/usr/share/doc/python-cryptography-doc/html/hazmat/primitives/asymmetric/ec.html is in python-cryptography-doc 2.1.4-1ubuntu1.1.
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 | <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Elliptic curve cryptography — Cryptography 2.1.4 documentation</title>
<link rel="stylesheet" href="../../../_static/classic.css" type="text/css" />
<link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: '../../../',
VERSION: '2.1.4',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt'
};
</script>
<script type="text/javascript" src="../../../_static/jquery.js"></script>
<script type="text/javascript" src="../../../_static/underscore.js"></script>
<script type="text/javascript" src="../../../_static/doctools.js"></script>
<link rel="index" title="Index" href="../../../genindex.html" />
<link rel="search" title="Search" href="../../../search.html" />
<link rel="next" title="RSA" href="rsa.html" />
<link rel="prev" title="DSA" href="dsa.html" />
</head>
<body>
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../../../genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="../../../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li class="right" >
<a href="rsa.html" title="RSA"
accesskey="N">next</a> |</li>
<li class="right" >
<a href="dsa.html" title="DSA"
accesskey="P">previous</a> |</li>
<li class="nav-item nav-item-0"><a href="../../../index.html">Cryptography 2.1.4 documentation</a> »</li>
<li class="nav-item nav-item-1"><a href="../index.html" >Primitives</a> »</li>
<li class="nav-item nav-item-2"><a href="index.html" accesskey="U">Asymmetric algorithms</a> »</li>
</ul>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<div class="admonition danger">
<p class="first admonition-title">Danger</p>
<p class="last">
This is a "Hazardous Materials" module. You should <strong>ONLY</strong> use it if you're
100% absolutely sure that you know what you're doing because this module is
full of land mines, dragons, and dinosaurs with laser guns.</p>
</div>
<div class="section" id="module-cryptography.hazmat.primitives.asymmetric.ec">
<span id="elliptic-curve-cryptography"></span><h1>Elliptic curve cryptography<a class="headerlink" href="#module-cryptography.hazmat.primitives.asymmetric.ec" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.generate_private_key">
<code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">generate_private_key</code><span class="sig-paren">(</span><em>curve</em>, <em>backend</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.generate_private_key" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>Generate a new private key on <code class="docutils literal"><span class="pre">curve</span></code> for use with <code class="docutils literal"><span class="pre">backend</span></code>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>curve</strong> -- An instance of <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurve</span></code></a>.</li>
<li><strong>backend</strong> -- An instance of
<a class="reference internal" href="../../backends/interfaces.html#cryptography.hazmat.backends.interfaces.EllipticCurveBackend" title="cryptography.hazmat.backends.interfaces.EllipticCurveBackend"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurveBackend</span></code></a>.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">A new instance of <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePrivateKey</span></code></a>.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.derive_private_key">
<code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">derive_private_key</code><span class="sig-paren">(</span><em>private_value</em>, <em>curve</em>, <em>backend</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.derive_private_key" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.6.</span></p>
</div>
<p>Derive a private key from <code class="docutils literal"><span class="pre">private_value</span></code> on <code class="docutils literal"><span class="pre">curve</span></code> for use with
<code class="docutils literal"><span class="pre">backend</span></code>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>private_value</strong> (<em>int</em>) -- The secret scalar value.</li>
<li><strong>curve</strong> -- An instance of <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurve</span></code></a>.</li>
<li><strong>backend</strong> -- An instance of
<a class="reference internal" href="../../backends/interfaces.html#cryptography.hazmat.backends.interfaces.EllipticCurveBackend" title="cryptography.hazmat.backends.interfaces.EllipticCurveBackend"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurveBackend</span></code></a>.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">A new instance of <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePrivateKey</span></code></a>.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<div class="section" id="elliptic-curve-signature-algorithms">
<h2>Elliptic Curve Signature Algorithms<a class="headerlink" href="#elliptic-curve-signature-algorithms" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.ECDSA">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">ECDSA</code><span class="sig-paren">(</span><em>algorithm</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.ECDSA" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>The ECDSA signature algorithm first standardized in NIST publication
<a class="reference external" href="https://csrc.nist.gov/csrc/media/publications/fips/186/3/archive/2009-06-25/documents/fips_186-3.pdf">FIPS 186-3</a>, and later in <a class="reference external" href="https://csrc.nist.gov/publications/detail/fips/186/4/final">FIPS 186-4</a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>algorithm</strong> -- An instance of
<a class="reference internal" href="../cryptographic-hashes.html#cryptography.hazmat.primitives.hashes.HashAlgorithm" title="cryptography.hazmat.primitives.hashes.HashAlgorithm"><code class="xref py py-class docutils literal"><span class="pre">HashAlgorithm</span></code></a>.</td>
</tr>
</tbody>
</table>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.backends</span> <span class="k">import</span> <span class="n">default_backend</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.primitives</span> <span class="k">import</span> <span class="n">hashes</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.primitives.asymmetric</span> <span class="k">import</span> <span class="n">ec</span>
<span class="gp">>>> </span><span class="n">private_key</span> <span class="o">=</span> <span class="n">ec</span><span class="o">.</span><span class="n">generate_private_key</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">SECP384R1</span><span class="p">(),</span> <span class="n">default_backend</span><span class="p">()</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="sa">b</span><span class="s2">"this is some data I'd like to sign"</span>
<span class="gp">>>> </span><span class="n">signature</span> <span class="o">=</span> <span class="n">private_key</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">data</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">ECDSA</span><span class="p">(</span><span class="n">hashes</span><span class="o">.</span><span class="n">SHA256</span><span class="p">())</span>
<span class="gp">... </span><span class="p">)</span>
</pre></div>
</div>
<p>The <code class="docutils literal"><span class="pre">signature</span></code> is a <code class="docutils literal"><span class="pre">bytes</span></code> object, whose contents is DER encoded as
described in <span class="target" id="index-0"></span><a class="rfc reference external" href="https://tools.ietf.org/html/rfc3279.html"><strong>RFC 3279</strong></a>. This can be decoded using
<a class="reference internal" href="utils.html#cryptography.hazmat.primitives.asymmetric.utils.decode_dss_signature" title="cryptography.hazmat.primitives.asymmetric.utils.decode_dss_signature"><code class="xref py py-func docutils literal"><span class="pre">decode_dss_signature()</span></code></a>.</p>
<p>If your data is too large to be passed in a single call, you can hash it
separately and pass that value using
<a class="reference internal" href="utils.html#cryptography.hazmat.primitives.asymmetric.utils.Prehashed" title="cryptography.hazmat.primitives.asymmetric.utils.Prehashed"><code class="xref py py-class docutils literal"><span class="pre">Prehashed</span></code></a>.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.primitives.asymmetric</span> <span class="k">import</span> <span class="n">utils</span>
<span class="gp">>>> </span><span class="n">chosen_hash</span> <span class="o">=</span> <span class="n">hashes</span><span class="o">.</span><span class="n">SHA256</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">hasher</span> <span class="o">=</span> <span class="n">hashes</span><span class="o">.</span><span class="n">Hash</span><span class="p">(</span><span class="n">chosen_hash</span><span class="p">,</span> <span class="n">default_backend</span><span class="p">())</span>
<span class="gp">>>> </span><span class="n">hasher</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="sa">b</span><span class="s2">"data & "</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">hasher</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="sa">b</span><span class="s2">"more data"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">digest</span> <span class="o">=</span> <span class="n">hasher</span><span class="o">.</span><span class="n">finalize</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">sig</span> <span class="o">=</span> <span class="n">private_key</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">digest</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">ECDSA</span><span class="p">(</span><span class="n">utils</span><span class="o">.</span><span class="n">Prehashed</span><span class="p">(</span><span class="n">chosen_hash</span><span class="p">))</span>
<span class="gp">... </span><span class="p">)</span>
</pre></div>
</div>
<p>Verification requires the public key, the signature itself, the signed
data, and knowledge of the hashing algorithm that was used when producing
the signature:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">public_key</span> <span class="o">=</span> <span class="n">private_key</span><span class="o">.</span><span class="n">public_key</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">public_key</span><span class="o">.</span><span class="n">verify</span><span class="p">(</span><span class="n">signature</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">ec</span><span class="o">.</span><span class="n">ECDSA</span><span class="p">(</span><span class="n">hashes</span><span class="o">.</span><span class="n">SHA256</span><span class="p">()))</span>
</pre></div>
</div>
<p>If the signature is not valid, an
<a class="reference internal" href="../../../exceptions.html#cryptography.exceptions.InvalidSignature" title="cryptography.exceptions.InvalidSignature"><code class="xref py py-class docutils literal"><span class="pre">InvalidSignature</span></code></a> exception will be raised.</p>
<p>If your data is too large to be passed in a single call, you can hash it
separately and pass that value using
<a class="reference internal" href="utils.html#cryptography.hazmat.primitives.asymmetric.utils.Prehashed" title="cryptography.hazmat.primitives.asymmetric.utils.Prehashed"><code class="xref py py-class docutils literal"><span class="pre">Prehashed</span></code></a>.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">chosen_hash</span> <span class="o">=</span> <span class="n">hashes</span><span class="o">.</span><span class="n">SHA256</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">hasher</span> <span class="o">=</span> <span class="n">hashes</span><span class="o">.</span><span class="n">Hash</span><span class="p">(</span><span class="n">chosen_hash</span><span class="p">,</span> <span class="n">default_backend</span><span class="p">())</span>
<span class="gp">>>> </span><span class="n">hasher</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="sa">b</span><span class="s2">"data & "</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">hasher</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="sa">b</span><span class="s2">"more data"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">digest</span> <span class="o">=</span> <span class="n">hasher</span><span class="o">.</span><span class="n">finalize</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">public_key</span><span class="o">.</span><span class="n">verify</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">sig</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">digest</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">ECDSA</span><span class="p">(</span><span class="n">utils</span><span class="o">.</span><span class="n">Prehashed</span><span class="p">(</span><span class="n">chosen_hash</span><span class="p">))</span>
<span class="gp">... </span><span class="p">)</span>
</pre></div>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Although in this case the public key was derived from the private one,
in a typical setting you will not possess the private key. The
<a class="reference internal" href="#key-loading">Key loading</a> section explains how to load the public key from other
sources.</p>
</div>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurvePrivateNumbers</code><span class="sig-paren">(</span><em>private_value</em>, <em>public_numbers</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>The collection of integers that make up an EC private key.</p>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers.public_numbers">
<code class="descname">public_numbers</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers.public_numbers" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body"><a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicNumbers</span></code></a></td>
</tr>
</tbody>
</table>
<p>The <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicNumbers</span></code></a> which makes up the EC public
key associated with this EC private key.</p>
</dd></dl>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers.private_value">
<code class="descname">private_value</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers.private_value" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body">int</td>
</tr>
</tbody>
</table>
<p>The private value.</p>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers.private_key">
<code class="descname">private_key</code><span class="sig-paren">(</span><em>backend</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers.private_key" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert a collection of numbers into a private key suitable for doing
actual cryptographic operations.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>backend</strong> -- An instance of
<a class="reference internal" href="../../backends/interfaces.html#cryptography.hazmat.backends.interfaces.EllipticCurveBackend" title="cryptography.hazmat.backends.interfaces.EllipticCurveBackend"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurveBackend</span></code></a>.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">A new instance of <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePrivateKey</span></code></a>.</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurvePublicNumbers</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>curve</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>The collection of integers that make up an EC public key.</p>
<blockquote>
<div><dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.curve">
<code class="descname">curve</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.curve" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body"><a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurve</span></code></a></td>
</tr>
</tbody>
</table>
<p>The elliptic curve for this key.</p>
</dd></dl>
</div></blockquote>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.x">
<code class="descname">x</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.x" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body">int</td>
</tr>
</tbody>
</table>
<p>The affine x component of the public point used for verifying.</p>
</dd></dl>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.y">
<code class="descname">y</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.y" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body">int</td>
</tr>
</tbody>
</table>
<p>The affine y component of the public point used for verifying.</p>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.public_key">
<code class="descname">public_key</code><span class="sig-paren">(</span><em>backend</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.public_key" title="Permalink to this definition">¶</a></dt>
<dd><p>Convert a collection of numbers into a public key suitable for doing
actual cryptographic operations.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>backend</strong> -- An instance of
<a class="reference internal" href="../../backends/interfaces.html#cryptography.hazmat.backends.interfaces.EllipticCurveBackend" title="cryptography.hazmat.backends.interfaces.EllipticCurveBackend"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurveBackend</span></code></a>.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">A new instance of <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicKey</span></code></a>.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.encode_point">
<code class="descname">encode_point</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.encode_point" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.1.</span></p>
</div>
<p>Encodes an elliptic curve point to a byte string as described in
<a class="reference external" href="http://www.secg.org/sec1-v2.pdf">SEC 1 v2.0</a> section 2.3.3. This method only supports uncompressed
points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Return bytes:</th><td class="field-body">The encoded point.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="classmethod">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.from_encoded_point">
<em class="property">classmethod </em><code class="descname">from_encoded_point</code><span class="sig-paren">(</span><em>curve</em>, <em>data</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers.from_encoded_point" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.1.</span></p>
</div>
<p>Decodes a byte string as described in <a class="reference external" href="http://www.secg.org/sec1-v2.pdf">SEC 1 v2.0</a> section 2.3.3 and
returns an <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicNumbers</span></code></a>. This method only
supports uncompressed points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>curve</strong> -- An
<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurve</span></code></a>
instance.</li>
<li><strong>data</strong> (<em>bytes</em>) -- The serialized point byte string.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">An <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicNumbers</span></code></a> instance.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Raises:</th><td class="field-body"><ul class="first last simple">
<li><strong>ValueError</strong> -- Raised on invalid point type or data length.</li>
<li><strong>TypeError</strong> -- Raised when curve is not an
<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurve</span></code></a>.</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
</div>
<div class="section" id="elliptic-curve-key-exchange-algorithm">
<h2>Elliptic Curve Key Exchange algorithm<a class="headerlink" href="#elliptic-curve-key-exchange-algorithm" title="Permalink to this headline">¶</a></h2>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.ECDH">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">ECDH</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.ECDH" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.1.</span></p>
</div>
<p>The Elliptic Curve Diffie-Hellman Key Exchange algorithm first standardized
in NIST publication <a class="reference external" href="https://csrc.nist.gov/publications/detail/sp/800-56a/revised/archive/2007-03-14">800-56A</a>, and later in <a class="reference external" href="https://csrc.nist.gov/publications/detail/sp/800-56a/rev-2/final">800-56Ar2</a>.</p>
<p>For most applications the <code class="docutils literal"><span class="pre">shared_key</span></code> should be passed to a key
derivation function.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.backends</span> <span class="k">import</span> <span class="n">default_backend</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.primitives.asymmetric</span> <span class="k">import</span> <span class="n">ec</span>
<span class="gp">>>> </span><span class="c1"># Generate a private key for use in the exchange.</span>
<span class="gp">>>> </span><span class="n">private_key</span> <span class="o">=</span> <span class="n">ec</span><span class="o">.</span><span class="n">generate_private_key</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">SECP384R1</span><span class="p">(),</span> <span class="n">default_backend</span><span class="p">()</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># In a real handshake the peer_public_key will be received from the</span>
<span class="gp">>>> </span><span class="c1"># other party. For this example we'll generate another private key</span>
<span class="gp">>>> </span><span class="c1"># and get a public key from that.</span>
<span class="gp">>>> </span><span class="n">peer_public_key</span> <span class="o">=</span> <span class="n">ec</span><span class="o">.</span><span class="n">generate_private_key</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">SECP384R1</span><span class="p">(),</span> <span class="n">default_backend</span><span class="p">()</span>
<span class="gp">... </span><span class="p">)</span><span class="o">.</span><span class="n">public_key</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">shared_key</span> <span class="o">=</span> <span class="n">private_key</span><span class="o">.</span><span class="n">exchange</span><span class="p">(</span><span class="n">ec</span><span class="o">.</span><span class="n">ECDH</span><span class="p">(),</span> <span class="n">peer_public_key</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># For the next handshake we MUST generate another private key.</span>
<span class="gp">>>> </span><span class="n">private_key_2</span> <span class="o">=</span> <span class="n">ec</span><span class="o">.</span><span class="n">generate_private_key</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">SECP384R1</span><span class="p">(),</span> <span class="n">default_backend</span><span class="p">()</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">peer_public_key_2</span> <span class="o">=</span> <span class="n">ec</span><span class="o">.</span><span class="n">generate_private_key</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">ec</span><span class="o">.</span><span class="n">SECP384R1</span><span class="p">(),</span> <span class="n">default_backend</span><span class="p">()</span>
<span class="gp">... </span><span class="p">)</span><span class="o">.</span><span class="n">public_key</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">shared_key_2</span> <span class="o">=</span> <span class="n">private_key_2</span><span class="o">.</span><span class="n">exchange</span><span class="p">(</span><span class="n">ec</span><span class="o">.</span><span class="n">ECDH</span><span class="p">(),</span> <span class="n">peer_public_key_2</span><span class="p">)</span>
</pre></div>
</div>
<p>ECDHE (or EECDH), the ephemeral form of this exchange, is <strong>strongly
preferred</strong> over simple ECDH and provides <a class="reference external" href="https://en.wikipedia.org/wiki/Forward_secrecy">forward secrecy</a> when used.
You must generate a new private key using <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.generate_private_key" title="cryptography.hazmat.primitives.asymmetric.ec.generate_private_key"><code class="xref py py-func docutils literal"><span class="pre">generate_private_key()</span></code></a> for
each <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.exchange" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.exchange"><code class="xref py py-meth docutils literal"><span class="pre">exchange()</span></code></a> when performing an ECDHE key
exchange.</p>
</dd></dl>
</div>
<div class="section" id="elliptic-curves">
<h2>Elliptic Curves<a class="headerlink" href="#elliptic-curves" title="Permalink to this headline">¶</a></h2>
<p>Elliptic curves provide equivalent security at much smaller key sizes than
other asymmetric cryptography systems such as RSA or DSA. For many operations
elliptic curves are also significantly faster; <a class="reference external" href="http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1100&context=cseconfwork">elliptic curve diffie-hellman
is faster than diffie-hellman</a>.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Curves with a size of <a class="reference external" href="http://www.ecrypt.eu.org/ecrypt2/documents/D.SPA.20.pdf">less than 224 bits</a> should not be used. You should
strongly consider using curves of at least 224 <a class="reference internal" href="../../../glossary.html#term-bits"><span class="xref std std-term">bits</span></a>.</p>
</div>
<p>Generally the NIST prime field ("P") curves are significantly faster than the
other types suggested by NIST at both signing and verifying with ECDSA.</p>
<p>Prime fields also <a class="reference external" href="https://cr.yp.to/ecdh/curve25519-20060209.pdf">minimize the number of security concerns for elliptic-curve
cryptography</a>. However, there is <a class="reference external" href="https://crypto.stackexchange.com/questions/10263/should-we-trust-the-nist-recommended-ecc-parameters">some concern</a> that both the prime field and
binary field ("B") NIST curves may have been weakened during their generation.</p>
<p>Currently <cite>cryptography</cite> only supports NIST curves, none of which are
considered "safe" by the <a class="reference external" href="https://safecurves.cr.yp.to/">SafeCurves</a> project run by Daniel J. Bernstein and
Tanja Lange.</p>
<p>All named curves are instances of <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurve</span></code></a>.</p>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT571K1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT571K1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT571K1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect571k1</span></code>. Also called NIST K-571.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT409K1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT409K1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT409K1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect409k1</span></code>. Also called NIST K-409.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT283K1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT283K1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT283K1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect283k1</span></code>. Also called NIST K-283.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT233K1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT233K1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT233K1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect233k1</span></code>. Also called NIST K-233.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT163K1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT163K1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT163K1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect163k1</span></code>. Also called NIST K-163.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT571R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT571R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT571R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect571r1</span></code>. Also called NIST B-571.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT409R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT409R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT409R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect409r1</span></code>. Also called NIST B-409.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT283R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT283R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT283R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect283r1</span></code>. Also called NIST B-283.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT233R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT233R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT233R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect233r1</span></code>. Also called NIST B-233.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECT163R2">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECT163R2</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECT163R2" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">sect163r2</span></code>. Also called NIST B-163.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECP521R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECP521R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECP521R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">secp521r1</span></code>. Also called NIST P-521.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECP384R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECP384R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECP384R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">secp384r1</span></code>. Also called NIST P-384.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECP256R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECP256R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECP256R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">secp256r1</span></code>. Also called NIST P-256.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECP224R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECP224R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECP224R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">secp224r1</span></code>. Also called NIST P-224.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECP192R1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECP192R1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECP192R1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">secp192r1</span></code>. Also called NIST P-192.</p>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.SECP256K1">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">SECP256K1</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.SECP256K1" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.9.</span></p>
</div>
<p>SECG curve <code class="docutils literal"><span class="pre">secp256k1</span></code>.</p>
</dd></dl>
<div class="section" id="key-interfaces">
<h3>Key Interfaces<a class="headerlink" href="#key-interfaces" title="Permalink to this headline">¶</a></h3>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurve</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>A named elliptic curve.</p>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve.name">
<code class="descname">name</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve.name" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body">string</td>
</tr>
</tbody>
</table>
<p>The name of the curve. Usually the name used for the ASN.1 OID such as
<code class="docutils literal"><span class="pre">secp256k1</span></code>.</p>
</dd></dl>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve.key_size">
<code class="descname">key_size</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve.key_size" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body">int</td>
</tr>
</tbody>
</table>
<p>Size (in <a class="reference internal" href="../../../glossary.html#term-bits"><span class="xref std std-term">bits</span></a>) of a secret scalar for the curve (as generated
by <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.generate_private_key" title="cryptography.hazmat.primitives.asymmetric.ec.generate_private_key"><code class="xref py py-func docutils literal"><span class="pre">generate_private_key()</span></code></a>).</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurveSignatureAlgorithm</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<div class="versionchanged">
<p><span class="versionmodified">Changed in version 1.6: </span><a class="reference internal" href="utils.html#cryptography.hazmat.primitives.asymmetric.utils.Prehashed" title="cryptography.hazmat.primitives.asymmetric.utils.Prehashed"><code class="xref py py-class docutils literal"><span class="pre">Prehashed</span></code></a>
can now be used as an <code class="docutils literal"><span class="pre">algorithm</span></code>.</p>
</div>
<p>A signature algorithm for use with elliptic curve keys.</p>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm.algorithm">
<code class="descname">algorithm</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm.algorithm" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body"><a class="reference internal" href="../cryptographic-hashes.html#cryptography.hazmat.primitives.hashes.HashAlgorithm" title="cryptography.hazmat.primitives.hashes.HashAlgorithm"><code class="xref py py-class docutils literal"><span class="pre">HashAlgorithm</span></code></a> or
<a class="reference internal" href="utils.html#cryptography.hazmat.primitives.asymmetric.utils.Prehashed" title="cryptography.hazmat.primitives.asymmetric.utils.Prehashed"><code class="xref py py-class docutils literal"><span class="pre">Prehashed</span></code></a></td>
</tr>
</tbody>
</table>
<p>The digest algorithm to be used with the signature scheme.</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurvePrivateKey</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>An elliptic curve private key for use with an algorithm such as <a class="reference external" href="https://en.wikipedia.org/wiki/ECDSA">ECDSA</a> or
<a class="reference external" href="https://en.wikipedia.org/wiki/EdDSA">EdDSA</a>. An elliptic curve private key that is not an
<a class="reference internal" href="../../../glossary.html#term-opaque-key"><span class="xref std std-term">opaque key</span></a> also implements
<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePrivateKeyWithSerialization</span></code></a> to provide serialization
methods.</p>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.exchange">
<code class="descname">exchange</code><span class="sig-paren">(</span><em>algorithm</em>, <em>peer_public_key</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.exchange" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.1.</span></p>
</div>
<p>Performs a key exchange operation using the provided algorithm with
the peer's public key.</p>
<p>For most applications the result should be passed to a key derivation
function.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>algorithm</strong> -- The key exchange algorithm, currently only
<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.ECDH" title="cryptography.hazmat.primitives.asymmetric.ec.ECDH"><code class="xref py py-class docutils literal"><span class="pre">ECDH</span></code></a> is
supported.</li>
<li><strong>peer_public_key</strong> (<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey"><em>EllipticCurvePublicKey</em></a>) -- The public key for the
peer.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns bytes:</th><td class="field-body"><p class="first last">A shared key.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.public_key">
<code class="descname">public_key</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.public_key" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicKey</span></code></a></td>
</tr>
</tbody>
</table>
<p>The EllipticCurvePublicKey object for this private key.</p>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.sign">
<code class="descname">sign</code><span class="sig-paren">(</span><em>data</em>, <em>signature_algorithm</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.sign" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.5.</span></p>
</div>
<p>Sign one block of data which can be verified later by others using the
public key.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>data</strong> (<em>bytes</em>) -- The message string to sign.</li>
<li><strong>signature_algorithm</strong> -- An instance of
<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurveSignatureAlgorithm</span></code></a>, such as <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.ECDSA" title="cryptography.hazmat.primitives.asymmetric.ec.ECDSA"><code class="xref py py-class docutils literal"><span class="pre">ECDSA</span></code></a>.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return bytes:</th><td class="field-body"><p class="first last">Signature.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.key_size">
<code class="descname">key_size</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey.key_size" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.9.</span></p>
</div>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body">int</td>
</tr>
</tbody>
</table>
<p>Size (in <a class="reference internal" href="../../../glossary.html#term-bits"><span class="xref std std-term">bits</span></a>) of a secret scalar for the curve (as generated
by <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.generate_private_key" title="cryptography.hazmat.primitives.asymmetric.ec.generate_private_key"><code class="xref py py-func docutils literal"><span class="pre">generate_private_key()</span></code></a>).</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurvePrivateKeyWithSerialization</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.8.</span></p>
</div>
<p>This interface contains additional methods relating to serialization.
Any object with this interface also has all the methods from
<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePrivateKey</span></code></a>.</p>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization.private_numbers">
<code class="descname">private_numbers</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization.private_numbers" title="Permalink to this definition">¶</a></dt>
<dd><p>Create a <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePrivateNumbers</span></code></a> object.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">An <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePrivateNumbers</span></code></a> instance.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization.private_bytes">
<code class="descname">private_bytes</code><span class="sig-paren">(</span><em>encoding</em>, <em>format</em>, <em>encryption_algorithm</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKeyWithSerialization.private_bytes" title="Permalink to this definition">¶</a></dt>
<dd><p>Allows serialization of the key to bytes. Encoding (
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.Encoding.PEM" title="cryptography.hazmat.primitives.serialization.Encoding.PEM"><code class="xref py py-attr docutils literal"><span class="pre">PEM</span></code></a> or
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.Encoding.DER" title="cryptography.hazmat.primitives.serialization.Encoding.DER"><code class="xref py py-attr docutils literal"><span class="pre">DER</span></code></a>),
format (
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.PrivateFormat.TraditionalOpenSSL" title="cryptography.hazmat.primitives.serialization.PrivateFormat.TraditionalOpenSSL"><code class="xref py py-attr docutils literal"><span class="pre">TraditionalOpenSSL</span></code></a>
or
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8" title="cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8"><code class="xref py py-attr docutils literal"><span class="pre">PKCS8</span></code></a>)
and encryption algorithm (such as
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.BestAvailableEncryption" title="cryptography.hazmat.primitives.serialization.BestAvailableEncryption"><code class="xref py py-class docutils literal"><span class="pre">BestAvailableEncryption</span></code></a>
or <a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.NoEncryption" title="cryptography.hazmat.primitives.serialization.NoEncryption"><code class="xref py py-class docutils literal"><span class="pre">NoEncryption</span></code></a>)
are chosen to define the exact serialization.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>encoding</strong> -- A value from the
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.Encoding" title="cryptography.hazmat.primitives.serialization.Encoding"><code class="xref py py-class docutils literal"><span class="pre">Encoding</span></code></a> enum.</li>
<li><strong>format</strong> -- A value from the
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.PrivateFormat" title="cryptography.hazmat.primitives.serialization.PrivateFormat"><code class="xref py py-class docutils literal"><span class="pre">PrivateFormat</span></code></a> enum.</li>
<li><strong>encryption_algorithm</strong> -- An instance of an object conforming to the
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.KeySerializationEncryption" title="cryptography.hazmat.primitives.serialization.KeySerializationEncryption"><code class="xref py py-class docutils literal"><span class="pre">KeySerializationEncryption</span></code></a>
interface.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return bytes:</th><td class="field-body"><p class="first last">Serialized key.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurvePublicKey</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.5.</span></p>
</div>
<p>An elliptic curve public key.</p>
<blockquote>
<div><dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.curve">
<code class="descname">curve</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.curve" title="Permalink to this definition">¶</a></dt>
<dd><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body"><a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurve"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurve</span></code></a></td>
</tr>
</tbody>
</table>
<p>The elliptic curve for this key.</p>
</dd></dl>
</div></blockquote>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.public_numbers">
<code class="descname">public_numbers</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.public_numbers" title="Permalink to this definition">¶</a></dt>
<dd><p>Create a <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicNumbers</span></code></a> object.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">An <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicNumbers"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicNumbers</span></code></a> instance.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.public_bytes">
<code class="descname">public_bytes</code><span class="sig-paren">(</span><em>encoding</em>, <em>format</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.public_bytes" title="Permalink to this definition">¶</a></dt>
<dd><p>Allows serialization of the key to bytes. Encoding (
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.Encoding.PEM" title="cryptography.hazmat.primitives.serialization.Encoding.PEM"><code class="xref py py-attr docutils literal"><span class="pre">PEM</span></code></a> or
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.Encoding.DER" title="cryptography.hazmat.primitives.serialization.Encoding.DER"><code class="xref py py-attr docutils literal"><span class="pre">DER</span></code></a>) and
format (
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.PublicFormat.SubjectPublicKeyInfo" title="cryptography.hazmat.primitives.serialization.PublicFormat.SubjectPublicKeyInfo"><code class="xref py py-attr docutils literal"><span class="pre">SubjectPublicKeyInfo</span></code></a>)
are chosen to define the exact serialization.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>encoding</strong> -- A value from the
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.Encoding" title="cryptography.hazmat.primitives.serialization.Encoding"><code class="xref py py-class docutils literal"><span class="pre">Encoding</span></code></a> enum.</li>
<li><strong>format</strong> -- A value from the
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.PublicFormat" title="cryptography.hazmat.primitives.serialization.PublicFormat"><code class="xref py py-class docutils literal"><span class="pre">PublicFormat</span></code></a> enum.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Return bytes:</th><td class="field-body"><p class="first last">Serialized key.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.verify">
<code class="descname">verify</code><span class="sig-paren">(</span><em>signature</em>, <em>data</em>, <em>signature_algorithm</em><span class="sig-paren">)</span><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.verify" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.5.</span></p>
</div>
<p>Verify one block of data was signed by the private key associated
with this public key.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>signature</strong> (<em>bytes</em>) -- The signature to verify.</li>
<li><strong>data</strong> (<em>bytes</em>) -- The message string that was signed.</li>
<li><strong>signature_algorithm</strong> -- An instance of
<a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurveSignatureAlgorithm"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurveSignatureAlgorithm</span></code></a>.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Raises:</th><td class="field-body"><p class="first last"><a class="reference internal" href="../../../exceptions.html#cryptography.exceptions.InvalidSignature" title="cryptography.exceptions.InvalidSignature"><strong>cryptography.exceptions.InvalidSignature</strong></a> -- If the signature does
not validate.</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="attribute">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.key_size">
<code class="descname">key_size</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey.key_size" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 1.9.</span></p>
</div>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Type:</th><td class="field-body">int</td>
</tr>
</tbody>
</table>
<p>Size (in <a class="reference internal" href="../../../glossary.html#term-bits"><span class="xref std std-term">bits</span></a>) of a secret scalar for the curve (as generated
by <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.generate_private_key" title="cryptography.hazmat.primitives.asymmetric.ec.generate_private_key"><code class="xref py py-func docutils literal"><span class="pre">generate_private_key()</span></code></a>).</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKeyWithSerialization">
<em class="property">class </em><code class="descclassname">cryptography.hazmat.primitives.asymmetric.ec.</code><code class="descname">EllipticCurvePublicKeyWithSerialization</code><a class="headerlink" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKeyWithSerialization" title="Permalink to this definition">¶</a></dt>
<dd><div class="versionadded">
<p><span class="versionmodified">New in version 0.6.</span></p>
</div>
<p>Alias for <a class="reference internal" href="#cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey" title="cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePublicKey"><code class="xref py py-class docutils literal"><span class="pre">EllipticCurvePublicKey</span></code></a>.</p>
</dd></dl>
</div>
<div class="section" id="serialization">
<h3>Serialization<a class="headerlink" href="#serialization" title="Permalink to this headline">¶</a></h3>
<p>This sample demonstrates how to generate a private key and serialize it.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.backends</span> <span class="k">import</span> <span class="n">default_backend</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.primitives</span> <span class="k">import</span> <span class="n">hashes</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.primitives.asymmetric</span> <span class="k">import</span> <span class="n">ec</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">cryptography.hazmat.primitives</span> <span class="k">import</span> <span class="n">serialization</span>
<span class="gp">>>> </span><span class="n">private_key</span> <span class="o">=</span> <span class="n">ec</span><span class="o">.</span><span class="n">generate_private_key</span><span class="p">(</span><span class="n">ec</span><span class="o">.</span><span class="n">SECP384R1</span><span class="p">(),</span> <span class="n">default_backend</span><span class="p">())</span>
<span class="gp">>>> </span><span class="n">serialized_private</span> <span class="o">=</span> <span class="n">private_key</span><span class="o">.</span><span class="n">private_bytes</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">encoding</span><span class="o">=</span><span class="n">serialization</span><span class="o">.</span><span class="n">Encoding</span><span class="o">.</span><span class="n">PEM</span><span class="p">,</span>
<span class="gp">... </span> <span class="nb">format</span><span class="o">=</span><span class="n">serialization</span><span class="o">.</span><span class="n">PrivateFormat</span><span class="o">.</span><span class="n">PKCS8</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">encryption_algorithm</span><span class="o">=</span><span class="n">serialization</span><span class="o">.</span><span class="n">BestAvailableEncryption</span><span class="p">(</span><span class="sa">b</span><span class="s1">'testpassword'</span><span class="p">)</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">serialized_private</span><span class="o">.</span><span class="n">splitlines</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span>
<span class="go">'-----BEGIN ENCRYPTED PRIVATE KEY-----'</span>
</pre></div>
</div>
<p>You can also serialize the key without a password, by relying on
<a class="reference internal" href="serialization.html#cryptography.hazmat.primitives.serialization.NoEncryption" title="cryptography.hazmat.primitives.serialization.NoEncryption"><code class="xref py py-class docutils literal"><span class="pre">NoEncryption</span></code></a>.</p>
<p>The public key is serialized as follows:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">public_key</span> <span class="o">=</span> <span class="n">private_key</span><span class="o">.</span><span class="n">public_key</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">serialized_public</span> <span class="o">=</span> <span class="n">public_key</span><span class="o">.</span><span class="n">public_bytes</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">encoding</span><span class="o">=</span><span class="n">serialization</span><span class="o">.</span><span class="n">Encoding</span><span class="o">.</span><span class="n">PEM</span><span class="p">,</span>
<span class="gp">... </span> <span class="nb">format</span><span class="o">=</span><span class="n">serialization</span><span class="o">.</span><span class="n">PublicFormat</span><span class="o">.</span><span class="n">SubjectPublicKeyInfo</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">serialized_public</span><span class="o">.</span><span class="n">splitlines</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span>
<span class="go">'-----BEGIN PUBLIC KEY-----'</span>
</pre></div>
</div>
<p>This is the part that you would normally share with the rest of the world.</p>
</div>
<div class="section" id="key-loading">
<h3>Key loading<a class="headerlink" href="#key-loading" title="Permalink to this headline">¶</a></h3>
<p>This extends the sample in the previous section, assuming that the variables
<code class="docutils literal"><span class="pre">serialized_private</span></code> and <code class="docutils literal"><span class="pre">serialized_public</span></code> contain the respective keys
in PEM format.</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">loaded_public_key</span> <span class="o">=</span> <span class="n">serialization</span><span class="o">.</span><span class="n">load_pem_public_key</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">serialized_public</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">backend</span><span class="o">=</span><span class="n">default_backend</span><span class="p">()</span>
<span class="gp">... </span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">loaded_private_key</span> <span class="o">=</span> <span class="n">serialization</span><span class="o">.</span><span class="n">load_pem_private_key</span><span class="p">(</span>
<span class="gp">... </span> <span class="n">serialized_private</span><span class="p">,</span>
<span class="gp">... </span> <span class="c1"># or password=None, if in plain text</span>
<span class="gp">... </span> <span class="n">password</span><span class="o">=</span><span class="sa">b</span><span class="s1">'testpassword'</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">backend</span><span class="o">=</span><span class="n">default_backend</span><span class="p">()</span>
<span class="gp">... </span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h3><a href="../../../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Elliptic curve cryptography</a><ul>
<li><a class="reference internal" href="#elliptic-curve-signature-algorithms">Elliptic Curve Signature Algorithms</a></li>
<li><a class="reference internal" href="#elliptic-curve-key-exchange-algorithm">Elliptic Curve Key Exchange algorithm</a></li>
<li><a class="reference internal" href="#elliptic-curves">Elliptic Curves</a><ul>
<li><a class="reference internal" href="#key-interfaces">Key Interfaces</a></li>
<li><a class="reference internal" href="#serialization">Serialization</a></li>
<li><a class="reference internal" href="#key-loading">Key loading</a></li>
</ul>
</li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
<p class="topless"><a href="dsa.html"
title="previous chapter">DSA</a></p>
<h4>Next topic</h4>
<p class="topless"><a href="rsa.html"
title="next chapter">RSA</a></p>
<div role="note" aria-label="source link">
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="../../../_sources/hazmat/primitives/asymmetric/ec.rst.txt"
rel="nofollow">Show Source</a></li>
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3>Quick search</h3>
<form class="search" action="../../../search.html" method="get">
<div><input type="text" name="q" /></div>
<div><input type="submit" value="Go" /></div>
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../../../genindex.html" title="General Index"
>index</a></li>
<li class="right" >
<a href="../../../py-modindex.html" title="Python Module Index"
>modules</a> |</li>
<li class="right" >
<a href="rsa.html" title="RSA"
>next</a> |</li>
<li class="right" >
<a href="dsa.html" title="DSA"
>previous</a> |</li>
<li class="nav-item nav-item-0"><a href="../../../index.html">Cryptography 2.1.4 documentation</a> »</li>
<li class="nav-item nav-item-1"><a href="../index.html" >Primitives</a> »</li>
<li class="nav-item nav-item-2"><a href="index.html" >Asymmetric algorithms</a> »</li>
</ul>
</div>
<div class="footer" role="contentinfo">
© Copyright 2013-2018, Individual Contributors.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.6.7.
</div>
</body>
</html>
|