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# ===================================================================
#
# Copyright (c) 2014, Legrandin <helderijs@gmail.com>
# 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 sys
from Crypto.Util.py3compat import tobytes, is_native_int
from Crypto.Util._raw_api import (backend, load_lib,
get_raw_buffer, get_c_string,
null_pointer, create_string_buffer,
c_ulong, c_size_t, c_uint8_ptr)
from ._IntegerBase import IntegerBase
gmp_defs = """typedef unsigned long UNIX_ULONG;
typedef struct { int a; int b; void *c; } MPZ;
typedef MPZ mpz_t[1];
typedef UNIX_ULONG mp_bitcnt_t;
void __gmpz_init (mpz_t x);
void __gmpz_init_set (mpz_t rop, const mpz_t op);
void __gmpz_init_set_ui (mpz_t rop, UNIX_ULONG op);
UNIX_ULONG __gmpz_get_ui (const mpz_t op);
void __gmpz_set (mpz_t rop, const mpz_t op);
void __gmpz_set_ui (mpz_t rop, UNIX_ULONG op);
void __gmpz_add (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_add_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_sub_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_addmul (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_addmul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_submul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
void __gmpz_import (mpz_t rop, size_t count, int order, size_t size,
int endian, size_t nails, const void *op);
void * __gmpz_export (void *rop, size_t *countp, int order,
size_t size,
int endian, size_t nails, const mpz_t op);
size_t __gmpz_sizeinbase (const mpz_t op, int base);
void __gmpz_sub (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_mul (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_mul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
int __gmpz_cmp (const mpz_t op1, const mpz_t op2);
void __gmpz_powm (mpz_t rop, const mpz_t base, const mpz_t exp, const
mpz_t mod);
void __gmpz_powm_ui (mpz_t rop, const mpz_t base, UNIX_ULONG exp,
const mpz_t mod);
void __gmpz_pow_ui (mpz_t rop, const mpz_t base, UNIX_ULONG exp);
void __gmpz_sqrt(mpz_t rop, const mpz_t op);
void __gmpz_mod (mpz_t r, const mpz_t n, const mpz_t d);
void __gmpz_neg (mpz_t rop, const mpz_t op);
void __gmpz_abs (mpz_t rop, const mpz_t op);
void __gmpz_and (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_ior (mpz_t rop, const mpz_t op1, const mpz_t op2);
void __gmpz_clear (mpz_t x);
void __gmpz_tdiv_q_2exp (mpz_t q, const mpz_t n, mp_bitcnt_t b);
void __gmpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d);
void __gmpz_mul_2exp (mpz_t rop, const mpz_t op1, mp_bitcnt_t op2);
int __gmpz_tstbit (const mpz_t op, mp_bitcnt_t bit_index);
int __gmpz_perfect_square_p (const mpz_t op);
int __gmpz_jacobi (const mpz_t a, const mpz_t b);
void __gmpz_gcd (mpz_t rop, const mpz_t op1, const mpz_t op2);
UNIX_ULONG __gmpz_gcd_ui (mpz_t rop, const mpz_t op1,
UNIX_ULONG op2);
void __gmpz_lcm (mpz_t rop, const mpz_t op1, const mpz_t op2);
int __gmpz_invert (mpz_t rop, const mpz_t op1, const mpz_t op2);
int __gmpz_divisible_p (const mpz_t n, const mpz_t d);
int __gmpz_divisible_ui_p (const mpz_t n, UNIX_ULONG d);
"""
if sys.platform == "win32":
raise ImportError("Not using GMP on Windows")
lib = load_lib("gmp", gmp_defs)
implementation = {"library": "gmp", "api": backend}
if hasattr(lib, "__mpir_version"):
raise ImportError("MPIR library detected")
# In order to create a function that returns a pointer to
# a new MPZ structure, we need to break the abstraction
# and know exactly what ffi backend we have
if implementation["api"] == "ctypes":
from ctypes import Structure, c_int, c_void_p, byref
class _MPZ(Structure):
_fields_ = [('_mp_alloc', c_int),
('_mp_size', c_int),
('_mp_d', c_void_p)]
def new_mpz():
return byref(_MPZ())
else:
# We are using CFFI
from Crypto.Util._raw_api import ffi
def new_mpz():
return ffi.new("MPZ*")
# Lazy creation of GMP methods
class _GMP(object):
def __getattr__(self, name):
if name.startswith("mpz_"):
func_name = "__gmpz_" + name[4:]
elif name.startswith("gmp_"):
func_name = "__gmp_" + name[4:]
else:
raise AttributeError("Attribute %s is invalid" % name)
func = getattr(lib, func_name)
setattr(self, name, func)
return func
_gmp = _GMP()
class IntegerGMP(IntegerBase):
"""A fast, arbitrary precision integer"""
_zero_mpz_p = new_mpz()
_gmp.mpz_init_set_ui(_zero_mpz_p, c_ulong(0))
def __init__(self, value):
"""Initialize the integer to the given value."""
self._mpz_p = new_mpz()
self._initialized = False
if isinstance(value, float):
raise ValueError("A floating point type is not a natural number")
if is_native_int(value):
_gmp.mpz_init(self._mpz_p)
self._initialized = True
if value == 0:
return
tmp = new_mpz()
_gmp.mpz_init(tmp)
try:
positive = value >= 0
reduce = abs(value)
slots = (reduce.bit_length() - 1) // 32 + 1
while slots > 0:
slots = slots - 1
_gmp.mpz_set_ui(tmp,
c_ulong(0xFFFFFFFF & (reduce >> (slots * 32))))
_gmp.mpz_mul_2exp(tmp, tmp, c_ulong(slots * 32))
_gmp.mpz_add(self._mpz_p, self._mpz_p, tmp)
finally:
_gmp.mpz_clear(tmp)
if not positive:
_gmp.mpz_neg(self._mpz_p, self._mpz_p)
elif isinstance(value, IntegerGMP):
_gmp.mpz_init_set(self._mpz_p, value._mpz_p)
self._initialized = True
else:
raise NotImplementedError
# Conversions
def __int__(self):
tmp = new_mpz()
_gmp.mpz_init_set(tmp, self._mpz_p)
try:
value = 0
slot = 0
while _gmp.mpz_cmp(tmp, self._zero_mpz_p) != 0:
lsb = _gmp.mpz_get_ui(tmp) & 0xFFFFFFFF
value |= lsb << (slot * 32)
_gmp.mpz_tdiv_q_2exp(tmp, tmp, c_ulong(32))
slot = slot + 1
finally:
_gmp.mpz_clear(tmp)
if self < 0:
value = -value
return int(value)
def __str__(self):
return str(int(self))
def __repr__(self):
return "Integer(%s)" % str(self)
# Only Python 2.x
def __hex__(self):
return hex(int(self))
# Only Python 3.x
def __index__(self):
return int(self)
def to_bytes(self, block_size=0, byteorder='big'):
"""Convert the number into a byte string.
This method encodes the number in network order and prepends
as many zero bytes as required. It only works for non-negative
values.
:Parameters:
block_size : integer
The exact size the output byte string must have.
If zero, the string has the minimal length.
byteorder : string
'big' for big-endian integers (default), 'little' for litte-endian.
:Returns:
A byte string.
:Raise ValueError:
If the value is negative or if ``block_size`` is
provided and the length of the byte string would exceed it.
"""
if self < 0:
raise ValueError("Conversion only valid for non-negative numbers")
buf_len = (_gmp.mpz_sizeinbase(self._mpz_p, 2) + 7) // 8
if buf_len > block_size > 0:
raise ValueError("Number is too big to convert to byte string"
" of prescribed length")
buf = create_string_buffer(buf_len)
_gmp.mpz_export(
buf,
null_pointer, # Ignore countp
1, # Big endian
c_size_t(1), # Each word is 1 byte long
0, # Endianess within a word - not relevant
c_size_t(0), # No nails
self._mpz_p)
result = b'\x00' * max(0, block_size - buf_len) + get_raw_buffer(buf)
if byteorder == 'big':
pass
elif byteorder == 'little':
result = bytearray(result)
result.reverse()
result = bytes(result)
else:
raise ValueError("Incorrect byteorder")
return result
@staticmethod
def from_bytes(byte_string, byteorder='big'):
"""Convert a byte string into a number.
:Parameters:
byte_string : byte string
The input number, encoded in network order.
It can only be non-negative.
byteorder : string
'big' for big-endian integers (default), 'little' for litte-endian.
:Return:
The ``Integer`` object carrying the same value as the input.
"""
result = IntegerGMP(0)
if byteorder == 'big':
pass
elif byteorder == 'little':
byte_string = bytearray(byte_string)
byte_string.reverse()
else:
raise ValueError("Incorrect byteorder")
_gmp.mpz_import(
result._mpz_p,
c_size_t(len(byte_string)), # Amount of words to read
1, # Big endian
c_size_t(1), # Each word is 1 byte long
0, # Endianess within a word - not relevant
c_size_t(0), # No nails
c_uint8_ptr(byte_string))
return result
# Relations
def _apply_and_return(self, func, term):
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
return func(self._mpz_p, term._mpz_p)
def __eq__(self, term):
if not (isinstance(term, IntegerGMP) or is_native_int(term)):
return False
return self._apply_and_return(_gmp.mpz_cmp, term) == 0
def __ne__(self, term):
if not (isinstance(term, IntegerGMP) or is_native_int(term)):
return True
return self._apply_and_return(_gmp.mpz_cmp, term) != 0
def __lt__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) < 0
def __le__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) <= 0
def __gt__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) > 0
def __ge__(self, term):
return self._apply_and_return(_gmp.mpz_cmp, term) >= 0
def __nonzero__(self):
return _gmp.mpz_cmp(self._mpz_p, self._zero_mpz_p) != 0
__bool__ = __nonzero__
def is_negative(self):
return _gmp.mpz_cmp(self._mpz_p, self._zero_mpz_p) < 0
# Arithmetic operations
def __add__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
try:
term = IntegerGMP(term)
except NotImplementedError:
return NotImplemented
_gmp.mpz_add(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __sub__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
try:
term = IntegerGMP(term)
except NotImplementedError:
return NotImplemented
_gmp.mpz_sub(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __mul__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
try:
term = IntegerGMP(term)
except NotImplementedError:
return NotImplemented
_gmp.mpz_mul(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __floordiv__(self, divisor):
if not isinstance(divisor, IntegerGMP):
divisor = IntegerGMP(divisor)
if _gmp.mpz_cmp(divisor._mpz_p,
self._zero_mpz_p) == 0:
raise ZeroDivisionError("Division by zero")
result = IntegerGMP(0)
_gmp.mpz_fdiv_q(result._mpz_p,
self._mpz_p,
divisor._mpz_p)
return result
def __mod__(self, divisor):
if not isinstance(divisor, IntegerGMP):
divisor = IntegerGMP(divisor)
comp = _gmp.mpz_cmp(divisor._mpz_p,
self._zero_mpz_p)
if comp == 0:
raise ZeroDivisionError("Division by zero")
if comp < 0:
raise ValueError("Modulus must be positive")
result = IntegerGMP(0)
_gmp.mpz_mod(result._mpz_p,
self._mpz_p,
divisor._mpz_p)
return result
def inplace_pow(self, exponent, modulus=None):
if modulus is None:
if exponent < 0:
raise ValueError("Exponent must not be negative")
# Normal exponentiation
if exponent > 256:
raise ValueError("Exponent is too big")
_gmp.mpz_pow_ui(self._mpz_p,
self._mpz_p, # Base
c_ulong(int(exponent))
)
else:
# Modular exponentiation
if not isinstance(modulus, IntegerGMP):
modulus = IntegerGMP(modulus)
if not modulus:
raise ZeroDivisionError("Division by zero")
if modulus.is_negative():
raise ValueError("Modulus must be positive")
if is_native_int(exponent):
if exponent < 0:
raise ValueError("Exponent must not be negative")
if exponent < 65536:
_gmp.mpz_powm_ui(self._mpz_p,
self._mpz_p,
c_ulong(exponent),
modulus._mpz_p)
return self
exponent = IntegerGMP(exponent)
elif exponent.is_negative():
raise ValueError("Exponent must not be negative")
_gmp.mpz_powm(self._mpz_p,
self._mpz_p,
exponent._mpz_p,
modulus._mpz_p)
return self
def __pow__(self, exponent, modulus=None):
result = IntegerGMP(self)
return result.inplace_pow(exponent, modulus)
def __abs__(self):
result = IntegerGMP(0)
_gmp.mpz_abs(result._mpz_p, self._mpz_p)
return result
def sqrt(self, modulus=None):
"""Return the largest Integer that does not
exceed the square root"""
if modulus is None:
if self < 0:
raise ValueError("Square root of negative value")
result = IntegerGMP(0)
_gmp.mpz_sqrt(result._mpz_p,
self._mpz_p)
else:
if modulus <= 0:
raise ValueError("Modulus must be positive")
modulus = int(modulus)
result = IntegerGMP(self._tonelli_shanks(int(self) % modulus, modulus))
return result
def __iadd__(self, term):
if is_native_int(term):
if 0 <= term < 65536:
_gmp.mpz_add_ui(self._mpz_p,
self._mpz_p,
c_ulong(term))
return self
if -65535 < term < 0:
_gmp.mpz_sub_ui(self._mpz_p,
self._mpz_p,
c_ulong(-term))
return self
term = IntegerGMP(term)
_gmp.mpz_add(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __isub__(self, term):
if is_native_int(term):
if 0 <= term < 65536:
_gmp.mpz_sub_ui(self._mpz_p,
self._mpz_p,
c_ulong(term))
return self
if -65535 < term < 0:
_gmp.mpz_add_ui(self._mpz_p,
self._mpz_p,
c_ulong(-term))
return self
term = IntegerGMP(term)
_gmp.mpz_sub(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __imul__(self, term):
if is_native_int(term):
if 0 <= term < 65536:
_gmp.mpz_mul_ui(self._mpz_p,
self._mpz_p,
c_ulong(term))
return self
if -65535 < term < 0:
_gmp.mpz_mul_ui(self._mpz_p,
self._mpz_p,
c_ulong(-term))
_gmp.mpz_neg(self._mpz_p, self._mpz_p)
return self
term = IntegerGMP(term)
_gmp.mpz_mul(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __imod__(self, divisor):
if not isinstance(divisor, IntegerGMP):
divisor = IntegerGMP(divisor)
comp = _gmp.mpz_cmp(divisor._mpz_p,
divisor._zero_mpz_p)
if comp == 0:
raise ZeroDivisionError("Division by zero")
if comp < 0:
raise ValueError("Modulus must be positive")
_gmp.mpz_mod(self._mpz_p,
self._mpz_p,
divisor._mpz_p)
return self
# Boolean/bit operations
def __and__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
_gmp.mpz_and(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __or__(self, term):
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
_gmp.mpz_ior(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __rshift__(self, pos):
result = IntegerGMP(0)
if pos < 0:
raise ValueError("negative shift count")
if pos > 65536:
if self < 0:
return -1
else:
return 0
_gmp.mpz_tdiv_q_2exp(result._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return result
def __irshift__(self, pos):
if pos < 0:
raise ValueError("negative shift count")
if pos > 65536:
if self < 0:
return -1
else:
return 0
_gmp.mpz_tdiv_q_2exp(self._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return self
def __lshift__(self, pos):
result = IntegerGMP(0)
if not 0 <= pos < 65536:
raise ValueError("Incorrect shift count")
_gmp.mpz_mul_2exp(result._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return result
def __ilshift__(self, pos):
if not 0 <= pos < 65536:
raise ValueError("Incorrect shift count")
_gmp.mpz_mul_2exp(self._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return self
def get_bit(self, n):
"""Return True if the n-th bit is set to 1.
Bit 0 is the least significant."""
if self < 0:
raise ValueError("no bit representation for negative values")
if n < 0:
raise ValueError("negative bit count")
if n > 65536:
return 0
return bool(_gmp.mpz_tstbit(self._mpz_p,
c_ulong(int(n))))
# Extra
def is_odd(self):
return _gmp.mpz_tstbit(self._mpz_p, 0) == 1
def is_even(self):
return _gmp.mpz_tstbit(self._mpz_p, 0) == 0
def size_in_bits(self):
"""Return the minimum number of bits that can encode the number."""
if self < 0:
raise ValueError("Conversion only valid for non-negative numbers")
return _gmp.mpz_sizeinbase(self._mpz_p, 2)
def size_in_bytes(self):
"""Return the minimum number of bytes that can encode the number."""
return (self.size_in_bits() - 1) // 8 + 1
def is_perfect_square(self):
return _gmp.mpz_perfect_square_p(self._mpz_p) != 0
def fail_if_divisible_by(self, small_prime):
"""Raise an exception if the small prime is a divisor."""
if is_native_int(small_prime):
if 0 < small_prime < 65536:
if _gmp.mpz_divisible_ui_p(self._mpz_p,
c_ulong(small_prime)):
raise ValueError("The value is composite")
return
small_prime = IntegerGMP(small_prime)
if _gmp.mpz_divisible_p(self._mpz_p,
small_prime._mpz_p):
raise ValueError("The value is composite")
def multiply_accumulate(self, a, b):
"""Increment the number by the product of a and b."""
if not isinstance(a, IntegerGMP):
a = IntegerGMP(a)
if is_native_int(b):
if 0 < b < 65536:
_gmp.mpz_addmul_ui(self._mpz_p,
a._mpz_p,
c_ulong(b))
return self
if -65535 < b < 0:
_gmp.mpz_submul_ui(self._mpz_p,
a._mpz_p,
c_ulong(-b))
return self
b = IntegerGMP(b)
_gmp.mpz_addmul(self._mpz_p,
a._mpz_p,
b._mpz_p)
return self
def set(self, source):
"""Set the Integer to have the given value"""
if not isinstance(source, IntegerGMP):
source = IntegerGMP(source)
_gmp.mpz_set(self._mpz_p,
source._mpz_p)
return self
def inplace_inverse(self, modulus):
"""Compute the inverse of this number in the ring of
modulo integers.
Raise an exception if no inverse exists.
"""
if not isinstance(modulus, IntegerGMP):
modulus = IntegerGMP(modulus)
comp = _gmp.mpz_cmp(modulus._mpz_p,
self._zero_mpz_p)
if comp == 0:
raise ZeroDivisionError("Modulus cannot be zero")
if comp < 0:
raise ValueError("Modulus must be positive")
result = _gmp.mpz_invert(self._mpz_p,
self._mpz_p,
modulus._mpz_p)
if not result:
raise ValueError("No inverse value can be computed")
return self
def inverse(self, modulus):
result = IntegerGMP(self)
result.inplace_inverse(modulus)
return result
def gcd(self, term):
"""Compute the greatest common denominator between this
number and another term."""
result = IntegerGMP(0)
if is_native_int(term):
if 0 < term < 65535:
_gmp.mpz_gcd_ui(result._mpz_p,
self._mpz_p,
c_ulong(term))
return result
term = IntegerGMP(term)
_gmp.mpz_gcd(result._mpz_p, self._mpz_p, term._mpz_p)
return result
def lcm(self, term):
"""Compute the least common multiplier between this
number and another term."""
result = IntegerGMP(0)
if not isinstance(term, IntegerGMP):
term = IntegerGMP(term)
_gmp.mpz_lcm(result._mpz_p, self._mpz_p, term._mpz_p)
return result
@staticmethod
def jacobi_symbol(a, n):
"""Compute the Jacobi symbol"""
if not isinstance(a, IntegerGMP):
a = IntegerGMP(a)
if not isinstance(n, IntegerGMP):
n = IntegerGMP(n)
if n <= 0 or n.is_even():
raise ValueError("n must be positive odd for the Jacobi symbol")
return _gmp.mpz_jacobi(a._mpz_p, n._mpz_p)
# Clean-up
def __del__(self):
try:
if self._mpz_p is not None:
if self._initialized:
_gmp.mpz_clear(self._mpz_p)
self._mpz_p = None
except AttributeError:
pass
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