115 lines
2.4 KiB
C
115 lines
2.4 KiB
C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is library that provides for multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library is 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, tomstdenis@iahu.ca, http://libtommath.iahu.ca
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*/
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#include <tommath.h>
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/* computes the jacobi c = (a | n) (or Legendre if b is prime)
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* HAC pp. 73 Algorithm 2.149
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*/
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int
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mp_jacobi (mp_int * a, mp_int * n, int *c)
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{
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mp_int a1, n1, e;
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int s, r, res;
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mp_digit residue;
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/* step 1. if a == 0, return 0 */
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if (mp_iszero (a) == 1) {
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*c = 0;
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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^e */
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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 (&n1)) != MP_OKAY) {
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goto __A1;
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}
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if ((res = mp_init (&e)) != MP_OKAY) {
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goto __N1;
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}
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while (mp_iseven (&a1) == 1) {
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if ((res = mp_add_d (&e, 1, &e)) != MP_OKAY) {
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goto __E;
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}
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if ((res = mp_div_2 (&a1, &a1)) != MP_OKAY) {
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goto __E;
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}
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}
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/* step 4. if e is even set s=1 */
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if (mp_iseven (&e) == 1) {
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s = 1;
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} else {
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/* else set s=1 if n = 1/7 (mod 8) or s=-1 if n = 3/5 (mod 8) */
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if ((res = mp_mod_d (n, 8, &residue)) != MP_OKAY) {
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goto __E;
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}
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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 n == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
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if ((res = mp_mod_d (n, 4, &residue)) != MP_OKAY) {
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goto __E;
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}
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if (residue == 3) {
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if ((res = mp_mod_d (&a1, 4, &residue)) != MP_OKAY) {
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goto __E;
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}
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if (residue == 3) {
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s = -s;
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}
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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, &n1)) != MP_OKAY) {
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goto __E;
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}
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if ((res = mp_jacobi (&n1, &a1, &r)) != MP_OKAY) {
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goto __E;
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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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__E:mp_clear (&e);
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__N1:mp_clear (&n1);
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__A1:mp_clear (&a1);
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return res;
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}
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