120 lines
2.7 KiB
C
120 lines
2.7 KiB
C
#include <tommath_private.h>
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#ifdef BN_MP_JACOBI_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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* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
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/* computes the jacobi c = (a | n) (or Legendre if n is prime)
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* HAC pp. 73 Algorithm 2.149
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* HAC is wrong here, as the special case of (0 | 1) is not
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* handled correctly.
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*/
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int mp_jacobi(const mp_int *a, const mp_int *n, int *c)
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{
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mp_int a1, p1;
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int k, s, r, res;
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mp_digit residue;
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/* if a < 0 return MP_VAL */
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if (mp_isneg(a) == MP_YES) {
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return MP_VAL;
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}
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/* if n <= 0 return MP_VAL */
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if (mp_cmp_d(n, 0) != MP_GT) {
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return MP_VAL;
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}
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/* step 1. handle case of a == 0 */
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if (mp_iszero(a) == MP_YES) {
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/* special case of a == 0 and n == 1 */
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if (mp_cmp_d(n, 1) == MP_EQ) {
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*c = 1;
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} else {
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*c = 0;
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}
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return MP_OKAY;
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}
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/* step 2. if a == 1, return 1 */
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if (mp_cmp_d(a, 1) == MP_EQ) {
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*c = 1;
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return MP_OKAY;
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}
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/* default */
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s = 0;
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/* step 3. write a = a1 * 2**k */
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if ((res = mp_init_copy(&a1, a)) != MP_OKAY) {
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return res;
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}
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if ((res = mp_init(&p1)) != MP_OKAY) {
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goto LBL_A1;
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}
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/* divide out larger power of two */
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k = mp_cnt_lsb(&a1);
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if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
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goto LBL_P1;
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}
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/* step 4. if e is even set s=1 */
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if ((k & 1) == 0) {
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s = 1;
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} else {
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/* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
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residue = n->dp[0] & 7;
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if ((residue == 1) || (residue == 7)) {
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s = 1;
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} else if ((residue == 3) || (residue == 5)) {
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s = -1;
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}
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}
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/* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
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if (((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
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s = -s;
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}
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/* if a1 == 1 we're done */
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if (mp_cmp_d(&a1, 1) == MP_EQ) {
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*c = s;
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} else {
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/* n1 = n mod a1 */
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if ((res = mp_mod(n, &a1, &p1)) != MP_OKAY) {
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goto LBL_P1;
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}
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if ((res = mp_jacobi(&p1, &a1, &r)) != MP_OKAY) {
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goto LBL_P1;
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}
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*c = s * r;
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}
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/* done */
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res = MP_OKAY;
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LBL_P1:
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mp_clear(&p1);
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LBL_A1:
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mp_clear(&a1);
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return res;
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}
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#endif
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/* ref: $Format:%D$ */
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/* git commit: $Format:%H$ */
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/* commit time: $Format:%ai$ */
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