/usr/lib/python3/dist-packages/rsa/key.py is in python3-rsa 3.4.2-1.
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 | # -*- coding: utf-8 -*-
#
# Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""RSA key generation code.
Create new keys with the newkeys() function. It will give you a PublicKey and a
PrivateKey object.
Loading and saving keys requires the pyasn1 module. This module is imported as
late as possible, such that other functionality will remain working in absence
of pyasn1.
.. note::
Storing public and private keys via the `pickle` module is possible.
However, it is insecure to load a key from an untrusted source.
The pickle module is not secure against erroneous or maliciously
constructed data. Never unpickle data received from an untrusted
or unauthenticated source.
"""
import logging
from rsa._compat import b
import rsa.prime
import rsa.pem
import rsa.common
import rsa.randnum
import rsa.core
log = logging.getLogger(__name__)
DEFAULT_EXPONENT = 65537
class AbstractKey(object):
"""Abstract superclass for private and public keys."""
__slots__ = ('n', 'e')
def __init__(self, n, e):
self.n = n
self.e = e
@classmethod
def load_pkcs1(cls, keyfile, format='PEM'):
"""Loads a key in PKCS#1 DER or PEM format.
:param keyfile: contents of a DER- or PEM-encoded file that contains
the public key.
:param format: the format of the file to load; 'PEM' or 'DER'
:return: a PublicKey object
"""
methods = {
'PEM': cls._load_pkcs1_pem,
'DER': cls._load_pkcs1_der,
}
method = cls._assert_format_exists(format, methods)
return method(keyfile)
@staticmethod
def _assert_format_exists(file_format, methods):
"""Checks whether the given file format exists in 'methods'.
"""
try:
return methods[file_format]
except KeyError:
formats = ', '.join(sorted(methods.keys()))
raise ValueError('Unsupported format: %r, try one of %s' % (file_format,
formats))
def save_pkcs1(self, format='PEM'):
"""Saves the public key in PKCS#1 DER or PEM format.
:param format: the format to save; 'PEM' or 'DER'
:returns: the DER- or PEM-encoded public key.
"""
methods = {
'PEM': self._save_pkcs1_pem,
'DER': self._save_pkcs1_der,
}
method = self._assert_format_exists(format, methods)
return method()
def blind(self, message, r):
"""Performs blinding on the message using random number 'r'.
:param message: the message, as integer, to blind.
:type message: int
:param r: the random number to blind with.
:type r: int
:return: the blinded message.
:rtype: int
The blinding is such that message = unblind(decrypt(blind(encrypt(message))).
See https://en.wikipedia.org/wiki/Blinding_%28cryptography%29
"""
return (message * pow(r, self.e, self.n)) % self.n
def unblind(self, blinded, r):
"""Performs blinding on the message using random number 'r'.
:param blinded: the blinded message, as integer, to unblind.
:param r: the random number to unblind with.
:return: the original message.
The blinding is such that message = unblind(decrypt(blind(encrypt(message))).
See https://en.wikipedia.org/wiki/Blinding_%28cryptography%29
"""
return (rsa.common.inverse(r, self.n) * blinded) % self.n
class PublicKey(AbstractKey):
"""Represents a public RSA key.
This key is also known as the 'encryption key'. It contains the 'n' and 'e'
values.
Supports attributes as well as dictionary-like access. Attribute accesss is
faster, though.
>>> PublicKey(5, 3)
PublicKey(5, 3)
>>> key = PublicKey(5, 3)
>>> key.n
5
>>> key['n']
5
>>> key.e
3
>>> key['e']
3
"""
__slots__ = ('n', 'e')
def __getitem__(self, key):
return getattr(self, key)
def __repr__(self):
return 'PublicKey(%i, %i)' % (self.n, self.e)
def __getstate__(self):
"""Returns the key as tuple for pickling."""
return self.n, self.e
def __setstate__(self, state):
"""Sets the key from tuple."""
self.n, self.e = state
def __eq__(self, other):
if other is None:
return False
if not isinstance(other, PublicKey):
return False
return self.n == other.n and self.e == other.e
def __ne__(self, other):
return not (self == other)
@classmethod
def _load_pkcs1_der(cls, keyfile):
"""Loads a key in PKCS#1 DER format.
:param keyfile: contents of a DER-encoded file that contains the public
key.
:return: a PublicKey object
First let's construct a DER encoded key:
>>> import base64
>>> b64der = 'MAwCBQCNGmYtAgMBAAE='
>>> der = base64.standard_b64decode(b64der)
This loads the file:
>>> PublicKey._load_pkcs1_der(der)
PublicKey(2367317549, 65537)
"""
from pyasn1.codec.der import decoder
from rsa.asn1 import AsnPubKey
(priv, _) = decoder.decode(keyfile, asn1Spec=AsnPubKey())
return cls(n=int(priv['modulus']), e=int(priv['publicExponent']))
def _save_pkcs1_der(self):
"""Saves the public key in PKCS#1 DER format.
@returns: the DER-encoded public key.
"""
from pyasn1.codec.der import encoder
from rsa.asn1 import AsnPubKey
# Create the ASN object
asn_key = AsnPubKey()
asn_key.setComponentByName('modulus', self.n)
asn_key.setComponentByName('publicExponent', self.e)
return encoder.encode(asn_key)
@classmethod
def _load_pkcs1_pem(cls, keyfile):
"""Loads a PKCS#1 PEM-encoded public key file.
The contents of the file before the "-----BEGIN RSA PUBLIC KEY-----" and
after the "-----END RSA PUBLIC KEY-----" lines is ignored.
:param keyfile: contents of a PEM-encoded file that contains the public
key.
:return: a PublicKey object
"""
der = rsa.pem.load_pem(keyfile, 'RSA PUBLIC KEY')
return cls._load_pkcs1_der(der)
def _save_pkcs1_pem(self):
"""Saves a PKCS#1 PEM-encoded public key file.
:return: contents of a PEM-encoded file that contains the public key.
"""
der = self._save_pkcs1_der()
return rsa.pem.save_pem(der, 'RSA PUBLIC KEY')
@classmethod
def load_pkcs1_openssl_pem(cls, keyfile):
"""Loads a PKCS#1.5 PEM-encoded public key file from OpenSSL.
These files can be recognised in that they start with BEGIN PUBLIC KEY
rather than BEGIN RSA PUBLIC KEY.
The contents of the file before the "-----BEGIN PUBLIC KEY-----" and
after the "-----END PUBLIC KEY-----" lines is ignored.
:param keyfile: contents of a PEM-encoded file that contains the public
key, from OpenSSL.
:return: a PublicKey object
"""
der = rsa.pem.load_pem(keyfile, 'PUBLIC KEY')
return cls.load_pkcs1_openssl_der(der)
@classmethod
def load_pkcs1_openssl_der(cls, keyfile):
"""Loads a PKCS#1 DER-encoded public key file from OpenSSL.
:param keyfile: contents of a DER-encoded file that contains the public
key, from OpenSSL.
:return: a PublicKey object
"""
from rsa.asn1 import OpenSSLPubKey
from pyasn1.codec.der import decoder
from pyasn1.type import univ
(keyinfo, _) = decoder.decode(keyfile, asn1Spec=OpenSSLPubKey())
if keyinfo['header']['oid'] != univ.ObjectIdentifier('1.2.840.113549.1.1.1'):
raise TypeError("This is not a DER-encoded OpenSSL-compatible public key")
return cls._load_pkcs1_der(keyinfo['key'][1:])
class PrivateKey(AbstractKey):
"""Represents a private RSA key.
This key is also known as the 'decryption key'. It contains the 'n', 'e',
'd', 'p', 'q' and other values.
Supports attributes as well as dictionary-like access. Attribute accesss is
faster, though.
>>> PrivateKey(3247, 65537, 833, 191, 17)
PrivateKey(3247, 65537, 833, 191, 17)
exp1, exp2 and coef can be given, but if None or omitted they will be calculated:
>>> pk = PrivateKey(3727264081, 65537, 3349121513, 65063, 57287, exp2=4)
>>> pk.exp1
55063
>>> pk.exp2 # this is of course not a correct value, but it is the one we passed.
4
>>> pk.coef
50797
If you give exp1, exp2 or coef, they will be used as-is:
>>> pk = PrivateKey(1, 2, 3, 4, 5, 6, 7, 8)
>>> pk.exp1
6
>>> pk.exp2
7
>>> pk.coef
8
"""
__slots__ = ('n', 'e', 'd', 'p', 'q', 'exp1', 'exp2', 'coef')
def __init__(self, n, e, d, p, q, exp1=None, exp2=None, coef=None):
AbstractKey.__init__(self, n, e)
self.d = d
self.p = p
self.q = q
# Calculate the other values if they aren't supplied
if exp1 is None:
self.exp1 = int(d % (p - 1))
else:
self.exp1 = exp1
if exp2 is None:
self.exp2 = int(d % (q - 1))
else:
self.exp2 = exp2
if coef is None:
self.coef = rsa.common.inverse(q, p)
else:
self.coef = coef
def __getitem__(self, key):
return getattr(self, key)
def __repr__(self):
return 'PrivateKey(%(n)i, %(e)i, %(d)i, %(p)i, %(q)i)' % self
def __getstate__(self):
"""Returns the key as tuple for pickling."""
return self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef
def __setstate__(self, state):
"""Sets the key from tuple."""
self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef = state
def __eq__(self, other):
if other is None:
return False
if not isinstance(other, PrivateKey):
return False
return (self.n == other.n and
self.e == other.e and
self.d == other.d and
self.p == other.p and
self.q == other.q and
self.exp1 == other.exp1 and
self.exp2 == other.exp2 and
self.coef == other.coef)
def __ne__(self, other):
return not (self == other)
def blinded_decrypt(self, encrypted):
"""Decrypts the message using blinding to prevent side-channel attacks.
:param encrypted: the encrypted message
:type encrypted: int
:returns: the decrypted message
:rtype: int
"""
blind_r = rsa.randnum.randint(self.n - 1)
blinded = self.blind(encrypted, blind_r) # blind before decrypting
decrypted = rsa.core.decrypt_int(blinded, self.d, self.n)
return self.unblind(decrypted, blind_r)
def blinded_encrypt(self, message):
"""Encrypts the message using blinding to prevent side-channel attacks.
:param message: the message to encrypt
:type message: int
:returns: the encrypted message
:rtype: int
"""
blind_r = rsa.randnum.randint(self.n - 1)
blinded = self.blind(message, blind_r) # blind before encrypting
encrypted = rsa.core.encrypt_int(blinded, self.d, self.n)
return self.unblind(encrypted, blind_r)
@classmethod
def _load_pkcs1_der(cls, keyfile):
"""Loads a key in PKCS#1 DER format.
:param keyfile: contents of a DER-encoded file that contains the private
key.
:return: a PrivateKey object
First let's construct a DER encoded key:
>>> import base64
>>> b64der = 'MC4CAQACBQDeKYlRAgMBAAECBQDHn4npAgMA/icCAwDfxwIDANcXAgInbwIDAMZt'
>>> der = base64.standard_b64decode(b64der)
This loads the file:
>>> PrivateKey._load_pkcs1_der(der)
PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
"""
from pyasn1.codec.der import decoder
(priv, _) = decoder.decode(keyfile)
# ASN.1 contents of DER encoded private key:
#
# RSAPrivateKey ::= SEQUENCE {
# version Version,
# modulus INTEGER, -- n
# publicExponent INTEGER, -- e
# privateExponent INTEGER, -- d
# prime1 INTEGER, -- p
# prime2 INTEGER, -- q
# exponent1 INTEGER, -- d mod (p-1)
# exponent2 INTEGER, -- d mod (q-1)
# coefficient INTEGER, -- (inverse of q) mod p
# otherPrimeInfos OtherPrimeInfos OPTIONAL
# }
if priv[0] != 0:
raise ValueError('Unable to read this file, version %s != 0' % priv[0])
as_ints = tuple(int(x) for x in priv[1:9])
return cls(*as_ints)
def _save_pkcs1_der(self):
"""Saves the private key in PKCS#1 DER format.
@returns: the DER-encoded private key.
"""
from pyasn1.type import univ, namedtype
from pyasn1.codec.der import encoder
class AsnPrivKey(univ.Sequence):
componentType = namedtype.NamedTypes(
namedtype.NamedType('version', univ.Integer()),
namedtype.NamedType('modulus', univ.Integer()),
namedtype.NamedType('publicExponent', univ.Integer()),
namedtype.NamedType('privateExponent', univ.Integer()),
namedtype.NamedType('prime1', univ.Integer()),
namedtype.NamedType('prime2', univ.Integer()),
namedtype.NamedType('exponent1', univ.Integer()),
namedtype.NamedType('exponent2', univ.Integer()),
namedtype.NamedType('coefficient', univ.Integer()),
)
# Create the ASN object
asn_key = AsnPrivKey()
asn_key.setComponentByName('version', 0)
asn_key.setComponentByName('modulus', self.n)
asn_key.setComponentByName('publicExponent', self.e)
asn_key.setComponentByName('privateExponent', self.d)
asn_key.setComponentByName('prime1', self.p)
asn_key.setComponentByName('prime2', self.q)
asn_key.setComponentByName('exponent1', self.exp1)
asn_key.setComponentByName('exponent2', self.exp2)
asn_key.setComponentByName('coefficient', self.coef)
return encoder.encode(asn_key)
@classmethod
def _load_pkcs1_pem(cls, keyfile):
"""Loads a PKCS#1 PEM-encoded private key file.
The contents of the file before the "-----BEGIN RSA PRIVATE KEY-----" and
after the "-----END RSA PRIVATE KEY-----" lines is ignored.
:param keyfile: contents of a PEM-encoded file that contains the private
key.
:return: a PrivateKey object
"""
der = rsa.pem.load_pem(keyfile, b('RSA PRIVATE KEY'))
return cls._load_pkcs1_der(der)
def _save_pkcs1_pem(self):
"""Saves a PKCS#1 PEM-encoded private key file.
:return: contents of a PEM-encoded file that contains the private key.
"""
der = self._save_pkcs1_der()
return rsa.pem.save_pem(der, b('RSA PRIVATE KEY'))
def find_p_q(nbits, getprime_func=rsa.prime.getprime, accurate=True):
"""Returns a tuple of two different primes of nbits bits each.
The resulting p * q has exacty 2 * nbits bits, and the returned p and q
will not be equal.
:param nbits: the number of bits in each of p and q.
:param getprime_func: the getprime function, defaults to
:py:func:`rsa.prime.getprime`.
*Introduced in Python-RSA 3.1*
:param accurate: whether to enable accurate mode or not.
:returns: (p, q), where p > q
>>> (p, q) = find_p_q(128)
>>> from rsa import common
>>> common.bit_size(p * q)
256
When not in accurate mode, the number of bits can be slightly less
>>> (p, q) = find_p_q(128, accurate=False)
>>> from rsa import common
>>> common.bit_size(p * q) <= 256
True
>>> common.bit_size(p * q) > 240
True
"""
total_bits = nbits * 2
# Make sure that p and q aren't too close or the factoring programs can
# factor n.
shift = nbits // 16
pbits = nbits + shift
qbits = nbits - shift
# Choose the two initial primes
log.debug('find_p_q(%i): Finding p', nbits)
p = getprime_func(pbits)
log.debug('find_p_q(%i): Finding q', nbits)
q = getprime_func(qbits)
def is_acceptable(p, q):
"""Returns True iff p and q are acceptable:
- p and q differ
- (p * q) has the right nr of bits (when accurate=True)
"""
if p == q:
return False
if not accurate:
return True
# Make sure we have just the right amount of bits
found_size = rsa.common.bit_size(p * q)
return total_bits == found_size
# Keep choosing other primes until they match our requirements.
change_p = False
while not is_acceptable(p, q):
# Change p on one iteration and q on the other
if change_p:
p = getprime_func(pbits)
else:
q = getprime_func(qbits)
change_p = not change_p
# We want p > q as described on
# http://www.di-mgt.com.au/rsa_alg.html#crt
return max(p, q), min(p, q)
def calculate_keys_custom_exponent(p, q, exponent):
"""Calculates an encryption and a decryption key given p, q and an exponent,
and returns them as a tuple (e, d)
:param p: the first large prime
:param q: the second large prime
:param exponent: the exponent for the key; only change this if you know
what you're doing, as the exponent influences how difficult your
private key can be cracked. A very common choice for e is 65537.
:type exponent: int
"""
phi_n = (p - 1) * (q - 1)
try:
d = rsa.common.inverse(exponent, phi_n)
except ValueError:
raise ValueError("e (%d) and phi_n (%d) are not relatively prime" %
(exponent, phi_n))
if (exponent * d) % phi_n != 1:
raise ValueError("e (%d) and d (%d) are not mult. inv. modulo "
"phi_n (%d)" % (exponent, d, phi_n))
return exponent, d
def calculate_keys(p, q):
"""Calculates an encryption and a decryption key given p and q, and
returns them as a tuple (e, d)
:param p: the first large prime
:param q: the second large prime
:return: tuple (e, d) with the encryption and decryption exponents.
"""
return calculate_keys_custom_exponent(p, q, DEFAULT_EXPONENT)
def gen_keys(nbits, getprime_func, accurate=True, exponent=DEFAULT_EXPONENT):
"""Generate RSA keys of nbits bits. Returns (p, q, e, d).
Note: this can take a long time, depending on the key size.
:param nbits: the total number of bits in ``p`` and ``q``. Both ``p`` and
``q`` will use ``nbits/2`` bits.
:param getprime_func: either :py:func:`rsa.prime.getprime` or a function
with similar signature.
:param exponent: the exponent for the key; only change this if you know
what you're doing, as the exponent influences how difficult your
private key can be cracked. A very common choice for e is 65537.
:type exponent: int
"""
# Regenerate p and q values, until calculate_keys doesn't raise a
# ValueError.
while True:
(p, q) = find_p_q(nbits // 2, getprime_func, accurate)
try:
(e, d) = calculate_keys_custom_exponent(p, q, exponent=exponent)
break
except ValueError:
pass
return p, q, e, d
def newkeys(nbits, accurate=True, poolsize=1, exponent=DEFAULT_EXPONENT):
"""Generates public and private keys, and returns them as (pub, priv).
The public key is also known as the 'encryption key', and is a
:py:class:`rsa.PublicKey` object. The private key is also known as the
'decryption key' and is a :py:class:`rsa.PrivateKey` object.
:param nbits: the number of bits required to store ``n = p*q``.
:param accurate: when True, ``n`` will have exactly the number of bits you
asked for. However, this makes key generation much slower. When False,
`n`` may have slightly less bits.
:param poolsize: the number of processes to use to generate the prime
numbers. If set to a number > 1, a parallel algorithm will be used.
This requires Python 2.6 or newer.
:param exponent: the exponent for the key; only change this if you know
what you're doing, as the exponent influences how difficult your
private key can be cracked. A very common choice for e is 65537.
:type exponent: int
:returns: a tuple (:py:class:`rsa.PublicKey`, :py:class:`rsa.PrivateKey`)
The ``poolsize`` parameter was added in *Python-RSA 3.1* and requires
Python 2.6 or newer.
"""
if nbits < 16:
raise ValueError('Key too small')
if poolsize < 1:
raise ValueError('Pool size (%i) should be >= 1' % poolsize)
# Determine which getprime function to use
if poolsize > 1:
from rsa import parallel
import functools
getprime_func = functools.partial(parallel.getprime, poolsize=poolsize)
else:
getprime_func = rsa.prime.getprime
# Generate the key components
(p, q, e, d) = gen_keys(nbits, getprime_func, accurate=accurate, exponent=exponent)
# Create the key objects
n = p * q
return (
PublicKey(n, e),
PrivateKey(n, e, d, p, q)
)
__all__ = ['PublicKey', 'PrivateKey', 'newkeys']
if __name__ == '__main__':
import doctest
try:
for count in range(100):
(failures, tests) = doctest.testmod()
if failures:
break
if (count and count % 10 == 0) or count == 1:
print('%i times' % count)
except KeyboardInterrupt:
print('Aborted')
else:
print('Doctests done')
|