41 lines
1.1 KiB
C
41 lines
1.1 KiB
C
#include "tommath_private.h"
|
|
#ifdef MP_MONTGOMERY_SETUP_C
|
|
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
|
|
/* SPDX-License-Identifier: Unlicense */
|
|
|
|
/* setups the montgomery reduction stuff */
|
|
mp_err 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 */
|
|
x *= 2u - (b * x); /* here x*a==1 mod 2**16 */
|
|
#if defined(MP_64BIT) || !(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)MP_DIGIT_BIT) - x) & MP_MASK;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|