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#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 */
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