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pycryptodome/lib/Crypto/Math/_Numbers_gmp.py
Legrandin 1cca0ff6c1 Add Integer.lcm() method
2015-03-05 21:54:07 +01:00

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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.
# ===================================================================
from Crypto.Util.py3compat import tobytes, b, bchr
from Crypto.Util._raw_api import (backend, load_lib,
get_raw_buffer, get_c_string,
null_pointer, create_string_buffer,
c_ulong, c_ulonglong, c_size_t)
# GMP uses unsigned longs in several functions prototypes.
# On a UNIX 64 bit platform that type takes 64 bits but in Windows 64
# it is still 32 bits.
# The intention of the MPIR developers is to maintain binary compatibility
# so they probably assumed that that GMP would compile on Windows 64
# by treating it as a UNIX platform.
gmp_defs_common = """
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);
int __gmp_sscanf (const char *s, const char *fmt, ...);
void __gmpz_set (mpz_t rop, const mpz_t op);
int __gmp_snprintf (char *buf, size_t size, const char *fmt, ...);
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);
"""
try:
gmp_defs = "typedef unsigned long UNIX_ULONG;" + gmp_defs_common
lib = load_lib("gmp", gmp_defs)
implementation = { "library":"gmp", "api":backend }
except OSError:
import platform
bits, linkage = platform.architecture()
if bits.startswith("64") and linkage.startswith("Win"):
# MPIR uses unsigned long long where GMP uses unsigned long
# (LLP64 vs LP64)
gmp_defs = "typedef unsigned long long UNIX_ULONG;" + gmp_defs_common
c_ulong = c_ulonglong
lib = load_lib("mpir", gmp_defs)
implementation = { "library":"mpir", "api":backend }
# 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*")
# Unfortunately, all symbols exported by the GMP library start with "__"
# and have no trailing underscore.
# You cannot directly refer to them as members of the ctypes' library
# object from within any class because Python will replace the double
# underscore with "_classname_".
class _GMP(object):
pass
_gmp = _GMP()
_gmp = _GMP()
_gmp.mpz_init = lib.__gmpz_init
_gmp.mpz_init_set = lib.__gmpz_init_set
_gmp.mpz_init_set_ui = lib.__gmpz_init_set_ui
_gmp.mpz_set = lib.__gmpz_set
_gmp.gmp_snprintf = lib.__gmp_snprintf
_gmp.gmp_sscanf = lib.__gmp_sscanf
_gmp.mpz_add = lib.__gmpz_add
_gmp.mpz_add_ui = lib.__gmpz_add_ui
_gmp.mpz_sub_ui = lib.__gmpz_sub_ui
_gmp.mpz_addmul = lib.__gmpz_addmul
_gmp.mpz_addmul_ui = lib.__gmpz_addmul_ui
_gmp.mpz_submul_ui = lib.__gmpz_submul_ui
_gmp.mpz_import = lib.__gmpz_import
_gmp.mpz_export = lib.__gmpz_export
_gmp.mpz_sizeinbase = lib.__gmpz_sizeinbase
_gmp.mpz_sub = lib.__gmpz_sub
_gmp.mpz_mul = lib.__gmpz_mul
_gmp.mpz_mul_ui = lib.__gmpz_mul_ui
_gmp.mpz_cmp = lib.__gmpz_cmp
_gmp.mpz_powm = lib.__gmpz_powm
_gmp.mpz_powm_ui = lib.__gmpz_powm_ui
_gmp.mpz_pow_ui = lib.__gmpz_pow_ui
_gmp.mpz_sqrt = lib.__gmpz_sqrt
_gmp.mpz_mod = lib.__gmpz_mod
_gmp.mpz_neg = lib.__gmpz_neg
_gmp.mpz_abs = lib.__gmpz_abs
_gmp.mpz_and = lib.__gmpz_and
_gmp.mpz_ior = lib.__gmpz_ior
_gmp.mpz_clear = lib.__gmpz_clear
_gmp.mpz_tdiv_q_2exp = lib.__gmpz_tdiv_q_2exp
_gmp.mpz_fdiv_q = lib.__gmpz_fdiv_q
_gmp.mpz_mul_2exp = lib.__gmpz_mul_2exp
_gmp.mpz_tstbit = lib.__gmpz_tstbit
_gmp.mpz_perfect_square_p = lib.__gmpz_perfect_square_p
_gmp.mpz_jacobi = lib.__gmpz_jacobi
_gmp.mpz_gcd = lib.__gmpz_gcd
_gmp.mpz_gcd_ui = lib.__gmpz_gcd_ui
_gmp.mpz_lcm = lib.__gmpz_lcm
_gmp.mpz_invert = lib.__gmpz_invert
_gmp.mpz_divisible_p = lib.__gmpz_divisible_p
_gmp.mpz_divisible_ui_p = lib.__gmpz_divisible_ui_p
class Integer(object):
_zero_mpz_p = new_mpz()
_gmp.mpz_init_set_ui(_zero_mpz_p, c_ulong(0))
def __init__(self, value):
self._mpz_p = new_mpz()
self._initialized = False
if isinstance(value, float):
raise ValueError("A floating point type is not a natural number")
self._initialized = True
if isinstance(value, (int, long)):
_gmp.mpz_init(self._mpz_p)
result = _gmp.gmp_sscanf(tobytes(str(value)), b("%Zd"), self._mpz_p)
if result != 1:
raise ValueError("Error converting '%d'" % value)
else:
_gmp.mpz_init_set(self._mpz_p, value._mpz_p)
# Conversions
def __int__(self):
# buf will contain the integer encoded in decimal plus the trailing
# zero, and possibly the negative sign.
# dig10(x) < log10(x) + 1 = log2(x)/log2(10) + 1 < log2(x)/3 + 1
buf_len = _gmp.mpz_sizeinbase(self._mpz_p, 2) // 3 + 3
buf = create_string_buffer(buf_len)
_gmp.gmp_snprintf(buf, c_size_t(buf_len), b("%Zd"), self._mpz_p)
return int(get_c_string(buf))
def __str__(self):
return str(int(self))
def __repr__(self):
return "Integer(%s)" % str(self)
def to_bytes(self, block_size=0):
"""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.
:Returns:
A byte string.
:Raises:
``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)
return bchr(0) * max(0, block_size - buf_len) + get_raw_buffer(buf)
@staticmethod
def from_bytes(byte_string):
"""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.
:Return:
The ``Integer`` object carrying the same value as the input.
"""
result = Integer(0)
_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
byte_string)
return result
# Relations
def _apply_and_return(self, func, term):
if not isinstance(term, Integer):
term = Integer(term)
return func(self._mpz_p, term._mpz_p)
def __eq__(self, term):
if not isinstance(term, (Integer, int, long)):
return False
return self._apply_and_return(_gmp.mpz_cmp, term) == 0
def __ne__(self, term):
if not isinstance(term, (Integer, int, long)):
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
def is_negative(self):
return _gmp.mpz_cmp(self._mpz_p, self._zero_mpz_p) < 0
# Arithmetic operations
def __add__(self, term):
result = Integer(0)
if not isinstance(term, Integer):
term = Integer(term)
_gmp.mpz_add(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __sub__(self, term):
result = Integer(0)
if not isinstance(term, Integer):
term = Integer(term)
_gmp.mpz_sub(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __mul__(self, term):
result = Integer(0)
if not isinstance(term, Integer):
term = Integer(term)
_gmp.mpz_mul(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __floordiv__(self, divisor):
if not isinstance(divisor, Integer):
divisor = Integer(divisor)
if _gmp.mpz_cmp(divisor._mpz_p,
self._zero_mpz_p) == 0:
raise ZeroDivisionError("Division by zero")
result = Integer(0)
_gmp.mpz_fdiv_q(result._mpz_p,
self._mpz_p,
divisor._mpz_p)
return result
def __mod__(self, divisor):
if not isinstance(divisor, Integer):
divisor = Integer(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 = Integer(0)
_gmp.mpz_mod(result._mpz_p,
self._mpz_p,
divisor._mpz_p)
return result
def __pow__(self, exponent, modulus=None):
result = Integer(0)
if modulus is None:
if exponent < 0:
raise ValueError("Exponent must not be negative")
# Normal exponentiation
result = Integer(0)
if exponent > 256:
raise ValueError("Exponent is too big")
_gmp.mpz_pow_ui(result._mpz_p,
self._mpz_p, # Base
c_ulong(int(exponent))
)
return result
else:
# Modular exponentiation
if not isinstance(modulus, Integer):
modulus = Integer(modulus)
if not modulus:
raise ZeroDivisionError("Division by zero")
if modulus.is_negative():
raise ValueError("Modulus must be positive")
if isinstance(exponent, (int, long)):
if exponent < 0:
raise ValueError("Exponent must not be negative")
if exponent < 65536:
_gmp.mpz_powm_ui(result._mpz_p,
self._mpz_p,
c_ulong(exponent),
modulus._mpz_p)
return result
exponent = Integer(exponent)
elif exponent.is_negative():
raise ValueError("Exponent must not be negative")
_gmp.mpz_powm(result._mpz_p,
self._mpz_p,
exponent._mpz_p,
modulus._mpz_p)
return result
def __abs__(self):
result = Integer(0)
_gmp.mpz_abs(result._mpz_p, self._mpz_p)
return result
def sqrt(self):
if self < 0:
raise ValueError("Square root of negative value")
result = Integer(0)
_gmp.mpz_sqrt(result._mpz_p,
self._mpz_p)
return result
def __iadd__(self, term):
if isinstance(term, (int, long)):
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 = Integer(term)
_gmp.mpz_add(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __imul__(self, term):
if isinstance(term, (int, long)):
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 = Integer(term)
_gmp.mpz_mul(self._mpz_p,
self._mpz_p,
term._mpz_p)
return self
def __imod__(self, divisor):
if not isinstance(divisor, Integer):
divisor = Integer(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 = Integer(0)
if not isinstance(term, Integer):
term = Integer(term)
_gmp.mpz_and(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __or__(self, term):
result = Integer(0)
if not isinstance(term, Integer):
term = Integer(term)
_gmp.mpz_ior(result._mpz_p,
self._mpz_p,
term._mpz_p)
return result
def __rshift__(self, pos):
result = Integer(0)
if not 0 <= pos < 65536:
raise ValueError("Incorrect shift count")
_gmp.mpz_tdiv_q_2exp(result._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return result
def __irshift__(self, pos):
if not 0 <= pos < 65536:
raise ValueError("Incorrect shift count")
_gmp.mpz_tdiv_q_2exp(self._mpz_p,
self._mpz_p,
c_ulong(int(pos)))
return self
def __lshift__(self, pos):
result = Integer(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 not 0 <= n < 65536:
raise ValueError("Incorrect bit position")
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 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 isinstance(small_prime, (int, long)):
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 = Integer(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, Integer):
a = Integer(a)
if isinstance(b, (int, long)):
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 = Integer(b)
_gmp.mpz_addmul(self._mpz_p,
a._mpz_p,
b._mpz_p)
return self
def set(self, source):
if not isinstance(source, Integer):
source = Integer(source)
_gmp.mpz_set(self._mpz_p,
source._mpz_p)
return self
def 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, Integer):
modulus = Integer(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 = Integer(0)
_gmp.mpz_invert(result._mpz_p,
self._mpz_p,
modulus._mpz_p)
if not result:
raise ValueError("No inverse value can be computed")
return result
def gcd(self, term):
"""Compute the greatest common denominator between this
number and another term."""
result = Integer(0)
if isinstance(term, (int, long)):
if 0 < term < 65535:
_gmp.mpz_gcd_ui(result._mpz_p,
self._mpz_p,
c_ulong(term))
return result
term = Integer(term)
_gmp.mpz_gcd(result._mpz_p, self._mpz_p, term._mpz_p)
return result
def lcm(self, term):
result = Integer(0)
if not isinstance(term, Integer):
term = Integer(term)
_gmp.mpz_lcm(result._mpz_p, self._mpz_p, term._mpz_p)
return result
@staticmethod
def jacobi_symbol(a, n):
if not isinstance(a, Integer):
a = Integer(a)
if not isinstance(n, Integer):
n = Integer(n)
if n <= 0 or n.is_even():
raise ValueError("n must be positive even 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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