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# This file is dual licensed under the terms of the Apache License, Version
# 2.0, and the BSD License. See the LICENSE file in the root of this repository
# for complete details.
from __future__ import annotations
import abc
import typing
from math import gcd
from cryptography.hazmat.primitives import _serialization, hashes
from cryptography.hazmat.primitives._asymmetric import AsymmetricPadding
from cryptography.hazmat.primitives.asymmetric import utils as asym_utils
class RSAPrivateKey(metaclass=abc.ABCMeta):
@abc.abstractmethod
def decrypt(self, ciphertext: bytes, padding: AsymmetricPadding) -> bytes:
"""
Decrypts the provided ciphertext.
"""
@property
@abc.abstractmethod
def key_size(self) -> int:
"""
The bit length of the public modulus.
"""
@abc.abstractmethod
def public_key(self) -> RSAPublicKey:
"""
The RSAPublicKey associated with this private key.
"""
@abc.abstractmethod
def sign(
self,
data: bytes,
padding: AsymmetricPadding,
algorithm: typing.Union[asym_utils.Prehashed, hashes.HashAlgorithm],
) -> bytes:
"""
Signs the data.
"""
@abc.abstractmethod
def private_numbers(self) -> RSAPrivateNumbers:
"""
Returns an RSAPrivateNumbers.
"""
@abc.abstractmethod
def private_bytes(
self,
encoding: _serialization.Encoding,
format: _serialization.PrivateFormat,
encryption_algorithm: _serialization.KeySerializationEncryption,
) -> bytes:
"""
Returns the key serialized as bytes.
"""
RSAPrivateKeyWithSerialization = RSAPrivateKey
class RSAPublicKey(metaclass=abc.ABCMeta):
@abc.abstractmethod
def encrypt(self, plaintext: bytes, padding: AsymmetricPadding) -> bytes:
"""
Encrypts the given plaintext.
"""
@property
@abc.abstractmethod
def key_size(self) -> int:
"""
The bit length of the public modulus.
"""
@abc.abstractmethod
def public_numbers(self) -> RSAPublicNumbers:
"""
Returns an RSAPublicNumbers
"""
@abc.abstractmethod
def public_bytes(
self,
encoding: _serialization.Encoding,
format: _serialization.PublicFormat,
) -> bytes:
"""
Returns the key serialized as bytes.
"""
@abc.abstractmethod
def verify(
self,
signature: bytes,
data: bytes,
padding: AsymmetricPadding,
algorithm: typing.Union[asym_utils.Prehashed, hashes.HashAlgorithm],
) -> None:
"""
Verifies the signature of the data.
"""
@abc.abstractmethod
def recover_data_from_signature(
self,
signature: bytes,
padding: AsymmetricPadding,
algorithm: typing.Optional[hashes.HashAlgorithm],
) -> bytes:
"""
Recovers the original data from the signature.
"""
@abc.abstractmethod
def __eq__(self, other: object) -> bool:
"""
Checks equality.
"""
RSAPublicKeyWithSerialization = RSAPublicKey
def generate_private_key(
public_exponent: int,
key_size: int,
backend: typing.Any = None,
) -> RSAPrivateKey:
from cryptography.hazmat.backends.openssl.backend import backend as ossl
_verify_rsa_parameters(public_exponent, key_size)
return ossl.generate_rsa_private_key(public_exponent, key_size)
def _verify_rsa_parameters(public_exponent: int, key_size: int) -> None:
if public_exponent not in (3, 65537):
raise ValueError(
"public_exponent must be either 3 (for legacy compatibility) or "
"65537. Almost everyone should choose 65537 here!"
)
if key_size < 512:
raise ValueError("key_size must be at least 512-bits.")
def _check_private_key_components(
p: int,
q: int,
private_exponent: int,
dmp1: int,
dmq1: int,
iqmp: int,
public_exponent: int,
modulus: int,
) -> None:
if modulus < 3:
raise ValueError("modulus must be >= 3.")
if p >= modulus:
raise ValueError("p must be < modulus.")
if q >= modulus:
raise ValueError("q must be < modulus.")
if dmp1 >= modulus:
raise ValueError("dmp1 must be < modulus.")
if dmq1 >= modulus:
raise ValueError("dmq1 must be < modulus.")
if iqmp >= modulus:
raise ValueError("iqmp must be < modulus.")
if private_exponent >= modulus:
raise ValueError("private_exponent must be < modulus.")
if public_exponent < 3 or public_exponent >= modulus:
raise ValueError("public_exponent must be >= 3 and < modulus.")
if public_exponent & 1 == 0:
raise ValueError("public_exponent must be odd.")
if dmp1 & 1 == 0:
raise ValueError("dmp1 must be odd.")
if dmq1 & 1 == 0:
raise ValueError("dmq1 must be odd.")
if p * q != modulus:
raise ValueError("p*q must equal modulus.")
def _check_public_key_components(e: int, n: int) -> None:
if n < 3:
raise ValueError("n must be >= 3.")
if e < 3 or e >= n:
raise ValueError("e must be >= 3 and < n.")
if e & 1 == 0:
raise ValueError("e must be odd.")
def _modinv(e: int, m: int) -> int:
"""
Modular Multiplicative Inverse. Returns x such that: (x*e) mod m == 1
"""
x1, x2 = 1, 0
a, b = e, m
while b > 0:
q, r = divmod(a, b)
xn = x1 - q * x2
a, b, x1, x2 = b, r, x2, xn
return x1 % m
def rsa_crt_iqmp(p: int, q: int) -> int:
"""
Compute the CRT (q ** -1) % p value from RSA primes p and q.
"""
return _modinv(q, p)
def rsa_crt_dmp1(private_exponent: int, p: int) -> int:
"""
Compute the CRT private_exponent % (p - 1) value from the RSA
private_exponent (d) and p.
"""
return private_exponent % (p - 1)
def rsa_crt_dmq1(private_exponent: int, q: int) -> int:
"""
Compute the CRT private_exponent % (q - 1) value from the RSA
private_exponent (d) and q.
"""
return private_exponent % (q - 1)
# Controls the number of iterations rsa_recover_prime_factors will perform
# to obtain the prime factors. Each iteration increments by 2 so the actual
# maximum attempts is half this number.
_MAX_RECOVERY_ATTEMPTS = 1000
def rsa_recover_prime_factors(
n: int, e: int, d: int
) -> typing.Tuple[int, int]:
"""
Compute factors p and q from the private exponent d. We assume that n has
no more than two factors. This function is adapted from code in PyCrypto.
"""
# See 8.2.2(i) in Handbook of Applied Cryptography.
ktot = d * e - 1
# The quantity d*e-1 is a multiple of phi(n), even,
# and can be represented as t*2^s.
t = ktot
while t % 2 == 0:
t = t // 2
# Cycle through all multiplicative inverses in Zn.
# The algorithm is non-deterministic, but there is a 50% chance
# any candidate a leads to successful factoring.
# See "Digitalized Signatures and Public Key Functions as Intractable
# as Factorization", M. Rabin, 1979
spotted = False
a = 2
while not spotted and a < _MAX_RECOVERY_ATTEMPTS:
k = t
# Cycle through all values a^{t*2^i}=a^k
while k < ktot:
cand = pow(a, k, n)
# Check if a^k is a non-trivial root of unity (mod n)
if cand != 1 and cand != (n - 1) and pow(cand, 2, n) == 1:
# We have found a number such that (cand-1)(cand+1)=0 (mod n).
# Either of the terms divides n.
p = gcd(cand + 1, n)
spotted = True
break
k *= 2
# This value was not any good... let's try another!
a += 2
if not spotted:
raise ValueError("Unable to compute factors p and q from exponent d.")
# Found !
q, r = divmod(n, p)
assert r == 0
p, q = sorted((p, q), reverse=True)
return (p, q)
class RSAPrivateNumbers:
def __init__(
self,
p: int,
q: int,
d: int,
dmp1: int,
dmq1: int,
iqmp: int,
public_numbers: RSAPublicNumbers,
):
if (
not isinstance(p, int)
or not isinstance(q, int)
or not isinstance(d, int)
or not isinstance(dmp1, int)
or not isinstance(dmq1, int)
or not isinstance(iqmp, int)
):
raise TypeError(
"RSAPrivateNumbers p, q, d, dmp1, dmq1, iqmp arguments must"
" all be an integers."
)
if not isinstance(public_numbers, RSAPublicNumbers):
raise TypeError(
"RSAPrivateNumbers public_numbers must be an RSAPublicNumbers"
" instance."
)
self._p = p
self._q = q
self._d = d
self._dmp1 = dmp1
self._dmq1 = dmq1
self._iqmp = iqmp
self._public_numbers = public_numbers
@property
def p(self) -> int:
return self._p
@property
def q(self) -> int:
return self._q
@property
def d(self) -> int:
return self._d
@property
def dmp1(self) -> int:
return self._dmp1
@property
def dmq1(self) -> int:
return self._dmq1
@property
def iqmp(self) -> int:
return self._iqmp
@property
def public_numbers(self) -> RSAPublicNumbers:
return self._public_numbers
def private_key(
self,
backend: typing.Any = None,
*,
unsafe_skip_rsa_key_validation: bool = False,
) -> RSAPrivateKey:
from cryptography.hazmat.backends.openssl.backend import (
backend as ossl,
)
return ossl.load_rsa_private_numbers(
self, unsafe_skip_rsa_key_validation
)
def __eq__(self, other: object) -> bool:
if not isinstance(other, RSAPrivateNumbers):
return NotImplemented
return (
self.p == other.p
and self.q == other.q
and self.d == other.d
and self.dmp1 == other.dmp1
and self.dmq1 == other.dmq1
and self.iqmp == other.iqmp
and self.public_numbers == other.public_numbers
)
def __hash__(self) -> int:
return hash(
(
self.p,
self.q,
self.d,
self.dmp1,
self.dmq1,
self.iqmp,
self.public_numbers,
)
)
class RSAPublicNumbers:
def __init__(self, e: int, n: int):
if not isinstance(e, int) or not isinstance(n, int):
raise TypeError("RSAPublicNumbers arguments must be integers.")
self._e = e
self._n = n
@property
def e(self) -> int:
return self._e
@property
def n(self) -> int:
return self._n
def public_key(self, backend: typing.Any = None) -> RSAPublicKey:
from cryptography.hazmat.backends.openssl.backend import (
backend as ossl,
)
return ossl.load_rsa_public_numbers(self)
def __repr__(self) -> str:
return "<RSAPublicNumbers(e={0.e}, n={0.n})>".format(self)
def __eq__(self, other: object) -> bool:
if not isinstance(other, RSAPublicNumbers):
return NotImplemented
return self.e == other.e and self.n == other.n
def __hash__(self) -> int:
return hash((self.e, self.n))