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119 lines
3.3 KiB
119 lines
3.3 KiB
#include "tommath_private.h"
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#ifdef BN_S_MP_INVMOD_FAST_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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/* computes the modular inverse via binary extended euclidean algorithm,
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* that is c = 1/a mod b
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*
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* Based on slow invmod except this is optimized for the case where b is
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* odd as per HAC Note 14.64 on pp. 610
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*/
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mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c)
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{
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mp_int x, y, u, v, B, D;
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mp_sign neg;
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mp_err err;
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/* 2. [modified] b must be odd */
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if (MP_IS_EVEN(b)) {
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return MP_VAL;
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}
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/* init all our temps */
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if ((err = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
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return err;
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}
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/* x == modulus, y == value to invert */
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if ((err = mp_copy(b, &x)) != MP_OKAY) goto LBL_ERR;
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/* we need y = |a| */
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if ((err = mp_mod(a, b, &y)) != MP_OKAY) goto LBL_ERR;
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/* if one of x,y is zero return an error! */
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if (MP_IS_ZERO(&x) || MP_IS_ZERO(&y)) {
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err = MP_VAL;
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goto LBL_ERR;
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}
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/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
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if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR;
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mp_set(&D, 1uL);
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top:
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/* 4. while u is even do */
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while (MP_IS_EVEN(&u)) {
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/* 4.1 u = u/2 */
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if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR;
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/* 4.2 if B is odd then */
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if (MP_IS_ODD(&B)) {
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if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR;
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}
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/* B = B/2 */
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if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR;
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}
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/* 5. while v is even do */
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while (MP_IS_EVEN(&v)) {
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/* 5.1 v = v/2 */
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if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR;
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/* 5.2 if D is odd then */
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if (MP_IS_ODD(&D)) {
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/* D = (D-x)/2 */
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if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR;
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}
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/* D = D/2 */
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if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR;
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}
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/* 6. if u >= v then */
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if (mp_cmp(&u, &v) != MP_LT) {
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/* u = u - v, B = B - D */
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if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR;
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} else {
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/* v - v - u, D = D - B */
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if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR;
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}
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/* if not zero goto step 4 */
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if (!MP_IS_ZERO(&u)) {
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goto top;
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}
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/* now a = C, b = D, gcd == g*v */
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/* if v != 1 then there is no inverse */
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if (mp_cmp_d(&v, 1uL) != MP_EQ) {
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err = MP_VAL;
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goto LBL_ERR;
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}
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/* b is now the inverse */
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neg = a->sign;
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while (D.sign == MP_NEG) {
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if ((err = mp_add(&D, b, &D)) != MP_OKAY) goto LBL_ERR;
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}
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/* too big */
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while (mp_cmp_mag(&D, b) != MP_LT) {
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if ((err = mp_sub(&D, b, &D)) != MP_OKAY) goto LBL_ERR;
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}
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mp_exch(&D, c);
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c->sign = neg;
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err = MP_OKAY;
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LBL_ERR:
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mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL);
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return err;
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}
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#endif
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