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