# ===================================================================
#
# Copyright (c) 2018, Helder Eijs <[email protected]>
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in
# the documentation and/or other materials provided with the
# distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
# ===================================================================
import abc
from Cryptodome.Util.py3compat import iter_range, bord, bchr, ABC
from Cryptodome import Random
class IntegerBase(ABC):
# Conversions
@abc.abstractmethod
def __int__(self):
pass
@abc.abstractmethod
def __str__(self):
pass
@abc.abstractmethod
def __repr__(self):
pass
@abc.abstractmethod
def to_bytes(self, block_size=0, byteorder='big'):
pass
@staticmethod
@abc.abstractmethod
def from_bytes(byte_string, byteorder='big'):
pass
# Relations
@abc.abstractmethod
def __eq__(self, term):
pass
@abc.abstractmethod
def __ne__(self, term):
pass
@abc.abstractmethod
def __lt__(self, term):
pass
@abc.abstractmethod
def __le__(self, term):
pass
@abc.abstractmethod
def __gt__(self, term):
pass
@abc.abstractmethod
def __ge__(self, term):
pass
@abc.abstractmethod
def __nonzero__(self):
pass
__bool__ = __nonzero__
@abc.abstractmethod
def is_negative(self):
pass
# Arithmetic operations
@abc.abstractmethod
def __add__(self, term):
pass
@abc.abstractmethod
def __sub__(self, term):
pass
@abc.abstractmethod
def __mul__(self, factor):
pass
@abc.abstractmethod
def __floordiv__(self, divisor):
pass
@abc.abstractmethod
def __mod__(self, divisor):
pass
@abc.abstractmethod
def inplace_pow(self, exponent, modulus=None):
pass
@abc.abstractmethod
def __pow__(self, exponent, modulus=None):
pass
@abc.abstractmethod
def __abs__(self):
pass
@abc.abstractmethod
def sqrt(self, modulus=None):
pass
@abc.abstractmethod
def __iadd__(self, term):
pass
@abc.abstractmethod
def __isub__(self, term):
pass
@abc.abstractmethod
def __imul__(self, term):
pass
@abc.abstractmethod
def __imod__(self, term):
pass
# Boolean/bit operations
@abc.abstractmethod
def __and__(self, term):
pass
@abc.abstractmethod
def __or__(self, term):
pass
@abc.abstractmethod
def __rshift__(self, pos):
pass
@abc.abstractmethod
def __irshift__(self, pos):
pass
@abc.abstractmethod
def __lshift__(self, pos):
pass
@abc.abstractmethod
def __ilshift__(self, pos):
pass
@abc.abstractmethod
def get_bit(self, n):
pass
# Extra
@abc.abstractmethod
def is_odd(self):
pass
@abc.abstractmethod
def is_even(self):
pass
@abc.abstractmethod
def size_in_bits(self):
pass
@abc.abstractmethod
def size_in_bytes(self):
pass
@abc.abstractmethod
def is_perfect_square(self):
pass
@abc.abstractmethod
def fail_if_divisible_by(self, small_prime):
pass
@abc.abstractmethod
def multiply_accumulate(self, a, b):
pass
@abc.abstractmethod
def set(self, source):
pass
@abc.abstractmethod
def inplace_inverse(self, modulus):
pass
@abc.abstractmethod
def inverse(self, modulus):
pass
@abc.abstractmethod
def gcd(self, term):
pass
@abc.abstractmethod
def lcm(self, term):
pass
@staticmethod
@abc.abstractmethod
def jacobi_symbol(a, n):
pass
@staticmethod
def _tonelli_shanks(n, p):
"""Tonelli-shanks algorithm for computing the square root
of n modulo a prime p.
n must be in the range [0..p-1].
p must be at least even.
The return value r is the square root of modulo p. If non-zero,
another solution will also exist (p-r).
Note we cannot assume that p is really a prime: if it's not,
we can either raise an exception or return the correct value.
"""
# See https://rosettacode.org/wiki/Tonelli-Shanks_algorithm
if n in (0, 1):
return n
if p % 4 == 3:
root = pow(n, (p + 1) // 4, p)
if pow(root, 2, p) != n:
raise ValueError("Cannot compute square root")
return root
s = 1
q = (p - 1) // 2
while not (q & 1):
s += 1
q >>= 1
z = n.__class__(2)
while True:
euler = pow(z, (p - 1) // 2, p)
if euler == 1:
z += 1
continue
if euler == p - 1:
break
# Most probably p is not a prime
raise ValueError("Cannot compute square root")
m = s
c = pow(z, q, p)
t = pow(n, q, p)
r = pow(n, (q + 1) // 2, p)
while t != 1:
for i in iter_range(0, m):
if pow(t, 2**i, p) == 1:
break
if i == m:
raise ValueError("Cannot compute square root of %d mod %d" % (n, p))
b = pow(c, 2**(m - i - 1), p)
m = i
c = b**2 % p
t = (t * b**2) % p
r = (r * b) % p
if pow(r, 2, p) != n:
raise ValueError("Cannot compute square root")
return r
@classmethod
def random(cls, **kwargs):
"""Generate a random natural integer of a certain size.
:Keywords:
exact_bits : positive integer
The length in bits of the resulting random Integer number.
The number is guaranteed to fulfil the relation:
2^bits > result >= 2^(bits - 1)
max_bits : positive integer
The maximum length in bits of the resulting random Integer number.
The number is guaranteed to fulfil the relation:
2^bits > result >=0
randfunc : callable
A function that returns a random byte string. The length of the
byte string is passed as parameter. Optional.
If not provided (or ``None``), randomness is read from the system RNG.
:Return: a Integer object
"""
exact_bits = kwargs.pop("exact_bits", None)
max_bits = kwargs.pop("max_bits", None)
randfunc = kwargs.pop("randfunc", None)
if randfunc is None:
randfunc = Random.new().read
if exact_bits is None and max_bits is None:
raise ValueError("Either 'exact_bits' or 'max_bits' must be specified")
if exact_bits is not None and max_bits is not None:
raise ValueError("'exact_bits' and 'max_bits' are mutually exclusive")
bits = exact_bits or max_bits
bytes_needed = ((bits - 1) // 8) + 1
significant_bits_msb = 8 - (bytes_needed * 8 - bits)
msb = bord(randfunc(1)[0])
if exact_bits is not None:
msb |= 1 << (significant_bits_msb - 1)
msb &= (1 << significant_bits_msb) - 1
return cls.from_bytes(bchr(msb) + randfunc(bytes_needed - 1))
@classmethod
def random_range(cls, **kwargs):
"""Generate a random integer within a given internal.
:Keywords:
min_inclusive : integer
The lower end of the interval (inclusive).
max_inclusive : integer
The higher end of the interval (inclusive).
max_exclusive : integer
The higher end of the interval (exclusive).
randfunc : callable
A function that returns a random byte string. The length of the
byte string is passed as parameter. Optional.
If not provided (or ``None``), randomness is read from the system RNG.
:Returns:
An Integer randomly taken in the given interval.
"""
min_inclusive = kwargs.pop("min_inclusive", None)
max_inclusive = kwargs.pop("max_inclusive", None)
max_exclusive = kwargs.pop("max_exclusive", None)
randfunc = kwargs.pop("randfunc", None)
if kwargs:
raise ValueError("Unknown keywords: " + str(kwargs.keys))
if None not in (max_inclusive, max_exclusive):
raise ValueError("max_inclusive and max_exclusive cannot be both"
" specified")
if max_exclusive is not None:
max_inclusive = max_exclusive - 1
if None in (min_inclusive, max_inclusive):
raise ValueError("Missing keyword to identify the interval")
if randfunc is None:
randfunc = Random.new().read
norm_maximum = max_inclusive - min_inclusive
bits_needed = cls(norm_maximum).size_in_bits()
norm_candidate = -1
while not 0 <= norm_candidate <= norm_maximum:
norm_candidate = cls.random(
max_bits=bits_needed,
randfunc=randfunc
)
return norm_candidate + min_inclusive
@staticmethod
@abc.abstractmethod
def _mult_modulo_bytes(term1, term2, modulus):
"""Multiply two integers, take the modulo, and encode as big endian.
This specialized method is used for RSA decryption.
Args:
term1 : integer
The first term of the multiplication, non-negative.
term2 : integer
The second term of the multiplication, non-negative.
modulus: integer
The modulus, a positive odd number.
:Returns:
A byte string, with the result of the modular multiplication
encoded in big endian mode.
It is as long as the modulus would be, with zero padding
on the left if needed.
"""
pass