140 lines
3.0 KiB
C
140 lines
3.0 KiB
C
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#include "tommath_private.h"
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#ifdef BN_MP_KRONECKER_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*/
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/*
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Kronecker symbol (a|p)
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Straightforward implementation of algorithm 1.4.10 in
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Henri Cohen: "A Course in Computational Algebraic Number Theory"
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@book{cohen2013course,
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title={A course in computational algebraic number theory},
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author={Cohen, Henri},
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volume={138},
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year={2013},
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publisher={Springer Science \& Business Media}
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}
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*/
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int mp_kronecker(const mp_int *a, const mp_int *p, int *c)
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{
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mp_int a1, p1, r;
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int e = MP_OKAY;
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int v, k;
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const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
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if (mp_iszero(p)) {
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if (a->used == 1 && a->dp[0] == 1) {
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*c = 1;
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return e;
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} else {
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*c = 0;
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return e;
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}
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}
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if (mp_iseven(a) && mp_iseven(p)) {
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*c = 0;
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return e;
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}
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if ((e = mp_init_copy(&a1, a)) != MP_OKAY) {
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return e;
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}
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if ((e = mp_init_copy(&p1, p)) != MP_OKAY) {
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goto LBL_KRON_0;
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}
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v = mp_cnt_lsb(&p1);
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if ((e = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
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goto LBL_KRON_1;
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}
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if ((v & 0x1) == 0) {
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k = 1;
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} else {
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k = table[a->dp[0] & 7];
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}
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if (p1.sign == MP_NEG) {
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p1.sign = MP_ZPOS;
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if (a1.sign == MP_NEG) {
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k = -k;
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}
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}
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if ((e = mp_init(&r)) != MP_OKAY) {
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goto LBL_KRON_1;
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}
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for (;;) {
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if (mp_iszero(&a1)) {
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if (mp_cmp_d(&p1, 1) == MP_EQ) {
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*c = k;
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goto LBL_KRON;
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} else {
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*c = 0;
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goto LBL_KRON;
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}
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}
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v = mp_cnt_lsb(&a1);
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if ((e = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
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goto LBL_KRON;
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}
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if ((v & 0x1) == 1) {
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k = k * table[p1.dp[0] & 7];
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}
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if (a1.sign == MP_NEG) {
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// compute k = (-1)^((a1)*(p1-1)/4) * k
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// a1.dp[0] + 1 cannot overflow because the MSB
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// of the type mp_digit is not set by definition
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if ((a1.dp[0] + 1) & p1.dp[0] & 2u) {
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k = -k;
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}
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} else {
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// compute k = (-1)^((a1-1)*(p1-1)/4) * k
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if (a1.dp[0] & p1.dp[0] & 2u) {
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k = -k;
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}
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}
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if ((e = mp_copy(&a1,&r)) != MP_OKAY) {
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goto LBL_KRON;
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}
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r.sign = MP_ZPOS;
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if ((e = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
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goto LBL_KRON;
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}
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if ((e = mp_copy(&r, &p1)) != MP_OKAY) {
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goto LBL_KRON;
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}
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}
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LBL_KRON:
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mp_clear(&r);
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LBL_KRON_0:
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mp_clear(&a1);
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LBL_KRON_1:
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mp_clear(&p1);
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return e;
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}
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#endif
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