view libtommath/bn_mp_prime_next_prime.c @ 1656:a36e545fb43d

Prime-related bugfixes (#81) * Merge pull request #180 from czurnieden/isprimeerror Fixed bug in mp_prime_isprime (cherry picked from commit f3ff7064f3301a2fc11b84d389fd67769862d437) * do 2 MR rounds for numbers >=2048bits * back-port modified mp_prime_next_prime()
author Steffen Jaeckel <s@jaeckel.eu>
date Tue, 17 Sep 2019 16:11:09 +0200
parents f52919ffd3b1
children 1051e4eea25a
line wrap: on
line source
#include "tommath_private.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.
 *
 * SPDX-License-Identifier: Unlicense
 */

/* 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 = MP_NO, x, y, cmp;
   mp_digit res_tab[PRIME_SIZE], step, kstep;
   mp_int   b;

   /* 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 "a" */
      for (x = 0; x < PRIME_SIZE; x++) {
         cmp = mp_cmp_d(a, ltm_prime_tab[x]);
         if (cmp == MP_EQ) {
            continue;
         }
         if (cmp != MP_GT) {
            if ((bbs_style == 1) && ((ltm_prime_tab[x] & 3u) != 3u)) {
               /* try again until we get a prime congruent to 3 mod 4 */
               continue;
            } else {
               mp_set(a, ltm_prime_tab[x]);
               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] & 3u) != 3u) {
         if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) {
            return err;
         }
      }
   } else {
      if (mp_iseven(a) == MP_YES) {
         /* force odd */
         if ((err = mp_sub_d(a, 1uL, 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] == 0u) {
               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;
      }

      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if (res == MP_YES) {
         break;
      }
   }

   err = MP_OKAY;
LBL_ERR:
   mp_clear(&b);
   return err;
}

#endif

/* ref:         HEAD -> master, tag: v1.1.0 */
/* git commit:  08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
/* commit time: 2019-01-28 20:32:32 +0100 */