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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)
commitef78ca64ce6ba6a8786f083318fe536f2bd52925 (patch)
tree47f8ad0d7291237c7f9af988c5e05275ed9286ee /libtommath/bn_mp_prime_next_prime.c
parentb23d942a1e86ddee18c2309afd7fa7e9afa79ef8 (diff)
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Import of libtommath 0.33
Diffstat (limited to 'libtommath/bn_mp_prime_next_prime.c')
-rw-r--r--libtommath/bn_mp_prime_next_prime.c166
1 files changed, 166 insertions, 0 deletions
diff --git a/libtommath/bn_mp_prime_next_prime.c b/libtommath/bn_mp_prime_next_prime.c
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+++ b/libtommath/bn_mp_prime_next_prime.c
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+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_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
+ */
+
+/* finds the next prime after the number "a" using "t" trials
+ * of Miller-Rabin.
+ *
+ * bbs_style = 1 means the prime must be congruent to 3 mod 4
+ */
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
+{
+ int err, res, x, y;
+ mp_digit res_tab[PRIME_SIZE], step, kstep;
+ mp_int b;
+
+ /* ensure t is valid */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* force positive */
+ a->sign = MP_ZPOS;
+
+ /* simple algo if a is less than the largest prime in the table */
+ if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
+ /* find which prime it is bigger than */
+ for (x = PRIME_SIZE - 2; x >= 0; x--) {
+ if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
+ if (bbs_style == 1) {
+ /* ok we found a prime smaller or
+ * equal [so the next is larger]
+ *
+ * however, the prime must be
+ * congruent to 3 mod 4
+ */
+ if ((ltm_prime_tab[x + 1] & 3) != 3) {
+ /* scan upwards for a prime congruent to 3 mod 4 */
+ for (y = x + 1; y < PRIME_SIZE; y++) {
+ if ((ltm_prime_tab[y] & 3) == 3) {
+ mp_set(a, ltm_prime_tab[y]);
+ return MP_OKAY;
+ }
+ }
+ }
+ } else {
+ mp_set(a, ltm_prime_tab[x + 1]);
+ return MP_OKAY;
+ }
+ }
+ }
+ /* at this point a maybe 1 */
+ if (mp_cmp_d(a, 1) == MP_EQ) {
+ mp_set(a, 2);
+ return MP_OKAY;
+ }
+ /* fall through to the sieve */
+ }
+
+ /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
+ if (bbs_style == 1) {
+ kstep = 4;
+ } else {
+ kstep = 2;
+ }
+
+ /* at this point we will use a combination of a sieve and Miller-Rabin */
+
+ if (bbs_style == 1) {
+ /* if a mod 4 != 3 subtract the correct value to make it so */
+ if ((a->dp[0] & 3) != 3) {
+ if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
+ }
+ } else {
+ if (mp_iseven(a) == 1) {
+ /* force odd */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
+ return err;
+ }
+ }
+ }
+
+ /* generate the restable */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
+ return err;
+ }
+ }
+
+ /* init temp used for Miller-Rabin Testing */
+ if ((err = mp_init(&b)) != MP_OKAY) {
+ return err;
+ }
+
+ for (;;) {
+ /* skip to the next non-trivially divisible candidate */
+ step = 0;
+ do {
+ /* y == 1 if any residue was zero [e.g. cannot be prime] */
+ y = 0;
+
+ /* increase step to next candidate */
+ step += kstep;
+
+ /* compute the new residue without using division */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ /* add the step to each residue */
+ res_tab[x] += kstep;
+
+ /* subtract the modulus [instead of using division] */
+ if (res_tab[x] >= ltm_prime_tab[x]) {
+ res_tab[x] -= ltm_prime_tab[x];
+ }
+
+ /* set flag if zero */
+ if (res_tab[x] == 0) {
+ y = 1;
+ }
+ }
+ } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
+
+ /* add the step */
+ if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* if didn't pass sieve and step == MAX then skip test */
+ if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
+ continue;
+ }
+
+ /* is this prime? */
+ for (x = 0; x < t; x++) {
+ mp_set(&b, ltm_prime_tab[t]);
+ if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if (res == MP_NO) {
+ break;
+ }
+ }
+
+ if (res == MP_YES) {
+ break;
+ }
+ }
+
+ err = MP_OKAY;
+LBL_ERR:
+ mp_clear(&b);
+ return err;
+}
+
+#endif