783 lines
27 KiB
Python
783 lines
27 KiB
Python
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# ===================================================================
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#
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# Copyright (c) 2014, Legrandin <helderijs@gmail.com>
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions
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# are met:
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#
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# 1. Redistributions of source code must retain the above copyright
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# notice, this list of conditions and the following disclaimer.
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# 2. Redistributions in binary form must reproduce the above copyright
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# notice, this list of conditions and the following disclaimer in
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# the documentation and/or other materials provided with the
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# distribution.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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# POSSIBILITY OF SUCH DAMAGE.
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# ===================================================================
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import sys
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from Cryptodome.Util.py3compat import tobytes, is_native_int
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from Cryptodome.Util._raw_api import (backend, load_lib,
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get_raw_buffer, get_c_string,
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null_pointer, create_string_buffer,
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c_ulong, c_size_t, c_uint8_ptr)
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from ._IntegerBase import IntegerBase
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gmp_defs = """typedef unsigned long UNIX_ULONG;
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typedef struct { int a; int b; void *c; } MPZ;
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typedef MPZ mpz_t[1];
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typedef UNIX_ULONG mp_bitcnt_t;
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void __gmpz_init (mpz_t x);
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void __gmpz_init_set (mpz_t rop, const mpz_t op);
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void __gmpz_init_set_ui (mpz_t rop, UNIX_ULONG op);
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UNIX_ULONG __gmpz_get_ui (const mpz_t op);
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void __gmpz_set (mpz_t rop, const mpz_t op);
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void __gmpz_set_ui (mpz_t rop, UNIX_ULONG op);
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void __gmpz_add (mpz_t rop, const mpz_t op1, const mpz_t op2);
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void __gmpz_add_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
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void __gmpz_sub_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
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void __gmpz_addmul (mpz_t rop, const mpz_t op1, const mpz_t op2);
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void __gmpz_addmul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
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void __gmpz_submul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
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void __gmpz_import (mpz_t rop, size_t count, int order, size_t size,
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int endian, size_t nails, const void *op);
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void * __gmpz_export (void *rop, size_t *countp, int order,
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size_t size,
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int endian, size_t nails, const mpz_t op);
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size_t __gmpz_sizeinbase (const mpz_t op, int base);
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void __gmpz_sub (mpz_t rop, const mpz_t op1, const mpz_t op2);
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void __gmpz_mul (mpz_t rop, const mpz_t op1, const mpz_t op2);
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void __gmpz_mul_ui (mpz_t rop, const mpz_t op1, UNIX_ULONG op2);
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int __gmpz_cmp (const mpz_t op1, const mpz_t op2);
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void __gmpz_powm (mpz_t rop, const mpz_t base, const mpz_t exp, const
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mpz_t mod);
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void __gmpz_powm_ui (mpz_t rop, const mpz_t base, UNIX_ULONG exp,
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const mpz_t mod);
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void __gmpz_pow_ui (mpz_t rop, const mpz_t base, UNIX_ULONG exp);
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void __gmpz_sqrt(mpz_t rop, const mpz_t op);
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void __gmpz_mod (mpz_t r, const mpz_t n, const mpz_t d);
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void __gmpz_neg (mpz_t rop, const mpz_t op);
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void __gmpz_abs (mpz_t rop, const mpz_t op);
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void __gmpz_and (mpz_t rop, const mpz_t op1, const mpz_t op2);
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void __gmpz_ior (mpz_t rop, const mpz_t op1, const mpz_t op2);
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void __gmpz_clear (mpz_t x);
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void __gmpz_tdiv_q_2exp (mpz_t q, const mpz_t n, mp_bitcnt_t b);
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void __gmpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d);
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void __gmpz_mul_2exp (mpz_t rop, const mpz_t op1, mp_bitcnt_t op2);
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int __gmpz_tstbit (const mpz_t op, mp_bitcnt_t bit_index);
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int __gmpz_perfect_square_p (const mpz_t op);
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int __gmpz_jacobi (const mpz_t a, const mpz_t b);
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void __gmpz_gcd (mpz_t rop, const mpz_t op1, const mpz_t op2);
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UNIX_ULONG __gmpz_gcd_ui (mpz_t rop, const mpz_t op1,
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UNIX_ULONG op2);
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void __gmpz_lcm (mpz_t rop, const mpz_t op1, const mpz_t op2);
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int __gmpz_invert (mpz_t rop, const mpz_t op1, const mpz_t op2);
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int __gmpz_divisible_p (const mpz_t n, const mpz_t d);
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int __gmpz_divisible_ui_p (const mpz_t n, UNIX_ULONG d);
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"""
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if sys.platform == "win32":
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raise ImportError("Not using GMP on Windows")
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lib = load_lib("gmp", gmp_defs)
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implementation = {"library": "gmp", "api": backend}
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if hasattr(lib, "__mpir_version"):
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raise ImportError("MPIR library detected")
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# In order to create a function that returns a pointer to
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# a new MPZ structure, we need to break the abstraction
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# and know exactly what ffi backend we have
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if implementation["api"] == "ctypes":
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from ctypes import Structure, c_int, c_void_p, byref
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class _MPZ(Structure):
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_fields_ = [('_mp_alloc', c_int),
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('_mp_size', c_int),
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('_mp_d', c_void_p)]
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def new_mpz():
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return byref(_MPZ())
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else:
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# We are using CFFI
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from Cryptodome.Util._raw_api import ffi
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def new_mpz():
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return ffi.new("MPZ*")
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# Lazy creation of GMP methods
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class _GMP(object):
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def __getattr__(self, name):
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if name.startswith("mpz_"):
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func_name = "__gmpz_" + name[4:]
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elif name.startswith("gmp_"):
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func_name = "__gmp_" + name[4:]
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else:
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raise AttributeError("Attribute %s is invalid" % name)
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func = getattr(lib, func_name)
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setattr(self, name, func)
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return func
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_gmp = _GMP()
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class IntegerGMP(IntegerBase):
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"""A fast, arbitrary precision integer"""
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_zero_mpz_p = new_mpz()
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_gmp.mpz_init_set_ui(_zero_mpz_p, c_ulong(0))
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def __init__(self, value):
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"""Initialize the integer to the given value."""
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self._mpz_p = new_mpz()
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self._initialized = False
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if isinstance(value, float):
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raise ValueError("A floating point type is not a natural number")
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if is_native_int(value):
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_gmp.mpz_init(self._mpz_p)
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self._initialized = True
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if value == 0:
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return
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tmp = new_mpz()
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_gmp.mpz_init(tmp)
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try:
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positive = value >= 0
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reduce = abs(value)
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slots = (reduce.bit_length() - 1) // 32 + 1
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while slots > 0:
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slots = slots - 1
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_gmp.mpz_set_ui(tmp,
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c_ulong(0xFFFFFFFF & (reduce >> (slots * 32))))
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_gmp.mpz_mul_2exp(tmp, tmp, c_ulong(slots * 32))
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_gmp.mpz_add(self._mpz_p, self._mpz_p, tmp)
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finally:
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_gmp.mpz_clear(tmp)
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if not positive:
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_gmp.mpz_neg(self._mpz_p, self._mpz_p)
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elif isinstance(value, IntegerGMP):
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_gmp.mpz_init_set(self._mpz_p, value._mpz_p)
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self._initialized = True
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else:
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raise NotImplementedError
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# Conversions
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def __int__(self):
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tmp = new_mpz()
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_gmp.mpz_init_set(tmp, self._mpz_p)
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try:
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value = 0
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slot = 0
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while _gmp.mpz_cmp(tmp, self._zero_mpz_p) != 0:
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lsb = _gmp.mpz_get_ui(tmp) & 0xFFFFFFFF
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value |= lsb << (slot * 32)
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_gmp.mpz_tdiv_q_2exp(tmp, tmp, c_ulong(32))
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slot = slot + 1
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finally:
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_gmp.mpz_clear(tmp)
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if self < 0:
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value = -value
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return int(value)
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def __str__(self):
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return str(int(self))
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def __repr__(self):
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return "Integer(%s)" % str(self)
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# Only Python 2.x
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def __hex__(self):
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return hex(int(self))
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# Only Python 3.x
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def __index__(self):
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return int(self)
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def to_bytes(self, block_size=0, byteorder='big'):
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"""Convert the number into a byte string.
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This method encodes the number in network order and prepends
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as many zero bytes as required. It only works for non-negative
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values.
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:Parameters:
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block_size : integer
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The exact size the output byte string must have.
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If zero, the string has the minimal length.
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byteorder : string
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'big' for big-endian integers (default), 'little' for litte-endian.
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:Returns:
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A byte string.
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:Raise ValueError:
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If the value is negative or if ``block_size`` is
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provided and the length of the byte string would exceed it.
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"""
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if self < 0:
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raise ValueError("Conversion only valid for non-negative numbers")
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buf_len = (_gmp.mpz_sizeinbase(self._mpz_p, 2) + 7) // 8
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if buf_len > block_size > 0:
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raise ValueError("Number is too big to convert to byte string"
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" of prescribed length")
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buf = create_string_buffer(buf_len)
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_gmp.mpz_export(
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buf,
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null_pointer, # Ignore countp
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1, # Big endian
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c_size_t(1), # Each word is 1 byte long
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0, # Endianess within a word - not relevant
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c_size_t(0), # No nails
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self._mpz_p)
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result = b'\x00' * max(0, block_size - buf_len) + get_raw_buffer(buf)
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if byteorder == 'big':
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pass
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elif byteorder == 'little':
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result = bytearray(result)
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result.reverse()
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result = bytes(result)
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else:
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raise ValueError("Incorrect byteorder")
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return result
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@staticmethod
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def from_bytes(byte_string, byteorder='big'):
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"""Convert a byte string into a number.
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:Parameters:
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byte_string : byte string
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The input number, encoded in network order.
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It can only be non-negative.
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byteorder : string
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'big' for big-endian integers (default), 'little' for litte-endian.
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:Return:
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The ``Integer`` object carrying the same value as the input.
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"""
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result = IntegerGMP(0)
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if byteorder == 'big':
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pass
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elif byteorder == 'little':
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byte_string = bytearray(byte_string)
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byte_string.reverse()
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else:
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raise ValueError("Incorrect byteorder")
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_gmp.mpz_import(
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result._mpz_p,
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c_size_t(len(byte_string)), # Amount of words to read
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1, # Big endian
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c_size_t(1), # Each word is 1 byte long
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0, # Endianess within a word - not relevant
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c_size_t(0), # No nails
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c_uint8_ptr(byte_string))
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return result
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# Relations
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def _apply_and_return(self, func, term):
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if not isinstance(term, IntegerGMP):
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term = IntegerGMP(term)
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return func(self._mpz_p, term._mpz_p)
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def __eq__(self, term):
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if not (isinstance(term, IntegerGMP) or is_native_int(term)):
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return False
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return self._apply_and_return(_gmp.mpz_cmp, term) == 0
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def __ne__(self, term):
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if not (isinstance(term, IntegerGMP) or is_native_int(term)):
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return True
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return self._apply_and_return(_gmp.mpz_cmp, term) != 0
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def __lt__(self, term):
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return self._apply_and_return(_gmp.mpz_cmp, term) < 0
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def __le__(self, term):
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return self._apply_and_return(_gmp.mpz_cmp, term) <= 0
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def __gt__(self, term):
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return self._apply_and_return(_gmp.mpz_cmp, term) > 0
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def __ge__(self, term):
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return self._apply_and_return(_gmp.mpz_cmp, term) >= 0
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def __nonzero__(self):
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return _gmp.mpz_cmp(self._mpz_p, self._zero_mpz_p) != 0
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__bool__ = __nonzero__
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|
|
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)
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
def _mult_modulo_bytes(term1, term2, modulus):
|
||
|
|
if not isinstance(term1, IntegerGMP):
|
||
|
|
term1 = IntegerGMP(term1)
|
||
|
|
if not isinstance(term2, IntegerGMP):
|
||
|
|
term2 = IntegerGMP(term2)
|
||
|
|
if not isinstance(modulus, IntegerGMP):
|
||
|
|
modulus = IntegerGMP(modulus)
|
||
|
|
|
||
|
|
if modulus < 0:
|
||
|
|
raise ValueError("Modulus must be positive")
|
||
|
|
if modulus == 0:
|
||
|
|
raise ZeroDivisionError("Modulus cannot be zero")
|
||
|
|
if (modulus & 1) == 0:
|
||
|
|
raise ValueError("Odd modulus is required")
|
||
|
|
|
||
|
|
numbers_len = len(modulus.to_bytes())
|
||
|
|
result = ((term1 * term2) % modulus).to_bytes(numbers_len)
|
||
|
|
return result
|
||
|
|
|
||
|
|
# 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
|