3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
12 * The library is free for all purposes without any express
15 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
18 /* computes the jacobi c = (a | n) (or Legendre if n is prime)
19 * HAC pp. 73 Algorithm 2.149
21 int mp_jacobi (mp_int * a, mp_int * p, int *c)
27 /* if p <= 0 return MP_VAL */
28 if (mp_cmp_d(p, 0) != MP_GT) {
32 /* step 1. if a == 0, return 0 */
33 if (mp_iszero (a) == 1) {
38 /* step 2. if a == 1, return 1 */
39 if (mp_cmp_d (a, 1) == MP_EQ) {
47 /* step 3. write a = a1 * 2**k */
48 if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
52 if ((res = mp_init (&p1)) != MP_OKAY) {
56 /* divide out larger power of two */
58 if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
62 /* step 4. if e is even set s=1 */
66 /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
67 residue = p->dp[0] & 7;
69 if (residue == 1 || residue == 7) {
71 } else if (residue == 3 || residue == 5) {
76 /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
77 if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
81 /* if a1 == 1 we're done */
82 if (mp_cmp_d (&a1, 1) == MP_EQ) {
86 if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
89 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
97 LBL_P1:mp_clear (&p1);
98 LBL_A1:mp_clear (&a1);
103 /* $Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v $ */
104 /* $Revision: 1.3 $ */
105 /* $Date: 2006/03/31 14:18:44 $ */