#include "tommath_private.h" #ifdef BN_MP_MONTGOMERY_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * SPDX-License-Identifier: Unlicense */ /* setups the montgomery reduction stuff */ int mp_montgomery_setup(const mp_int *n, mp_digit *rho) { mp_digit x, b; /* fast inversion mod 2**k * * Based on the fact that * * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) * => 2*X*A - X*X*A*A = 1 * => 2*(1) - (1) = 1 */ b = n->dp[0]; if ((b & 1u) == 0u) { return MP_VAL; } x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */ x *= 2u - (b * x); /* here x*a==1 mod 2**8 */ #if !defined(MP_8BIT) x *= 2u - (b * x); /* here x*a==1 mod 2**16 */ #endif #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) x *= 2u - (b * x); /* here x*a==1 mod 2**32 */ #endif #ifdef MP_64BIT x *= 2u - (b * x); /* here x*a==1 mod 2**64 */ #endif /* rho = -1/m mod b */ *rho = (mp_digit)(((mp_word)1 << (mp_word)DIGIT_BIT) - x) & MP_MASK; return MP_OKAY; } #endif /* ref: HEAD -> master, tag: v1.1.0 */ /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ /* commit time: 2019-01-28 20:32:32 +0100 */