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Exports the following items: - inverse_mod() Source code is derived from http://webpages.charter.net/curryfans/peter/downloads.html, but has been heavily modified to fit into this projects lint settings. The original project license is listed below: Copyright (c) 2014 Peter Pearson Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ from __future__ import unicode_literals, division, absolute_import, print_function import math import platform from .util import int_to_bytes, int_from_bytes # First try to use ctypes with OpenSSL for better performance try: from ._ffi import ( buffer_from_bytes, bytes_from_buffer, FFIEngineError, LibraryNotFoundError, null, ) # Some versions of PyPy have segfault issues, so we just punt on PyPy if platform.python_implementation() == 'PyPy': raise EnvironmentError() try: from ._perf._big_num_ctypes import libcrypto def inverse_mod(a, p): """ Compute the modular inverse of a (mod p) :param a: An integer :param p: An integer :return: An integer """ ctx = libcrypto.BN_CTX_new() a_bytes = int_to_bytes(abs(a)) p_bytes = int_to_bytes(abs(p)) a_buf = buffer_from_bytes(a_bytes) a_bn = libcrypto.BN_bin2bn(a_buf, len(a_bytes), null()) if a < 0: libcrypto.BN_set_negative(a_bn, 1) p_buf = buffer_from_bytes(p_bytes) p_bn = libcrypto.BN_bin2bn(p_buf, len(p_bytes), null()) if p < 0: libcrypto.BN_set_negative(p_bn, 1) r_bn = libcrypto.BN_mod_inverse(null(), a_bn, p_bn, ctx) r_len_bits = libcrypto.BN_num_bits(r_bn) r_len = int(math.ceil(r_len_bits / 8)) r_buf = buffer_from_bytes(r_len) libcrypto.BN_bn2bin(r_bn, r_buf) r_bytes = bytes_from_buffer(r_buf, r_len) result = int_from_bytes(r_bytes) libcrypto.BN_free(a_bn) libcrypto.BN_free(p_bn) libcrypto.BN_free(r_bn) libcrypto.BN_CTX_free(ctx) return result except (LibraryNotFoundError, FFIEngineError): raise EnvironmentError() # If there was an issue using ctypes or OpenSSL, we fall back to pure python except (EnvironmentError, ImportError): def inverse_mod(a, p): """ Compute the modular inverse of a (mod p) :param a: An integer :param p: An integer :return: An integer """ if a < 0 or p <= a: a = a % p # From Ferguson and Schneier, roughly: c, d = a, p uc, vc, ud, vd = 1, 0, 0, 1 while c != 0: q, c, d = divmod(d, c) + (c,) uc, vc, ud, vd = ud - q * uc, vd - q * vc, uc, vc # At this point, d is the GCD, and ud*a+vd*p = d. # If d == 1, this means that ud is a inverse. assert d == 1 if ud > 0: return ud else: return ud + p def fill_width(bytes_, width): """ Ensure a byte string representing a positive integer is a specific width (in bytes) :param bytes_: The integer byte string :param width: The desired width as an integer :return: A byte string of the width specified """ while len(bytes_) < width: bytes_ = b'\x00' + bytes_ return bytes_