#include "tommath_private.h" #ifdef BN_FAST_MP_INVMOD_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 */ /* 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 */ int fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) { mp_int x, y, u, v, B, D; int res, neg; /* 2. [modified] b must be odd */ if (mp_iseven(b) == MP_YES) { return MP_VAL; } /* init all our temps */ if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { return res; } /* x == modulus, y == value to invert */ if ((res = mp_copy(b, &x)) != MP_OKAY) { goto LBL_ERR; } /* we need y = |a| */ if ((res = mp_mod(a, b, &y)) != MP_OKAY) { goto LBL_ERR; } /* if one of x,y is zero return an error! */ if ((mp_iszero(&x) == MP_YES) || (mp_iszero(&y) == MP_YES)) { res = MP_VAL; goto LBL_ERR; } /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ if ((res = mp_copy(&x, &u)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_copy(&y, &v)) != MP_OKAY) { goto LBL_ERR; } mp_set(&D, 1uL); top: /* 4. while u is even do */ while (mp_iseven(&u) == MP_YES) { /* 4.1 u = u/2 */ if ((res = mp_div_2(&u, &u)) != MP_OKAY) { goto LBL_ERR; } /* 4.2 if B is odd then */ if (mp_isodd(&B) == MP_YES) { if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) { goto LBL_ERR; } } /* B = B/2 */ if ((res = mp_div_2(&B, &B)) != MP_OKAY) { goto LBL_ERR; } } /* 5. while v is even do */ while (mp_iseven(&v) == MP_YES) { /* 5.1 v = v/2 */ if ((res = mp_div_2(&v, &v)) != MP_OKAY) { goto LBL_ERR; } /* 5.2 if D is odd then */ if (mp_isodd(&D) == MP_YES) { /* D = (D-x)/2 */ if ((res = mp_sub(&D, &x, &D)) != MP_OKAY) { goto LBL_ERR; } } /* D = D/2 */ if ((res = 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 ((res = mp_sub(&u, &v, &u)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_sub(&B, &D, &B)) != MP_OKAY) { goto LBL_ERR; } } else { /* v - v - u, D = D - B */ if ((res = mp_sub(&v, &u, &v)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_sub(&D, &B, &D)) != MP_OKAY) { goto LBL_ERR; } } /* if not zero goto step 4 */ if (mp_iszero(&u) == MP_NO) { 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) { res = MP_VAL; goto LBL_ERR; } /* b is now the inverse */ neg = a->sign; while (D.sign == MP_NEG) { if ((res = mp_add(&D, b, &D)) != MP_OKAY) { goto LBL_ERR; } } /* too big */ while (mp_cmp_mag(&D, b) != MP_LT) { if ((res = mp_sub(&D, b, &D)) != MP_OKAY) { goto LBL_ERR; } } mp_exch(&D, c); c->sign = neg; res = MP_OKAY; LBL_ERR: mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL); return res; } #endif /* ref: HEAD -> master, tag: v1.1.0 */ /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ /* commit time: 2019-01-28 20:32:32 +0100 */