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authorKevin B Kenny <kennykb@acm.org>2005-01-19 22:41:26 (GMT)
committerKevin B Kenny <kennykb@acm.org>2005-01-19 22:41:26 (GMT)
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parentb23d942a1e86ddee18c2309afd7fa7e9afa79ef8 (diff)
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Import of libtommath 0.33
Diffstat (limited to 'libtommath/bn_mp_jacobi.c')
-rw-r--r--libtommath/bn_mp_jacobi.c101
1 files changed, 101 insertions, 0 deletions
diff --git a/libtommath/bn_mp_jacobi.c b/libtommath/bn_mp_jacobi.c
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+#include <tommath.h>
+#ifdef BN_MP_JACOBI_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.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* computes the jacobi c = (a | n) (or Legendre if n is prime)
+ * HAC pp. 73 Algorithm 2.149
+ */
+int mp_jacobi (mp_int * a, mp_int * p, int *c)
+{
+ mp_int a1, p1;
+ int k, s, r, res;
+ mp_digit residue;
+
+ /* if p <= 0 return MP_VAL */
+ if (mp_cmp_d(p, 0) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* step 1. if a == 0, return 0 */
+ if (mp_iszero (a) == 1) {
+ *c = 0;
+ return MP_OKAY;
+ }
+
+ /* step 2. if a == 1, return 1 */
+ if (mp_cmp_d (a, 1) == MP_EQ) {
+ *c = 1;
+ return MP_OKAY;
+ }
+
+ /* default */
+ s = 0;
+
+ /* step 3. write a = a1 * 2**k */
+ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&p1)) != MP_OKAY) {
+ goto LBL_A1;
+ }
+
+ /* divide out larger power of two */
+ k = mp_cnt_lsb(&a1);
+ if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+
+ /* step 4. if e is even set s=1 */
+ if ((k & 1) == 0) {
+ s = 1;
+ } else {
+ /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
+ residue = p->dp[0] & 7;
+
+ if (residue == 1 || residue == 7) {
+ s = 1;
+ } else if (residue == 3 || residue == 5) {
+ s = -1;
+ }
+ }
+
+ /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
+ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
+ s = -s;
+ }
+
+ /* if a1 == 1 we're done */
+ if (mp_cmp_d (&a1, 1) == MP_EQ) {
+ *c = s;
+ } else {
+ /* n1 = n mod a1 */
+ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ *c = s * r;
+ }
+
+ /* done */
+ res = MP_OKAY;
+LBL_P1:mp_clear (&p1);
+LBL_A1:mp_clear (&a1);
+ return res;
+}
+#endif