em>(struct ecc_point *<var>p</var>, const mpz_t <var>x</var>, const mpz_t <var>y</var>)</em></dt>
<dd><p>Check that the given coordinates represent a point on the curve. If so,
the coordinates are copied and converted to internal representation, and
the function returns 1. Otherwise, it returns 0. Currently, the
infinity point (or zero point, with additive notation) is not allowed.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fpoint_005fget"></a>Function: <em>void</em> <strong>ecc_point_get</strong> <em>(const struct ecc_point *<var>p</var>, mpz_t <var>x</var>, mpz_t <var>y</var>)</em></dt>
<dd><p>Extracts the coordinate of the point <var>p</var>. The output parameters
<var>x</var> or <var>y</var> may be NULL if the caller doesn&rsquo;t want that
coordinate.
</p></dd></dl>

<dl>
<dt><a name="index-struct-ecc_005fscalar"></a>struct: <strong>struct ecc_scalar</strong></dt>
<dd><p>Represents an integer in the range <em>0 &lt; x &lt; group order</em>, where the
&ldquo;group order&rdquo; refers to the order of an ECC group. In particular, it
is used to represent an ECDSA private key.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fscalar_005finit"></a>Function: <em>void</em> <strong>ecc_scalar_init</strong> <em>(struct ecc_scalar *<var>s</var>, const struct ecc_curve *<var>ecc</var>)</em></dt>
<dd><p>Initializes <var>s</var> to represent a scalar suitable for the given curve
<var>ecc</var>. Allocates storage using the same allocation functions as GMP.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fscalar_005fclear"></a>Function: <em>void</em> <strong>ecc_scalar_clear</strong> <em>(struct ecc_scalar *<var>s</var>)</em></dt>
<dd><p>Deallocate storage.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fscalar_005fset"></a>Function: <em>int</em> <strong>ecc_scalar_set</strong> <em>(struct ecc_scalar *<var>s</var>, const mpz_t <var>z</var>)</em></dt>
<dd><p>Check that <var>z</var> is in the correct range. If so, copies the value to
<var>s</var> and returns 1, otherwise returns 0.
</p></dd></dl>

<dl>
<dt><a name="index-ecc_005fscalar_005fget"></a>Function: <em>void</em> <strong>ecc_scalar_get</strong> <em>(const struct ecc_scalar *<var>s</var>, mpz_t <var>z</var>)</em></dt>
<dd><p>Extracts the scalar, in GMP <code>mpz_t</code> representation.
</p></dd></dl>

<p>To create and verify ECDSA signatures, the following functions are used.
</p>
<dl>
<dt><a name="index-ecdsa_005fsign"></a>Function: <em>void</em> <strong>ecdsa_sign</strong> <em>(const struct ecc_scalar *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>, size_t <var>digest_length</var>, const uint8_t *<var>digest</var>, struct dsa_signature *<var>signature</var>)</em></dt>
<dd><p>Uses the private key <var>key</var> to create a signature on <var>digest</var>.
<var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. The signature is stored in
<var>signature</var>, in the same was as for plain DSA.
</p></dd></dl>

<dl>
<dt><a name="index-ecdsa_005fverify"></a>Function: <em>int</em> <strong>ecdsa_verify</strong> <em>(const struct ecc_point *<var>pub</var>, size_t <var>length</var>, const uint8_t *<var>digest</var>, const struct dsa_signature *<var>signature</var>)</em></dt>
<dd><p>Uses the public key <var>pub</var> to verify that <var>signature</var> is a valid
signature for the message digest <var>digest</var> (of <var>length</var> octets).
Returns 1 if the signature is valid, otherwise 0.
</p></dd></dl>

<p>Finally, to generation of new an ECDSA key pairs
</p>
<dl>
<dt><a name="index-ecdsa_005fgenerate_005fkeypair"></a>Function: <em>void</em> <strong>ecdsa_generate_keypair</strong> <em>(struct ecc_point *<var>pub</var>, struct ecc_scalar *<var>key</var>, void *<var>random_ctx</var>, nettle_random_func *<var>random</var>);</em></dt>
<dd><p><var>pub</var> and <var>key</var> is where the resulting key pair is stored. The
structs should be initialized, for the desired ECC curve, before you call this function.
</p>
<p><var>random_ctx</var> and <var>random</var> is a randomness generator.
<code>random(random_ctx, length, dst)</code> should generate <code>length</code>
random octets and store them at <code>dst</code>. For advice, see
See <a href="#Randomness">Randomness</a>.
</p></dd></dl>

<hr>
<a name="Curve-25519"></a>
<div class="header">
<p>
Previous: <a href="#ECDSA" accesskey="p" rel="prev">ECDSA</a>, Up: <a href="#Elliptic-curves" accesskey="u" rel="up">Elliptic curves</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Curve25519"></a>
<h4 class="subsubsection">6.7.3.3 Curve25519</h4>
<a name="index-Curve-25519"></a>


<p>Curve25519 is an elliptic curve of Montgomery type, <em>y^2 = x^3 +
486662 x^2 + x (mod p)</em>, with <em>p = 2^255 - 19</em>. Montgomery curves
have the advantage of simple and efficient point addition based on the
x-coordinate only. This particular curve was proposed by D. J. Bernstein
in 2006, for fast Diffie-Hellman key exchange, and is also described in
<cite>RFC 7748</cite>. The group generator is defined by <em>x = 9</em> (there
are actually two points with <em>x = 9</em>, differing by the sign of the
y-coordinate, but that doesn&rsquo;t matter for the curve25519 operations
which work with the x-coordinate only).
</p>
<p>The curve25519 functions are defined as operations on octet strings,
representing 255-bit scalars or x-coordinates, in little-endian byte
order. The most significant input bit, i.e, the most significant bit of
the last octet, is always ignored.
</p>
<p>For scalars, in addition, the least significant three bits are ignored,
and treated as zero, and the second most significant bit is ignored too,
and treated as one. Then the scalar input string always represents 8
times a number in the range <em>2^251 &lt;= s &lt; 2^252</em>.
</p>
<p>Of all the possible input strings, only about half correspond to
x-coordinates of points on curve25519, i.e., a value <em>x</em> for which
the the curve equation can be solved for <em>y</em>. The other half
correspond to points on a related &ldquo;twist curve&rdquo;. The function
<code>curve25519_mul</code> uses a Montgomery ladder for the scalar
multiplication, as suggested in the curve25519 literature, and required
by <cite>RFC 7748</cite>. The output is therefore well defined for
<em>all</em> possible inputs, no matter if the input string represents a
valid point on the curve or not.
</p>
<p>Note that the curve25519 implementation in earlier versions of Nettle
deviates slightly from <cite>RFC 7748</cite>, in that bit 255 of the <em>x</em>
coordinate of the point input to curve25519_mul was not ignored. The
<samp>nette/curve25519.h</samp> defines a preprocessor symbol
<code>NETTLE_CURVE25519_RFC7748</code> to indicate conformance with the
standard.
</p>
<p>Nettle defines Curve 25519 in <samp>&lt;nettle/curve25519.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-NETTLE_005fCURVE25519_005fRFC7748"></a>Constant: <strong>NETTLE_CURVE25519_RFC7748</strong></dt>
<dd><p>Defined to 1 in Nettle versions conforming to RFC 7748. Undefined in
earlier versions.
</p></dd></dl>

<dl>
<dt><a name="index-CURVE25519_005fSIZE"></a>Constant: <strong>CURVE25519_SIZE</strong></dt>
<dd><p>The size of the strings representing curve25519 points and scalars, 32.
</p></dd></dl>

<dl>
<dt><a name="index-curve25519_005fmul_005fg"></a>Function: <em>void</em> <strong>curve25519_mul_g</strong> <em>(uint8_t *<var>q</var>, const uint8_t *<var>n</var>)</em></dt>
<dd><p>Computes <em>Q = N G</em>, where <em>G</em> is the group generator and
<em>N</em> is an integer. The input argument <var>n</var> and the output
argument <var>q</var> use a little-endian representation of the scalar and
the x-coordinate, respectively. They are both of size
<code>CURVE25519_SIZE</code>.
</p>
<p>This function is intended to be compatible with the function
<code>crypto_scalar_mult_base</code> in the NaCl library.
</p></dd></dl>

<dl>
<dt><a name="index-curve25519_005fmul"></a>Function: <em>void</em> <strong>curve25519_mul</strong> <em>(uint8_t *<var>q</var>, const uint8_t *<var>n</var>, const uint8_t *<var>p</var>)</em></dt>
<dd><p>Computes <em>Q = N P</em>, where <em>P</em> is an input point and <em>N</em>
is an integer. The input arguments <var>n</var> and <var>p</var> and the output
argument <var>q</var> use a little-endian representation of the scalar and
the x-coordinates, respectively. They are all of size
<code>CURVE25519_SIZE</code>.
</p>
<p>This function is intended to be compatible with the function
<code>crypto_scalar_mult</code> in the NaCl library.
</p></dd></dl>

<a name="EdDSA"></a>
<h4 class="subsubsection">6.7.3.4 EdDSA</h4>
<a name="index-eddsa"></a>

<p>EdDSA is a signature scheme proposed by D. J. Bernstein et al. in 2011.
It is defined using a &ldquo;Twisted Edwards curve&rdquo;, of the form <em>-x^2
+ y^2 = 1 + d x^2 y^2</em>. The specific signature scheme Ed25519 uses a
curve which is equivalent to curve25519: The two groups used differ only
by a simple change of coordinates, so that the discrete logarithm
problem is of equal difficulty in both groups.
</p>
<p>Unlike other signature schemes in Nettle, the input to the EdDSA sign
and verify functions is the possibly large message itself, not a hash
digest. EdDSA is a variant of Schnorr signatures, where the message is
hashed together with other data during the signature process, providing
resilience to hash-collisions: A successful attack finding collisions in
the hash function does not automatically translate into an attack to
forge signatures. EdDSA also avoids the use of a randomness source by
generating the needed signature nonce from a hash of the private key and
the message, which means that the message is actually hashed twice when
creating a signature. If signing huge messages, it is possible to hash
the message first and pass the short message digest as input to the sign
and verify functions, however, the resilience to hash collision is then
lost.
</p>
<dl>
<dt><a name="index-ED25519_005fKEY_005fSIZE"></a>Constant: <strong>ED25519_KEY_SIZE</strong></dt>
<dd><p>The size of a private or public Ed25519 key, 32 octets.
</p></dd></dl>

<dl>
<dt><a name="index-ED25519_005fSIGNATURE_005fSIZE"></a>Constant: <strong>ED25519_SIGNATURE_SIZE</strong></dt>
<dd><p>The size of an Ed25519 signature, 64 octets.
</p></dd></dl>

<dl>
<dt><a name="index-ed25519_005fsha512_005fpublic_005fkey"></a>Function: <em>void</em> <strong>ed25519_sha512_public_key</strong> <em>(uint8_t *<var>pub</var>, const uint8_t *<var>priv</var>)</em></dt>
<dd><p>Computes the public key corresponding to the given private key. Both
input and output are of size <code>ED25519_KEY_SIZE</code>.
</p></dd></dl>

<dl>
<dt><a name="index-ed25519_005fsha512_005fsign"></a>Function: <em>void</em> <strong>ed25519_sha512_sign</strong> <em>(const uint8_t *<var>pub</var>, const uint8_t *<var>priv</var>, size_t <var>length</var>, const uint8_t *<var>msg</var>, uint8_t *<var>signature</var>)</em></dt>
<dd><p>Signs a message using the provided key pair.
</p></dd></dl>

<dl>
<dt><a name="index-ed25519_005fsha512_005fverify"></a>Function: <em>int</em> <strong>ed25519_sha512_verify</strong> <em>(const uint8_t *<var>pub</var>, size_t <var>length</var>, const uint8_t *<var>msg</var>, const uint8_t *<var>signature</var>)</em></dt>
<dd><p>Verifies a message using the provided public key. Returns 1 if the
signature is valid, otherwise 0.
</p></dd></dl>

<hr>
<a name="Randomness"></a>
<div class="header">
<p>
Next: <a href="#ASCII-encoding" accesskey="n" rel="next">ASCII encoding</a>, Previous: <a href="#Public_002dkey-algorithms" accesskey="p" rel="prev">Public-key algorithms</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Randomness-1"></a>
<h3 class="section">6.8 Randomness</h3>

<a name="index-Randomness"></a>

<p>A crucial ingredient in many cryptographic contexts is randomness: Let
<code>p</code> be a random prime, choose a random initialization vector
<code>iv</code>, a random key <code>k</code> and a random exponent <code>e</code>, etc. In
the theories, it is assumed that you have plenty of randomness around.
If this assumption is not true in practice, systems that are otherwise
perfectly secure, can be broken. Randomness has often turned out to be
the weakest link in the chain.
</p>
<p>In non-cryptographic applications, such as games as well as scientific
simulation, a good randomness generator usually means a generator that
has good statistical properties, and is seeded by some simple function
of things like the current time, process id, and host name.
</p>
<p>However, such a generator is inadequate for cryptography, for at least
two reasons:
</p>

<ul>
<li> It&rsquo;s too easy for an attacker to guess the initial seed. Even if it will
take some 2^32 tries before he guesses right, that&rsquo;s far too easy. For
example, if the process id is 16 bits, the resolution of &ldquo;current time&rdquo;
is one second, and the attacker knows what day the generator was seeded,
there are only about 2^32 possibilities to try if all possible values
for the process id and time-of-day are tried.

</li><li> The generator output reveals too much. By observing only a small segment
of the generator&rsquo;s output, its internal state can be recovered, and from
there, all previous output and all future output can be computed by the
attacker. 
</li></ul>

<p>A randomness generator that is used for cryptographic purposes must have
better properties. Let&rsquo;s first look at the seeding, as the issues here
are mostly independent of the rest of the generator. The initial state
of the generator (its seed) must be unguessable by the attacker. So
what&rsquo;s unguessable? It depends on what the attacker already knows. The
concept used in information theory to reason about such things is called
&ldquo;entropy&rdquo;, or &ldquo;conditional entropy&rdquo; (not to be confused with the
thermodynamic concept with the same name). A reasonable requirement is
that the seed contains a conditional entropy of at least some 80-100
bits. This property can be explained as follows: Allow the attacker to
ask <code>n</code> yes-no-questions, of his own choice, about the seed. If
the attacker, using this question-and-answer session, as well as any
other information he knows about the seeding process, still can&rsquo;t guess
the seed correctly, then the conditional entropy is more than <code>n</code>
bits.
</p>
<a name="index-Entropy"></a>
<a name="index-Conditional-entropy"></a>

<p>Let&rsquo;s look at an example. Say information about timing of received
network packets is used in the seeding process. If there is some random
network traffic going on, this will contribute some bits of entropy or
&ldquo;unguessability&rdquo; to the seed. However, if the attacker can listen in to
the local network, or if all but a small number of the packets were
transmitted by machines that the attacker can monitor, this additional
information makes the seed easier for the attacker to figure out. Even
if the information is exactly the same, the conditional entropy, or
unguessability, is smaller for an attacker that knows some of it already
before the hypothetical question-and-answer session.
</p>
<p>Seeding of good generators is usually based on several sources. The key
point here is that the amount of unguessability that each source
contributes, depends on who the attacker is. Some sources that have been
used are:
</p>
<dl compact="compact">
<dt>High resolution timing of i/o activities</dt>
<dd><p>Such as completed blocks from spinning hard disks, network packets, etc.
Getting access to such information is quite system dependent, and not
all systems include suitable hardware. If available, it&rsquo;s one of the
better randomness source one can find in a digital, mostly predictable,
computer.
</p>
</dd>
<dt>User activity</dt>
<dd><p>Timing and contents of user interaction events is another popular source
that is available for interactive programs (even if I suspect that it is
sometimes used in order to make the user feel good, not because the
quality of the input is needed or used properly). Obviously, not
available when a machine is unattended. Also beware of networks: User
interaction that happens across a long serial cable, <acronym>TELNET</acronym>
session, or even <acronym>SSH</acronym> session may be visible to an attacker, in
full or partially.
</p>
</dd>
<dt>Audio input</dt>
<dd><p>Any room, or even a microphone input that&rsquo;s left unconnected, is a
source of some random background noise, which can be fed into the
seeding process.
</p>
</dd>
<dt>Specialized hardware</dt>
<dd><p>Hardware devices with the sole purpose of generating random data have
been designed. They range from radioactive samples with an attached
Geiger counter, to amplification of the inherent noise in electronic
components such as diodes and resistors, to low-frequency sampling of
chaotic systems. Hashing successive images of a Lava lamp is a
spectacular example of the latter type.
</p>
</dd>
<dt>Secret information</dt>
<dd><p>Secret information, such as user passwords or keys, or private files
stored on disk, can provide some unguessability. A problem is that if
the information is revealed at a later time, the unguessability
vanishes. Another problem is that this kind of information tends to be
fairly constant, so if you rely on it and seed your generator regularly,
you risk constructing almost similar seeds or even constructing the same
seed more than once.
</p></dd>
</dl>

<p>For all practical sources, it&rsquo;s difficult but important to provide a
reliable lower bound on the amount of unguessability that it provides.
Two important points are to make sure that the attacker can&rsquo;t observe
your sources (so if you like the Lava lamp idea, remember that you have
to get your own lamp, and not put it by a window or anywhere else where
strangers can see it), and that hardware failures are detected. What if
the bulb in the Lava lamp, which you keep locked into a cupboard
following the above advice, breaks after a few months?
</p>
<p>So let&rsquo;s assume that we have been able to find an unguessable seed,
which contains at least 80 bits of conditional entropy, relative to all
attackers that we care about (typically, we must at the very least
assume that no attacker has root privileges on our machine).
</p>
<p>How do we generate output from this seed, and how much can we get? Some
generators (notably the Linux <samp>/dev/random</samp> generator) tries to
estimate available entropy and restrict the amount of output. The goal
is that if you read 128 bits from <samp>/dev/random</samp>, you should get 128
&ldquo;truly random&rdquo; bits. This is a property that is useful in some
specialized circumstances, for instance when generating key material for
a one time pad, or when working with unconditional blinding, but in most
cases, it doesn&rsquo;t matter much. For most application, there&rsquo;s no limit on
the amount of useful &ldquo;random&rdquo; data that we can generate from a small
seed; what matters is that the seed is unguessable and that the
generator has good cryptographic properties.
</p>
<p>At the heart of all generators lies its internal state. Future output
is determined by the internal state alone. Let&rsquo;s call it the generator&rsquo;s
key. The key is initialized from the unguessable seed. Important
properties of a generator are:
</p>
<dl compact="compact">
<dt><em>Key-hiding</em></dt>
<dd><p>An attacker observing the output should not be able to recover the
generator&rsquo;s key.
</p>
</dd>
<dt><em>Independence of outputs</em></dt>
<dd><p>Observing some of the output should not help the attacker to guess
previous or future output.
</p>
</dd>
<dt><em>Forward secrecy</em></dt>
<dd><p>Even if an attacker compromises the generator&rsquo;s key, he should not be
able to guess the generator output <em>before</em> the key compromise.
</p>
</dd>
<dt><em>Recovery from key compromise</em></dt>
<dd><p>If an attacker compromises the generator&rsquo;s key, he can compute
<em>all</em> future output. This is inevitable if the generator is seeded
only once, at startup. However, the generator can provide a reseeding
mechanism, to achieve recovery from key compromise. More precisely: If
the attacker compromises the key at a particular time <code>t_1</code>, there
is another later time <code>t_2</code>, such that if the attacker observes all
output generated between <code>t_1</code> and <code>t_2</code>, he still can&rsquo;t guess
what output is generated after <code>t_2</code>.
</p>
</dd>
</dl>

<p>Nettle includes one randomness generator that is believed to have all
the above properties, and two simpler ones.
</p>
<p><acronym>ARCFOUR</acronym>, like any stream cipher, can be used as a randomness
generator. Its output should be of reasonable quality, if the seed is
hashed properly before it is used with <code>arcfour_set_key</code>. There&rsquo;s
no single natural way to reseed it, but if you need reseeding, you
should be using Yarrow instead.
</p>
<p>The &ldquo;lagged Fibonacci&rdquo; generator in <samp>&lt;nettle/knuth-lfib.h&gt;</samp> is a
fast generator with good statistical properties, but is <strong>not</strong> for
cryptographic use, and therefore not documented here. It is included
mostly because the Nettle test suite needs to generate some test data
from a small seed.
</p>
<p>The recommended generator to use is Yarrow, described below.
</p>
<a name="Yarrow"></a>
<h4 class="subsection">6.8.1 Yarrow</h4>

<p>Yarrow is a family of pseudo-randomness generators, designed for
cryptographic use, by John Kelsey, Bruce Schneier and Niels Ferguson.
Yarrow-160 is described in a paper at
<a href="http://www.counterpane.com/yarrow.html">http://www.counterpane.com/yarrow.html</a>, and it uses <acronym>SHA1</acronym>
and triple-DES, and has a 160-bit internal state. Nettle implements
Yarrow-256, which is similar, but uses <acronym>SHA256</acronym> and
<acronym>AES</acronym> to get an internal state of 256 bits.
</p>
<p>Yarrow was an almost finished project, the paper mentioned above is the
closest thing to a specification for it, but some smaller details are
left out. There is no official reference implementation or test cases.
This section includes an overview of Yarrow, but for the details of
Yarrow-256, as implemented by Nettle, you have to consult the source
code. Maybe a complete specification can be written later.
</p>
<p>Yarrow can use many sources (at least two are needed for proper
reseeding), and two randomness &ldquo;pools&rdquo;, referred to as the &ldquo;slow pool&rdquo; and
the &ldquo;fast pool&rdquo;. Input from the sources is fed alternatingly into the
two pools. When one of the sources has contributed 100 bits of entropy
to the fast pool, a &ldquo;fast reseed&rdquo; happens and the fast pool is mixed
into the internal state. When at least two of the sources have
contributed at least 160 bits each to the slow pool, a &ldquo;slow reseed&rdquo;
takes place. The contents of both pools are mixed into the internal
state. These procedures should ensure that the generator will eventually
recover after a key compromise.
</p>
<p>The output is generated by using <acronym>AES</acronym> to encrypt a counter,
using the generator&rsquo;s current key. After each request for output,
another 256 bits are generated which replace the key. This ensures
forward secrecy.
</p>
<p>Yarrow can also use a <em>seed file</em> to save state across restarts.
Yarrow is seeded by either feeding it the contents of the previous seed
file, or feeding it input from its sources until a slow reseed happens.
</p>
<p>Nettle defines Yarrow-256 in <samp>&lt;nettle/yarrow.h&gt;</samp>. 
</p>
<dl>
<dt><a name="index-struct-yarrow256_005fctx"></a>Context struct: <strong>struct yarrow256_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-struct-yarrow_005fsource"></a>Context struct: <strong>struct yarrow_source</strong></dt>
<dd><p>Information about a single source.
</p></dd></dl>

<dl>
<dt><a name="index-YARROW256_005fSEED_005fFILE_005fSIZE"></a>Constant: <strong>YARROW256_SEED_FILE_SIZE</strong></dt>
<dd><p>Recommended size of the Yarrow-256 seed file.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow256_005finit"></a>Function: <em>void</em> <strong>yarrow256_init</strong> <em>(struct yarrow256_ctx *<var>ctx</var>, unsigned <var>nsources</var>, struct yarrow_source *<var>sources</var>)</em></dt>
<dd><p>Initializes the yarrow context, and its <var>nsources</var> sources. It&rsquo;s
possible to call it with <var>nsources</var>=0 and <var>sources</var>=NULL, if
you don&rsquo;t need the update features.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow256_005fseed"></a>Function: <em>void</em> <strong>yarrow256_seed</strong> <em>(struct yarrow256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>seed_file</var>)</em></dt>
<dd><p>Seeds Yarrow-256 from a previous seed file. <var>length</var> should be at least
<code>YARROW256_SEED_FILE_SIZE</code>, but it can be larger.
</p>
<p>The generator will trust you that the <var>seed_file</var> data really is
unguessable. After calling this function, you <em>must</em> overwrite the old
seed file with newly generated data from <code>yarrow256_random</code>. If it&rsquo;s
possible for several processes to read the seed file at about the same
time, access must be coordinated using some locking mechanism.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow256_005fupdate"></a>Function: <em>int</em> <strong>yarrow256_update</strong> <em>(struct yarrow256_ctx *<var>ctx</var>, unsigned <var>source</var>, unsigned <var>entropy</var>, size_t <var>length</var>, const uint8_t *<var>data</var>)</em></dt>
<dd><p>Updates the generator with data from source <var>SOURCE</var> (an index that
must be smaller than the number of sources). <var>entropy</var> is your
estimated lower bound for the entropy in the data, measured in bits.
Calling update with zero <var>entropy</var> is always safe, no matter if the
data is random or not.
</p>
<p>Returns 1 if a reseed happened, in which case an application using a
seed file may want to generate new seed data with
<code>yarrow256_random</code> and overwrite the seed file. Otherwise, the
function returns 0.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow256_005frandom"></a>Function: <em>void</em> <strong>yarrow256_random</strong> <em>(struct yarrow256_ctx *<var>ctx</var>, size_t <var>length</var>, uint8_t *<var>dst</var>)</em></dt>
<dd><p>Generates <var>length</var> octets of output. The generator must be seeded
before you call this function.
</p>
<p>If you don&rsquo;t need forward secrecy, e.g. if you need non-secret
randomness for initialization vectors or padding, you can gain some
efficiency by buffering, calling this function for reasonably large
blocks of data, say 100-1000 octets at a time.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow256_005fis_005fseeded"></a>Function: <em>int</em> <strong>yarrow256_is_seeded</strong> <em>(struct yarrow256_ctx *<var>ctx</var>)</em></dt>
<dd><p>Returns 1 if the generator is seeded and ready to generate output,
otherwise 0.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow256_005fneeded_005fsources"></a>Function: <em>unsigned</em> <strong>yarrow256_needed_sources</strong> <em>(struct yarrow256_ctx *<var>ctx</var>)</em></dt>
<dd><p>Returns the number of sources that must reach the threshold before a
slow reseed will happen. Useful primarily when the generator is unseeded.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow256_005ffast_005freseed"></a>Function: <em>void</em> <strong>yarrow256_fast_reseed</strong> <em>(struct yarrow256_ctx *<var>ctx</var>)</em></dt>
<dt><a name="index-yarrow256_005fslow_005freseed"></a>Function: <em>void</em> <strong>yarrow256_slow_reseed</strong> <em>(struct yarrow256_ctx *<var>ctx</var>)</em></dt>
<dd><p>Causes a fast or slow reseed to take place immediately, regardless of the
current entropy estimates of the two pools. Use with care.
</p></dd></dl>

<p>Nettle includes an entropy estimator for one kind of input source: User
keyboard input.
</p>
<dl>
<dt><a name="index-struct-yarrow_005fkey_005fevent_005fctx"></a>Context struct: <strong>struct yarrow_key_event_ctx</strong></dt>
<dd><p>Information about recent key events.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow_005fkey_005fevent_005finit"></a>Function: <em>void</em> <strong>yarrow_key_event_init</strong> <em>(struct yarrow_key_event_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initializes the context.
</p></dd></dl>

<dl>
<dt><a name="index-yarrow_005fkey_005fevent_005festimate"></a>Function: <em>unsigned</em> <strong>yarrow_key_event_estimate</strong> <em>(struct yarrow_key_event_ctx *<var>ctx</var>, unsigned <var>key</var>, unsigned <var>time</var>)</em></dt>
<dd><p><var>key</var> is the id of the key (ASCII value, hardware key code, X
keysym, &hellip;, it doesn&rsquo;t matter), and <var>time</var> is the timestamp of
the event. The time must be given in units matching the resolution by
which you read the clock. If you read the clock with microsecond
precision, <var>time</var> should be provided in units of microseconds. But
if you use <code>gettimeofday</code> on a typical Unix system where the clock
ticks 10 or so microseconds at a time, <var>time</var> should be given in
units of 10 microseconds.
</p>
<p>Returns an entropy estimate, in bits, suitable for calling
<code>yarrow256_update</code>. Usually, 0, 1 or 2 bits.
</p></dd></dl>

<hr>
<a name="ASCII-encoding"></a>
<div class="header">
<p>
Next: <a href="#Miscellaneous-functions" accesskey="n" rel="next">Miscellaneous functions</a>, Previous: <a href="#Randomness" accesskey="p" rel="prev">Randomness</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="ASCII-encoding-1"></a>
<h3 class="section">6.9 ASCII encoding</h3>

<p>Encryption will transform your data from text into binary format, and that
may be a problem if, for example, you want to send the data as if it was
plain text in an email, or store it along with descriptive text in a
file. You may then use an encoding from binary to text: each binary byte
is translated into a number of bytes of plain text.
</p>
<p>A base-N encoding of data is one representation of data that only uses N
different symbols (instead of the 256 possible values of a byte).
</p>
<p>The base64 encoding will always use alphanumeric (upper and lower case)
characters and the &rsquo;+&rsquo;, &rsquo;/&rsquo; and &rsquo;=&rsquo; symbols to represent the data. Four
output characters are generated for each three bytes of input. In case
the length of the input is not a multiple of three, padding characters
are added at the end. There&rsquo;s also a &ldquo;URL safe&rdquo; variant, which is
useful for encoding binary data into URLs and filenames. See <cite>RFC
4648</cite>.
</p>
<p>The base16 encoding, also known as &ldquo;hexadecimal&rdquo;, uses the decimal
digits and the letters from A to F. Two hexadecimal digits are generated
for each input byte.
</p>
<p>Nettle supports both base64 and base16 encoding and decoding.
</p>
<p>Encoding and decoding uses a context struct to maintain its state (with
the exception of base16 encoding, which doesn&rsquo;t need any). To encode or
decode the data, first initialize the context, then call the update
function as many times as necessary, and complete the operation by
calling the final function.
</p>
<p>The following functions can be used to perform base64 encoding and decoding.
They are defined in <samp>&lt;nettle/base64.h&gt;</samp>.
</p>
<dl>
<dt><a name="index-struct-base64_005fencode_005fctx"></a>Context struct: <strong>struct base64_encode_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-base64_005fencode_005finit"></a>Function: <em>void</em> <strong>base64_encode_init</strong> <em>(struct base64_encode_ctx *<var>ctx</var>)</em></dt>
<dt><a name="index-base64url_005fencode_005finit"></a>Function: <em>void</em> <strong>base64url_encode_init</strong> <em>(struct base64_encode_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initializes a base64 context. This is necessary before starting an
encoding session. <code>base64_encode_init</code> selects the standard base64
alphabet, while <code>base64url_encode_init</code> selects the URL safe
alphabet.
</p></dd></dl>


<dl>
<dt><a name="index-base64_005fencode_005fsingle"></a>Function: <em>size_t</em> <strong>base64_encode_single</strong> <em>(struct base64_encode_ctx *<var>ctx</var>, uint8_t *<var>dst</var>, uint8_t <var>src</var>)</em></dt>
<dd><p>Encodes a single byte. Returns amount of output (always 1 or 2).
</p></dd></dl>

<dl>
<dt><a name="index-BASE64_005fENCODE_005fLENGTH"></a>Macro: <strong>BASE64_ENCODE_LENGTH</strong> <em>(<var>length</var>)</em></dt>
<dd><p>The maximum number of output bytes when passing <var>length</var> input bytes
to <code>base64_encode_update</code>.
</p></dd></dl>

<dl>
<dt><a name="index-base64_005fencode_005fupdate"></a>Function: <em>size_t</em> <strong>base64_encode_update</strong> <em>(struct base64_encode_ctx *<var>ctx</var>, uint8_t *<var>dst</var>, size_t <var>length</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>After <var>ctx</var> is initialized, this function may be called to encode <var>length</var>
bytes from <var>src</var>. The result will be placed in <var>dst</var>, and the return value
will be the number of bytes generated. Note that <var>dst</var> must be at least of size
BASE64_ENCODE_LENGTH(<var>length</var>).
</p></dd></dl>

<dl>
<dt><a name="index-BASE64_005fENCODE_005fFINAL_005fLENGTH"></a>Constant: <strong>BASE64_ENCODE_FINAL_LENGTH</strong></dt>
<dd><p>The maximum amount of output from <code>base64_encode_final</code>.
</p></dd></dl>

<dl>
<dt><a name="index-base64_005fencode_005ffinal"></a>Function: <em>size_t</em> <strong>base64_encode_final</strong> <em>(struct base64_encode_ctx *<var>ctx</var>, uint8_t *<var>dst</var>)</em></dt>
<dd><p>After calling base64_encode_update one or more times, this function
should be called to generate the final output bytes, including any
needed paddding. The return value is the number of output bytes
generated.
</p></dd></dl>

<dl>
<dt><a name="index-struct-base64_005fdecode_005fctx"></a>Context struct: <strong>struct base64_decode_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-base64_005fdecode_005finit"></a>Function: <em>void</em> <strong>base64_decode_init</strong> <em>(struct base64_decode_ctx *<var>ctx</var>)</em></dt>
<dt><a name="index-base64url_005fdecode_005finit"></a>Function: <em>void</em> <strong>base64url_decode_init</strong> <em>(struct base64_decode_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initializes a base64 decoding context. This is necessary before starting
a decoding session. <code>base64_decode_init</code> selects the standard
base64 alphabet, while <code>base64url_decode_init</code> selects the URL safe
alphabet.
</p></dd></dl>

<dl>
<dt><a name="index-base64_005fdecode_005fsingle"></a>Function: <em>int</em> <strong>base64_decode_single</strong> <em>(struct base64_decode_ctx *<var>ctx</var>, uint8_t *<var>dst</var>, uint8_t <var>src</var>)</em></dt>
<dd><p>Decodes a single byte (<var>src</var>) and stores the result in <var>dst</var>.
Returns amount of output (0 or 1), or -1 on errors.
</p></dd></dl>

<dl>
<dt><a name="index-BASE64_005fDECODE_005fLENGTH"></a>Macro: <strong>BASE64_DECODE_LENGTH</strong> <em>(<var>length</var>)</em></dt>
<dd><p>The maximum number of output bytes when passing <var>length</var> input bytes
to <code>base64_decode_update</code>.
</p></dd></dl>

<dl>
<dt><a name="index-base64_005fdecode_005fupdate"></a>Function: <em>void</em> <strong>base64_decode_update</strong> <em>(struct base64_decode_ctx *<var>ctx</var>, size_t *<var>dst_length</var>, uint8_t *<var>dst</var>, size_t <var>src_length</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>After <var>ctx</var> is initialized, this function may be called to decode
<var>src_length</var> bytes from <var>src</var>. <var>dst</var> should point to an area
of size at least BASE64_DECODE_LENGTH(<var>src_length</var>). The amount of data
generated is returned in *<var>dst_length</var>. Returns 1 on success
and 0 on error.
</p></dd></dl>

<dl>
<dt><a name="index-base64_005fdecode_005ffinal"></a>Function: <em>int</em> <strong>base64_decode_final</strong> <em>(struct base64_decode_ctx *<var>ctx</var>)</em></dt>
<dd><p>Check that final padding is correct. Returns 1 on success, and 0 on
error.
</p></dd></dl>

<p>Similarly to the base64 functions, the following functions perform base16 encoding,
and are defined in <samp>&lt;nettle/base16.h&gt;</samp>. Note that there is no encoding context
necessary for doing base16 encoding.
</p>
<dl>
<dt><a name="index-base16_005fencode_005fsingle"></a>Function: <em>void</em> <strong>base16_encode_single</strong> <em>(uint8_t *<var>dst</var>, uint8_t <var>src</var>)</em></dt>
<dd><p>Encodes a single byte. Always stores two digits in <var>dst</var>[0] and <var>dst</var>[1].
</p></dd></dl>

<dl>
<dt><a name="index-BASE16_005fENCODE_005fLENGTH"></a>Macro: <strong>BASE16_ENCODE_LENGTH</strong> <em>(<var>length</var>)</em></dt>
<dd><p>The number of output bytes when passing <var>length</var> input bytes to
<code>base16_encode_update</code>.
</p></dd></dl>

<dl>
<dt><a name="index-base16_005fencode_005fupdate"></a>Function: <em>void</em> <strong>base16_encode_update</strong> <em>(uint8_t *<var>dst</var>, size_t <var>length</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>Always stores BASE16_ENCODE_LENGTH(<var>length</var>) digits in <var>dst</var>.
</p></dd></dl>

<dl>
<dt><a name="index-struct-base16_005fdecode_005fctx"></a>Context struct: <strong>struct base16_decode_ctx</strong></dt>
</dl>

<dl>
<dt><a name="index-base16_005fdecode_005finit"></a>Function: <em>void</em> <strong>base16_decode_init</strong> <em>(struct base16_decode_ctx *<var>ctx</var>)</em></dt>
<dd><p>Initializes a base16 decoding context. This is necessary before starting a decoding
session.
</p></dd></dl>

<dl>
<dt><a name="index-base16_005fdecode_005fsingle"></a>Function: <em>int</em> <strong>base16_decode_single</strong> <em>(struct base16_decode_ctx *<var>ctx</var>, uint8_t *<var>dst</var>, uint8_t <var>src</var>)</em></dt>
<dd><p>Decodes a single byte from <var>src</var> into <var>dst</var>. Returns amount of output (0 or 1), or -1 on errors.
</p></dd></dl>

<dl>
<dt><a name="index-BASE16_005fDECODE_005fLENGTH"></a>Macro: <strong>BASE16_DECODE_LENGTH</strong> <em>(<var>length</var>)</em></dt>
<dd><p>The maximum number of output bytes when passing <var>length</var> input bytes
to <code>base16_decode_update</code>.
</p></dd></dl>

<dl>
<dt><a name="index-base16_005fdecode_005fupdate"></a>Function: <em>int</em> <strong>base16_decode_update</strong> <em>(struct base16_decode_ctx *<var>ctx</var>, size_t *<var>dst_length</var>, uint8_t *<var>dst</var>, size_t <var>src_length</var>, const uint8_t *<var>src</var>)</em></dt>
<dd><p>After <var>ctx</var> is initialized, this function may be called to decode
<var>src_length</var> bytes from <var>src</var>. <var>dst</var> should point to an area
of size at least BASE16_DECODE_LENGTH(<var>src_length</var>). The amount of data
generated is returned in *<var>dst_length</var>. Returns 1 on success
and 0 on error.
</p></dd></dl>

<dl>
<dt><a name="index-base16_005fdecode_005ffinal"></a>Function: <em>int</em> <strong>base16_decode_final</strong> <em>(struct base16_decode_ctx *<var>ctx</var>)</em></dt>
<dd><p>Checks that the end of data is correct (i.e., an even number of
hexadecimal digits have been seen). Returns 1 on success, and 0 on
error.
</p></dd></dl>

<hr>
<a name="Miscellaneous-functions"></a>
<div class="header">
<p>
Next: <a href="#Compatibility-functions" accesskey="n" rel="next">Compatibility functions</a>, Previous: <a href="#ASCII-encoding" accesskey="p" rel="prev">ASCII encoding</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Miscellaneous-functions-1"></a>
<h3 class="section">6.10 Miscellaneous functions</h3>

<dl>
<dt><a name="index-memxor"></a>Function: <em>void *</em> <strong>memxor</strong> <em>(void *<var>dst</var>, const void *<var>src</var>, size_t <var>n</var>)</em></dt>
<dd><p>XORs the source area on top of the destination area. The interface
doesn&rsquo;t follow the Nettle conventions, because it is intended to be
similar to the ANSI-C <code>memcpy</code> function.
</p></dd></dl>

<dl>
<dt><a name="index-memxor3"></a>Function: <em>void *</em> <strong>memxor3</strong> <em>(void *<var>dst</var>, const void *<var>a</var>, const void *<var>b</var>, size_t <var>n</var>)</em></dt>
<dd><p>Like <code>memxor</code>, but takes two source areas and separate
destination area.
</p></dd></dl>

<dl>
<dt><a name="index-memeql_005fsec"></a>Function: <em>int</em> <strong>memeql_sec</strong> <em>(const void *<var>a</var>, const void *<var>b</var>, size_t <var>n</var>)</em></dt>
<dd><p>Side-channel silent comparison of the <var>n</var> bytes at <var>a</var> and
<var>b</var>. I.e., instructions executed and memory accesses are identical
no matter where the areas differ, see <a href="#Side_002dchannel-silence">Side-channel silence</a>. Return
non-zero if the areas are equal, and zero if they differ.
</p></dd></dl>

<p>These functions are declared in <samp>&lt;nettle/memops.h&gt;</samp>. For
compatibility with earlier versions of Nettle, <code>memxor</code> and
<code>memxor3</code> are also declared in <samp>&lt;nettle/memxor.h&gt;</samp>.
</p>
<hr>
<a name="Compatibility-functions"></a>
<div class="header">
<p>
Previous: <a href="#Miscellaneous-functions" accesskey="p" rel="prev">Miscellaneous functions</a>, Up: <a href="#Reference" accesskey="u" rel="up">Reference</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Compatibility-functions-1"></a>
<h3 class="section">6.11 Compatibility functions</h3>

<p>For convenience, Nettle includes alternative interfaces to some
algorithms, for compatibility with some other popular crypto toolkits.
These are not fully documented here; refer to the source or to the
documentation for the original implementation.
</p>
<p>MD5 is defined in [RFC 1321], which includes a reference implementation.
Nettle defines a compatible interface to MD5 in
<samp>&lt;nettle/md5-compat.h&gt;</samp>. This file defines the typedef
<code>MD5_CTX</code>, and declares the functions <code>MD5Init</code>, <code>MD5Update</code> and
<code>MD5Final</code>.
</p>
<p>Eric Young&rsquo;s &ldquo;libdes&rdquo; (also part of OpenSSL) is a quite popular DES
implementation. Nettle includes a subset if its interface in
<samp>&lt;nettle/des-compat.h&gt;</samp>. This file defines the typedefs
<code>des_key_schedule</code> and <code>des_cblock</code>, two constants
<code>DES_ENCRYPT</code> and <code>DES_DECRYPT</code>, and declares one global
variable <code>des_check_key</code>, and the functions <code>des_cbc_cksum</code>
<code>des_cbc_encrypt</code>, <code>des_ecb2_encrypt</code>,
<code>des_ecb3_encrypt</code>, <code>des_ecb_encrypt</code>,
<code>des_ede2_cbc_encrypt</code>, <code>des_ede3_cbc_encrypt</code>,
<code>des_is_weak_key</code>, <code>des_key_sched</code>, <code>des_ncbc_encrypt</code>
<code>des_set_key</code>, and <code>des_set_odd_parity</code>.
</p>
<hr>
<a name="Nettle-soup"></a>
<div class="header">
<p>
Next: <a href="#Installation" accesskey="n" rel="next">Installation</a>, Previous: <a href="#Reference" accesskey="p" rel="prev">Reference</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Traditional-Nettle-Soup"></a>
<h2 class="chapter">7 Traditional Nettle Soup</h2>
<p>For the serious nettle hacker, here is a recipe for nettle soup. 4 servings.
</p>
<ul class="no-bullet">
<li><!-- /@w --> 1 liter fresh nettles (urtica dioica)
</li><li><!-- /@w --> 2 tablespoons butter
</li><li><!-- /@w --> 3 tablespoons flour
</li><li><!-- /@w --> 1 liter stock (meat or vegetable)
</li><li><!-- /@w --> 1/2 teaspoon salt
</li><li><!-- /@w --> a tad white pepper
</li><li><!-- /@w --> some cream or milk
</li></ul>

<p>Gather 1 liter fresh nettles. Use gloves! Small, tender shoots are
preferable but the tops of larger nettles can also be used.
</p>
<p>Rinse the nettles very well. Boil them for 10 minutes in lightly salted
water. Strain the nettles and save the water. Hack the nettles. Melt the
butter and mix in the flour. Dilute with stock and the nettle-water you
saved earlier. Add the hacked nettles. If you wish you can add some milk
or cream at this stage. Bring to a boil and let boil for a few minutes.
Season with salt and pepper.
</p>
<p>Serve with boiled egg-halves.
</p>

<hr>
<a name="Installation"></a>
<div class="header">
<p>
Next: <a href="#Index" accesskey="n" rel="next">Index</a>, Previous: <a href="#Nettle-soup" accesskey="p" rel="prev">Nettle soup</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Installation-1"></a>
<h2 class="chapter">8 Installation</h2>

<p>Nettle uses <code>autoconf</code>. To build it, unpack the source and run
</p>
<div class="example">
<pre class="example">./configure
make
make check
make install
</pre></div>

<p>to install it under the default prefix, <samp>/usr/local</samp>. Using GNU
make is strongly recommended. By default, both static and shared
libraries are built and installed.
</p>
<p>To get a list of configure options, use <code>./configure --help</code>. Some
of the more interesting are:
</p>
<dl compact="compact">
<dt><samp>--enable-fat</samp></dt>
<dd><p>Include multiple versions of certain functions in the library, and
select the ones to use at run-time, depending on available processor
features. Supported for ARM and x86_64.
</p>
</dd>
<dt><samp>--enable-mini-gmp</samp></dt>
<dd><p>Use the smaller and slower &ldquo;mini-gmp&rdquo; implementation of the bignum
functions needed for public-key cryptography, instead of the real GNU
GMP library. This option is intended primarily for smaller embedded
systems. Note that builds using mini-gmp are <strong>not</strong> binary compatible
with regular builds of Nettle, and more likely to leak side-channel
information.
</p>
</dd>
<dt><samp>--disable-shared</samp></dt>
<dd><p>Omit building the shared libraries.
</p>
</dd>
<dt><samp>--disable-dependency-tracking</samp></dt>
<dd><p>Disable the automatic dependency tracking. You will likely need this
option to be able to build with BSD make.
</p>
</dd>
</dl>

<hr>
<a name="Index"></a>
<div class="header">
<p>
Previous: <a href="#Installation" accesskey="p" rel="prev">Installation</a>, Up: <a href="#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Function-and-Concept-Index"></a>
<h2 class="unnumbered">Function and Concept Index</h2>

<table><tr><th valign="top">Jump to: &nbsp; </th><td><a class="summary-letter" href="#Index_cp_letter-A"><b>A</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-B"><b>B</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-C"><b>C</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-D"><b>D</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-E"><b>E</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-G"><b>G</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-H"><b>H</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-K"><b>K</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-M"><b>M</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-N"><b>N</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-O"><b>O</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-P"><b>P</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-R"><b>R</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-S"><b>S</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-T"><b>T</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-U"><b>U</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-Y"><b>Y</b></a>
 &nbsp; 
</td></tr></table>
<table class="index-cp" border="0">
<tr><td></td><th align="left">Index Entry</th><td>&nbsp;</td><th align="left"> Section</th></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-A">A</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-AEAD">AEAD</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Authenticated-encryption">Authenticated encryption</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes128_005fdecrypt"><code>aes128_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes128_005fencrypt"><code>aes128_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes128_005finvert_005fkey"><code>aes128_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes128_005fset_005fdecrypt_005fkey"><code>aes128_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes128_005fset_005fencrypt_005fkey"><code>aes128_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes192_005fdecrypt"><code>aes192_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes192_005fencrypt"><code>aes192_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes192_005finvert_005fkey"><code>aes192_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes192_005fset_005fdecrypt_005fkey"><code>aes192_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes192_005fset_005fencrypt_005fkey"><code>aes192_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes256_005fdecrypt"><code>aes256_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes256_005fencrypt"><code>aes256_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes256_005finvert_005fkey"><code>aes256_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes256_005fset_005fdecrypt_005fkey"><code>aes256_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes256_005fset_005fencrypt_005fkey"><code>aes256_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes_005fdecrypt"><code>aes_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes_005fencrypt"><code>aes_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes_005finvert_005fkey"><code>aes_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes_005fset_005fdecrypt_005fkey"><code>aes_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-aes_005fset_005fencrypt_005fkey"><code>aes_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-arcfour_005fcrypt"><code>arcfour_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-arcfour_005fset_005fkey"><code>arcfour_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-arctwo_005fdecrypt"><code>arctwo_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-arctwo_005fencrypt"><code>arctwo_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-arctwo_005fset_005fkey"><code>arctwo_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-arctwo_005fset_005fkey_005fekb"><code>arctwo_set_key_ekb</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-arctwo_005fset_005fkey_005fgutmann"><code>arctwo_set_key_gutmann</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Authenticated-encryption">Authenticated encryption</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Authenticated-encryption">Authenticated encryption</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-B">B</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-base16_005fdecode_005ffinal"><code>base16_decode_final</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base16_005fdecode_005finit"><code>base16_decode_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-BASE16_005fDECODE_005fLENGTH"><code>BASE16_DECODE_LENGTH</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base16_005fdecode_005fsingle"><code>base16_decode_single</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base16_005fdecode_005fupdate"><code>base16_decode_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-BASE16_005fENCODE_005fLENGTH"><code>BASE16_ENCODE_LENGTH</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base16_005fencode_005fsingle"><code>base16_encode_single</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base16_005fencode_005fupdate"><code>base16_encode_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64url_005fdecode_005finit"><code>base64url_decode_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64url_005fencode_005finit"><code>base64url_encode_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fdecode_005ffinal"><code>base64_decode_final</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fdecode_005finit"><code>base64_decode_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-BASE64_005fDECODE_005fLENGTH"><code>BASE64_DECODE_LENGTH</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fdecode_005fsingle"><code>base64_decode_single</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fdecode_005fupdate"><code>base64_decode_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fencode_005ffinal"><code>base64_encode_final</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fencode_005finit"><code>base64_encode_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-BASE64_005fENCODE_005fLENGTH"><code>BASE64_ENCODE_LENGTH</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fencode_005fsingle"><code>base64_encode_single</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-base64_005fencode_005fupdate"><code>base64_encode_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ASCII-encoding">ASCII encoding</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Block-Cipher">Block Cipher</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-blowfish_005fdecrypt"><code>blowfish_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-blowfish_005fencrypt"><code>blowfish_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-blowfish_005fset_005fkey"><code>blowfish_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-C">C</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia128_005fcrypt"><code>camellia128_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia128_005finvert_005fkey"><code>camellia128_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia128_005fset_005fdecrypt_005fkey"><code>camellia128_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia128_005fset_005fencrypt_005fkey"><code>camellia128_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia192_005fcrypt"><code>camellia192_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia192_005finvert_005fkey"><code>camellia192_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia192_005fset_005fdecrypt_005fkey"><code>camellia192_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia192_005fset_005fencrypt_005fkey"><code>camellia192_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia256_005fcrypt"><code>camellia256_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia256_005finvert_005fkey"><code>camellia256_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia256_005fset_005fdecrypt_005fkey"><code>camellia256_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia256_005fset_005fencrypt_005fkey"><code>camellia256_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia_005fcrypt"><code>camellia_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia_005finvert_005fkey"><code>camellia_invert_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia_005fset_005fdecrypt_005fkey"><code>camellia_set_decrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-camellia_005fset_005fencrypt_005fkey"><code>camellia_set_encrypt_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-cast128_005fdecrypt"><code>cast128_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-cast128_005fencrypt"><code>cast128_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-cast128_005fset_005fkey"><code>cast128_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CBC-Mode">CBC Mode</a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CBC_005fCTX"><code>CBC_CTX</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-cbc_005fdecrypt"><code>cbc_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CBC_005fDECRYPT"><code>CBC_DECRYPT</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-cbc_005fencrypt"><code>cbc_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CBC_005fENCRYPT"><code>CBC_ENCRYPT</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CBC_005fSET_005fIV"><code>CBC_SET_IV</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CCM-Mode">CCM Mode</a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fdecrypt"><code>ccm_aes128_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fdecrypt_005fmessage"><code>ccm_aes128_decrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fdigest"><code>ccm_aes128_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fencrypt"><code>ccm_aes128_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fencrypt_005fmessage"><code>ccm_aes128_encrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fset_005fkey"><code>ccm_aes128_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fset_005fnonce"><code>ccm_aes128_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes128_005fupdate"><code>ccm_aes128_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fdecrypt"><code>ccm_aes192_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fdecrypt_005fmessage"><code>ccm_aes192_decrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fdecrypt_005fmessage-1"><code>ccm_aes192_decrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fdigest"><code>ccm_aes192_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fencrypt"><code>ccm_aes192_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fencrypt_005fmessage"><code>ccm_aes192_encrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fset_005fkey"><code>ccm_aes192_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fset_005fnonce"><code>ccm_aes192_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes192_005fupdate"><code>ccm_aes192_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes256_005fdecrypt"><code>ccm_aes256_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes256_005fdigest"><code>ccm_aes256_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes256_005fencrypt"><code>ccm_aes256_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes256_005fencrypt_005fmessage"><code>ccm_aes256_encrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes256_005fset_005fkey"><code>ccm_aes256_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes256_005fset_005fnonce"><code>ccm_aes256_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005faes256_005fupdate"><code>ccm_aes256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005fdecrypt"><code>ccm_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005fdecrypt_005fmessage"><code>ccm_decrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005fdigest"><code>ccm_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005fencrypt"><code>ccm_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005fencrypt_005fmessage"><code>ccm_encrypt_message</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CCM_005fMAX_005fMSG_005fSIZE"><code>CCM_MAX_MSG_SIZE</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005fset_005fnonce"><code>ccm_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ccm_005fupdate"><code>ccm_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fcrypt"><code>chacha_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fpoly1305_005fdecrypt"><code>chacha_poly1305_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ChaCha_002dPoly1305">ChaCha-Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fpoly1305_005fdigest"><code>chacha_poly1305_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ChaCha_002dPoly1305">ChaCha-Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fpoly1305_005fencrypt"><code>chacha_poly1305_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ChaCha_002dPoly1305">ChaCha-Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fpoly1305_005fset_005fkey"><code>chacha_poly1305_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ChaCha_002dPoly1305">ChaCha-Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fpoly1305_005fset_005fnonce"><code>chacha_poly1305_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ChaCha_002dPoly1305">ChaCha-Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fpoly1305_005fupdate"><code>chacha_poly1305_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ChaCha_002dPoly1305">ChaCha-Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fset_005fkey"><code>chacha_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-chacha_005fset_005fnonce"><code>chacha_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Cipher">Cipher</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Cipher-Block-Chaining">Cipher Block Chaining</a>:</td><td>&nbsp;</td><td valign="top"><a href="#CBC">CBC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Collision_002dresistant">Collision-resistant</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Hash-functions">Hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Conditional-entropy">Conditional entropy</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Counter-Mode">Counter Mode</a>:</td><td>&nbsp;</td><td valign="top"><a href="#CTR">CTR</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Counter-with-CBC_002dMAC-Mode">Counter with CBC-MAC Mode</a>:</td><td>&nbsp;</td><td valign="top"><a href="#CCM">CCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CTR-Mode">CTR Mode</a>:</td><td>&nbsp;</td><td valign="top"><a href="#CTR">CTR</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ctr_005fcrypt"><code>ctr_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CTR">CTR</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CTR_005fCRYPT"><code>CTR_CRYPT</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CTR">CTR</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CTR_005fCTX"><code>CTR_CTX</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CTR">CTR</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-CTR_005fSET_005fCOUNTER"><code>CTR_SET_COUNTER</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#CTR">CTR</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Curve-25519">Curve 25519</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Curve-25519">Curve 25519</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-curve25519_005fmul"><code>curve25519_mul</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Curve-25519">Curve 25519</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-curve25519_005fmul_005fg"><code>curve25519_mul_g</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Curve-25519">Curve 25519</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-D">D</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-des3_005fdecrypt"><code>des3_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-des3_005fencrypt"><code>des3_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-des3_005fset_005fkey"><code>des3_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-des_005fcheck_005fparity"><code>des_check_parity</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-des_005fdecrypt"><code>des_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-des_005fencrypt"><code>des_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-des_005ffix_005fparity"><code>des_fix_parity</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-des_005fset_005fkey"><code>des_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fcompat_005fgenerate_005fkeypair"><code>dsa_compat_generate_keypair</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fgenerate_005fkeypair"><code>dsa_generate_keypair</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fgenerate_005fparams"><code>dsa_generate_params</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fparams_005fclear"><code>dsa_params_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fparams_005finit"><code>dsa_params_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fprivate_005fkey_005fclear"><code>dsa_private_key_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fprivate_005fkey_005finit"><code>dsa_private_key_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fpublic_005fkey_005fclear"><code>dsa_public_key_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fpublic_005fkey_005finit"><code>dsa_public_key_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha1_005fsign"><code>dsa_sha1_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha1_005fsign_005fdigest"><code>dsa_sha1_sign_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha1_005fverify"><code>dsa_sha1_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha1_005fverify_005fdigest"><code>dsa_sha1_verify_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha256_005fsign"><code>dsa_sha256_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha256_005fsign_005fdigest"><code>dsa_sha256_sign_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha256_005fverify"><code>dsa_sha256_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsha256_005fverify_005fdigest"><code>dsa_sha256_verify_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsign"><code>dsa_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsignature_005fclear"><code>dsa_signature_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fsignature_005finit"><code>dsa_signature_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-dsa_005fverify"><code>dsa_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#DSA">DSA</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-E">E</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005faes128_005fdecrypt"><code>eax_aes128_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005faes128_005fdigest"><code>eax_aes128_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005faes128_005fencrypt"><code>eax_aes128_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005faes128_005fset_005fkey"><code>eax_aes128_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005faes128_005fset_005fnonce"><code>eax_aes128_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005faes128_005fupdate"><code>eax_aes128_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-EAX_005fCTX"><code>EAX_CTX</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005fdecrypt"><code>eax_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-EAX_005fDECRYPT"><code>EAX_DECRYPT</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005fdigest"><code>eax_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-EAX_005fDIGEST"><code>EAX_DIGEST</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005fencrypt"><code>eax_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-EAX_005fENCRYPT"><code>EAX_ENCRYPT</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005fset_005fkey"><code>eax_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-EAX_005fSET_005fKEY"><code>EAX_SET_KEY</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005fset_005fnonce"><code>eax_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-EAX_005fSET_005fNONCE"><code>EAX_SET_NONCE</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eax_005fupdate"><code>eax_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-EAX_005fUPDATE"><code>EAX_UPDATE</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#EAX">EAX</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fpoint_005fclear"><code>ecc_point_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fpoint_005fget"><code>ecc_point_get</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fpoint_005finit"><code>ecc_point_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fpoint_005fset"><code>ecc_point_set</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fscalar_005fclear"><code>ecc_scalar_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fscalar_005fget"><code>ecc_scalar_get</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fscalar_005finit"><code>ecc_scalar_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecc_005fscalar_005fset"><code>ecc_scalar_set</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecdsa_005fgenerate_005fkeypair"><code>ecdsa_generate_keypair</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecdsa_005fsign"><code>ecdsa_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ecdsa_005fverify"><code>ecdsa_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#ECDSA">ECDSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ed25519_005fsha512_005fpublic_005fkey"><code>ed25519_sha512_public_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Curve-25519">Curve 25519</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ed25519_005fsha512_005fsign"><code>ed25519_sha512_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Curve-25519">Curve 25519</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ed25519_005fsha512_005fverify"><code>ed25519_sha512_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Curve-25519">Curve 25519</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-eddsa">eddsa</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Curve-25519">Curve 25519</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Entropy">Entropy</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-G">G</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-Galois-Counter-Mode">Galois Counter Mode</a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM">GCM</a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes128_005fdecrypt"><code>gcm_aes128_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes128_005fdigest"><code>gcm_aes128_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes128_005fencrypt"><code>gcm_aes128_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes128_005fset_005fiv"><code>gcm_aes128_set_iv</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes128_005fset_005fkey"><code>gcm_aes128_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes128_005fupdate"><code>gcm_aes128_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes192_005fdecrypt"><code>gcm_aes192_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes192_005fdigest"><code>gcm_aes192_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes192_005fencrypt"><code>gcm_aes192_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes192_005fset_005fiv"><code>gcm_aes192_set_iv</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes192_005fset_005fkey"><code>gcm_aes192_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes192_005fupdate"><code>gcm_aes192_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes256_005fdecrypt"><code>gcm_aes256_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes256_005fdigest"><code>gcm_aes256_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes256_005fencrypt"><code>gcm_aes256_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes256_005fset_005fiv"><code>gcm_aes256_set_iv</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes256_005fset_005fkey"><code>gcm_aes256_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes256_005fupdate"><code>gcm_aes256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes_005fdecrypt"><code>gcm_aes_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes_005fdigest"><code>gcm_aes_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes_005fencrypt"><code>gcm_aes_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes_005fset_005fiv"><code>gcm_aes_set_iv</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes_005fset_005fkey"><code>gcm_aes_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005faes_005fupdate"><code>gcm_aes_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia128_005fdecrypt"><code>gcm_camellia128_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia128_005fdigest"><code>gcm_camellia128_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia128_005fencrypt"><code>gcm_camellia128_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia128_005fset_005fiv"><code>gcm_camellia128_set_iv</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia128_005fset_005fkey"><code>gcm_camellia128_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia128_005fupdate"><code>gcm_camellia128_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia192_005fdigest"><code>gcm_camellia192_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia256_005fdecrypt"><code>gcm_camellia256_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia256_005fdigest"><code>gcm_camellia256_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia256_005fencrypt"><code>gcm_camellia256_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia256_005fset_005fiv"><code>gcm_camellia256_set_iv</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia256_005fset_005fkey"><code>gcm_camellia256_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia256_005fupdate"><code>gcm_camellia256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fcamellia_005fdigest"><code>gcm_camellia_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM_005fCTX"><code>GCM_CTX</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fdecrypt"><code>gcm_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM_005fDECRYPT"><code>GCM_DECRYPT</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fdigest"><code>gcm_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM_005fDIGEST"><code>GCM_DIGEST</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fencrypt"><code>gcm_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM_005fENCRYPT"><code>GCM_ENCRYPT</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fset_005fiv"><code>gcm_set_iv</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM_005fSET_005fIV"><code>GCM_SET_IV</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fset_005fkey"><code>gcm_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM_005fSET_005fKEY"><code>GCM_SET_KEY</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gcm_005fupdate"><code>gcm_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-GCM_005fUPDATE"><code>GCM_UPDATE</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#GCM">GCM</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gosthash94_005fdigest"><code>gosthash94_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gosthash94_005finit"><code>gosthash94_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-gosthash94_005fupdate"><code>gosthash94_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-H">H</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-Hash-function">Hash function</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Hash-functions">Hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-HMAC">HMAC</a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-HMAC_005fCTX"><code>HMAC_CTX</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fdigest"><code>hmac_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-HMAC_005fDIGEST"><code>HMAC_DIGEST</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fmd5_005fdigest"><code>hmac_md5_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fmd5_005fset_005fkey"><code>hmac_md5_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fmd5_005fupdate"><code>hmac_md5_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fripemd160_005fdigest"><code>hmac_ripemd160_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fripemd160_005fset_005fkey"><code>hmac_ripemd160_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fripemd160_005fupdate"><code>hmac_ripemd160_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fset_005fkey"><code>hmac_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-HMAC_005fSET_005fKEY"><code>HMAC_SET_KEY</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha1_005fdigest"><code>hmac_sha1_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha1_005fset_005fkey"><code>hmac_sha1_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha1_005fupdate"><code>hmac_sha1_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha256_005fdigest"><code>hmac_sha256_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha256_005fset_005fkey"><code>hmac_sha256_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha256_005fupdate"><code>hmac_sha256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha512_005fdigest"><code>hmac_sha512_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha512_005fset_005fkey"><code>hmac_sha512_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fsha512_005fupdate"><code>hmac_sha512_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-hmac_005fupdate"><code>hmac_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#HMAC">HMAC</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-K">K</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-KDF">KDF</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Key-Derivation-Function">Key Derivation Function</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Keyed-Hash-Function">Keyed Hash Function</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Keyed-hash-functions">Keyed hash functions</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-M">M</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-MAC">MAC</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Keyed-hash-functions">Keyed hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md2_005fdigest"><code>md2_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md2_005finit"><code>md2_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md2_005fupdate"><code>md2_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md4_005fdigest"><code>md4_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md4_005finit"><code>md4_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md4_005fupdate"><code>md4_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md5_005fdigest"><code>md5_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md5_005finit"><code>md5_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-md5_005fupdate"><code>md5_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-memeql_005fsec"><code>memeql_sec</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Miscellaneous-functions">Miscellaneous functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-memxor"><code>memxor</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Miscellaneous-functions">Miscellaneous functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-memxor3"><code>memxor3</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Miscellaneous-functions">Miscellaneous functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Message-Authentication-Code">Message Authentication Code</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Keyed-hash-functions">Keyed hash functions</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-N">N</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-nettle_005faead">nettle_aead</a>:</td><td>&nbsp;</td><td valign="top"><a href="#nettle_005faead-abstraction">nettle_aead abstraction</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-nettle_005faeads">nettle_aeads</a>:</td><td>&nbsp;</td><td valign="top"><a href="#nettle_005faead-abstraction">nettle_aead abstraction</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-nettle_005fcipher">nettle_cipher</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-nettle_005fciphers">nettle_ciphers</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-nettle_005fhash">nettle_hash</a>:</td><td>&nbsp;</td><td valign="top"><a href="#nettle_005fhash-abstraction">nettle_hash abstraction</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-nettle_005fhashes">nettle_hashes</a>:</td><td>&nbsp;</td><td valign="top"><a href="#nettle_005fhash-abstraction">nettle_hash abstraction</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-O">O</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-One_002dway">One-way</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Hash-functions">Hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-One_002dway-function">One-way function</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Public_002dkey-algorithms">Public-key algorithms</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-P">P</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-Password-Based-Key-Derivation-Function">Password Based Key Derivation Function</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-PBKDF">PBKDF</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-pbkdf2"><code>pbkdf2</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-PBKDF2"><code>PBKDF2</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-pbkdf2_005fhmac_005fsha1"><code>pbkdf2_hmac_sha1</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-pbkdf2_005fhmac_005fsha256"><code>pbkdf2_hmac_sha256</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-PKCS-_00235">PKCS #5</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Key-derivation-functions">Key derivation functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-poly1305_005faes_005fdigest"><code>poly1305_aes_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Poly1305">Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-poly1305_005faes_005fset_005fkey"><code>poly1305_aes_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Poly1305">Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-poly1305_005faes_005fset_005fnonce"><code>poly1305_aes_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Poly1305">Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-poly1305_005faes_005fupdate"><code>poly1305_aes_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Poly1305">Poly1305</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Public-Key-Cryptography">Public Key Cryptography</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Public_002dkey-algorithms">Public-key algorithms</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-R">R</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-Randomness">Randomness</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ripemd160_005fdigest"><code>ripemd160_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ripemd160_005finit"><code>ripemd160_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-ripemd160_005fupdate"><code>ripemd160_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fcompute_005froot"><code>rsa_compute_root</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fcompute_005froot_005ftr_0028const"><code>rsa_compute_root_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fdecrypt"><code>rsa_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fdecrypt_005ftr"><code>rsa_decrypt_tr</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fencrypt"><code>rsa_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fgenerate_005fkeypair"><code>rsa_generate_keypair</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fmd5_005fsign"><code>rsa_md5_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fmd5_005fsign_005fdigest"><code>rsa_md5_sign_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fmd5_005fsign_005fdigest_005ftr_0028const"><code>rsa_md5_sign_digest_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fmd5_005fsign_005ftr_0028const"><code>rsa_md5_sign_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fmd5_005fverify"><code>rsa_md5_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fmd5_005fverify_005fdigest"><code>rsa_md5_verify_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fpkcs1_005fsign_0028const"><code>rsa_pkcs1_sign(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fpkcs1_005fsign_005ftr_0028const"><code>rsa_pkcs1_sign_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fpkcs1_005fverify_0028const"><code>rsa_pkcs1_verify(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fprivate_005fkey_005fclear"><code>rsa_private_key_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fprivate_005fkey_005finit"><code>rsa_private_key_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fprivate_005fkey_005fprepare"><code>rsa_private_key_prepare</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fpublic_005fkey_005fclear"><code>rsa_public_key_clear</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fpublic_005fkey_005finit"><code>rsa_public_key_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fpublic_005fkey_005fprepare"><code>rsa_public_key_prepare</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha1_005fsign"><code>rsa_sha1_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha1_005fsign_005fdigest"><code>rsa_sha1_sign_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha1_005fsign_005fdigest_005ftr_0028const"><code>rsa_sha1_sign_digest_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha1_005fsign_005ftr_0028const"><code>rsa_sha1_sign_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha1_005fverify"><code>rsa_sha1_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha1_005fverify_005fdigest"><code>rsa_sha1_verify_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha256_005fsign"><code>rsa_sha256_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha256_005fsign_005fdigest"><code>rsa_sha256_sign_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha256_005fsign_005fdigest_005ftr_0028const"><code>rsa_sha256_sign_digest_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha256_005fsign_005ftr_0028const"><code>rsa_sha256_sign_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha256_005fverify"><code>rsa_sha256_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha256_005fverify_005fdigest"><code>rsa_sha256_verify_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha512_005fsign"><code>rsa_sha512_sign</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha512_005fsign_005fdigest"><code>rsa_sha512_sign_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha512_005fsign_005fdigest_005ftr_0028const"><code>rsa_sha512_sign_digest_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha512_005fsign_005ftr_0028const"><code>rsa_sha512_sign_tr(const</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha512_005fverify"><code>rsa_sha512_verify</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-rsa_005fsha512_005fverify_005fdigest"><code>rsa_sha512_verify_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#RSA">RSA</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-S">S</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-salsa20r12_005fcrypt"><code>salsa20r12_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-salsa20_005f128_005fset_005fkey"><code>salsa20_128_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-salsa20_005f256_005fset_005fkey"><code>salsa20_256_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-salsa20_005fcrypt"><code>salsa20_crypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-salsa20_005fset_005fkey"><code>salsa20_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-salsa20_005fset_005fnonce"><code>salsa20_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-serpent_005fdecrypt"><code>serpent_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-serpent_005fencrypt"><code>serpent_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-serpent_005fset_005fkey"><code>serpent_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha1_005fdigest"><code>sha1_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha1_005finit"><code>sha1_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha1_005fupdate"><code>sha1_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Legacy-hash-functions">Legacy hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha224_005fdigest"><code>sha224_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha224_005finit"><code>sha224_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha224_005fupdate"><code>sha224_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha256_005fdigest"><code>sha256_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha256_005finit"><code>sha256_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha256_005fupdate"><code>sha256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-SHA3">SHA3</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha384_005fdigest"><code>sha384_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha384_005finit"><code>sha384_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha384_005fupdate"><code>sha384_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f224_005fdigest"><code>sha3_224_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f224_005finit"><code>sha3_224_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f224_005fupdate"><code>sha3_224_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f256_005fdigest"><code>sha3_256_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f256_005finit"><code>sha3_256_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f256_005fupdate"><code>sha3_256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f384_005fdigest"><code>sha3_384_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f384_005finit"><code>sha3_384_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f384_005fupdate"><code>sha3_384_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f512_005fdigest"><code>sha3_512_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f512_005finit"><code>sha3_512_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha3_005f512_005fupdate"><code>sha3_512_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005f224_005fdigest"><code>sha512_224_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005f224_005finit"><code>sha512_224_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005f224_005fupdate"><code>sha512_224_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005f256_005fdigest"><code>sha512_256_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005f256_005finit"><code>sha512_256_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005f256_005fupdate"><code>sha512_256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005fdigest"><code>sha512_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005finit"><code>sha512_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-sha512_005fupdate"><code>sha512_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Recommended-hash-functions">Recommended hash functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Side_002dchannel-attack">Side-channel attack</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Side_002dchannel-silence">Side-channel silence</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-Stream-Cipher">Stream Cipher</a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-T">T</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-twofish_005fdecrypt"><code>twofish_decrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-twofish_005fencrypt"><code>twofish_encrypt</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-twofish_005fset_005fkey"><code>twofish_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Cipher-functions">Cipher functions</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-U">U</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-UMAC">UMAC</a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac128_005fdigest"><code>umac128_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac128_005fset_005fkey"><code>umac128_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac128_005fset_005fnonce"><code>umac128_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac128_005fupdate"><code>umac128_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac32_005fdigest"><code>umac32_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac32_005fset_005fkey"><code>umac32_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac32_005fset_005fnonce"><code>umac32_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac32_005fupdate"><code>umac32_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac64_005fdigest"><code>umac64_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac64_005fset_005fkey"><code>umac64_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac64_005fset_005fnonce"><code>umac64_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac64_005fupdate"><code>umac64_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac96_005fdigest"><code>umac96_digest</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac96_005fset_005fkey"><code>umac96_set_key</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac96_005fset_005fnonce"><code>umac96_set_nonce</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-umac96_005fupdate"><code>umac96_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#UMAC">UMAC</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
<tr><th><a name="Index_cp_letter-Y">Y</a></th><td></td><td></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005ffast_005freseed"><code>yarrow256_fast_reseed</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005finit"><code>yarrow256_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005fis_005fseeded"><code>yarrow256_is_seeded</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005fneeded_005fsources"><code>yarrow256_needed_sources</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005frandom"><code>yarrow256_random</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005fseed"><code>yarrow256_seed</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005fslow_005freseed"><code>yarrow256_slow_reseed</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow256_005fupdate"><code>yarrow256_update</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow_005fkey_005fevent_005festimate"><code>yarrow_key_event_estimate</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td></td><td valign="top"><a href="#index-yarrow_005fkey_005fevent_005finit"><code>yarrow_key_event_init</code></a>:</td><td>&nbsp;</td><td valign="top"><a href="#Randomness">Randomness</a></td></tr>
<tr><td colspan="4"> <hr></td></tr>
</table>
<table><tr><th valign="top">Jump to: &nbsp; </th><td><a class="summary-letter" href="#Index_cp_letter-A"><b>A</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-B"><b>B</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-C"><b>C</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-D"><b>D</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-E"><b>E</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-G"><b>G</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-H"><b>H</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-K"><b>K</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-M"><b>M</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-N"><b>N</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-O"><b>O</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-P"><b>P</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-R"><b>R</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-S"><b>S</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-T"><b>T</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-U"><b>U</b></a>
 &nbsp; 
<a class="summary-letter" href="#Index_cp_letter-Y"><b>Y</b></a>
 &nbsp; 
</td></tr></table>

<hr>
<a name="SEC_Foot"></a>
<div class="header">
<p>
 &nbsp; [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Index" title="Index" rel="index">Index</a>]</p>
</div>
<h4 class="footnotes-heading">Footnotes</h4>

<h3><a name="FOOT1" href="#DOCF1">(1)</a></h3>
<p>Actually, the computation is not done like this, it is
done more efficiently using <code>p</code>, <code>q</code> and the Chinese remainder
theorem (<acronym>CRT</acronym>). But the result is the same.</p>
<hr>



</body>
</html>