| /* mpz_millerrabin(n,reps) -- An implementation of the probabilistic primality |
| test found in Knuth's Seminumerical Algorithms book. If the function |
| mpz_millerrabin() returns 0 then n is not prime. If it returns 1, then n is |
| 'probably' prime. The probability of a false positive is (1/4)**reps, where |
| reps is the number of internal passes of the probabilistic algorithm. Knuth |
| indicates that 25 passes are reasonable. |
| |
| THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST |
| CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN |
| FUTURE GNU MP RELEASES. |
| |
| Copyright 1991, 1993, 1994, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2005 Free |
| Software Foundation, Inc. Contributed by John Amanatides. |
| |
| This file is part of the GNU MP Library. |
| |
| The GNU MP Library is free software; you can redistribute it and/or modify |
| it under the terms of the GNU Lesser General Public License as published by |
| the Free Software Foundation; either version 3 of the License, or (at your |
| option) any later version. |
| |
| The GNU MP Library is distributed in the hope that it will be useful, but |
| WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
| or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public |
| License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public License |
| along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ |
| |
| #include "gmp.h" |
| #include "gmp-impl.h" |
| |
| static int millerrabin __GMP_PROTO ((mpz_srcptr, mpz_srcptr, |
| mpz_ptr, mpz_ptr, |
| mpz_srcptr, unsigned long int)); |
| |
| int |
| mpz_millerrabin (mpz_srcptr n, int reps) |
| { |
| int r; |
| mpz_t nm1, nm3, x, y, q; |
| unsigned long int k; |
| gmp_randstate_t rstate; |
| int is_prime; |
| TMP_DECL; |
| TMP_MARK; |
| |
| MPZ_TMP_INIT (nm1, SIZ (n) + 1); |
| mpz_sub_ui (nm1, n, 1L); |
| |
| MPZ_TMP_INIT (x, SIZ (n) + 1); |
| MPZ_TMP_INIT (y, 2 * SIZ (n)); /* mpz_powm_ui needs excessive memory!!! */ |
| |
| /* Perform a Fermat test. */ |
| mpz_set_ui (x, 210L); |
| mpz_powm (y, x, nm1, n); |
| if (mpz_cmp_ui (y, 1L) != 0) |
| { |
| TMP_FREE; |
| return 0; |
| } |
| |
| MPZ_TMP_INIT (q, SIZ (n)); |
| |
| /* Find q and k, where q is odd and n = 1 + 2**k * q. */ |
| k = mpz_scan1 (nm1, 0L); |
| mpz_tdiv_q_2exp (q, nm1, k); |
| |
| /* n-3 */ |
| MPZ_TMP_INIT (nm3, SIZ (n) + 1); |
| mpz_sub_ui (nm3, n, 3L); |
| ASSERT (mpz_cmp_ui (nm3, 1L) >= 0); |
| |
| gmp_randinit_default (rstate); |
| |
| is_prime = 1; |
| for (r = 0; r < reps && is_prime; r++) |
| { |
| /* 2 to n-2 inclusive, don't want 1, 0 or -1 */ |
| mpz_urandomm (x, rstate, nm3); |
| mpz_add_ui (x, x, 2L); |
| |
| is_prime = millerrabin (n, nm1, x, y, q, k); |
| } |
| |
| gmp_randclear (rstate); |
| |
| TMP_FREE; |
| return is_prime; |
| } |
| |
| static int |
| millerrabin (mpz_srcptr n, mpz_srcptr nm1, mpz_ptr x, mpz_ptr y, |
| mpz_srcptr q, unsigned long int k) |
| { |
| unsigned long int i; |
| |
| mpz_powm (y, x, q, n); |
| |
| if (mpz_cmp_ui (y, 1L) == 0 || mpz_cmp (y, nm1) == 0) |
| return 1; |
| |
| for (i = 1; i < k; i++) |
| { |
| mpz_powm_ui (y, y, 2L, n); |
| if (mpz_cmp (y, nm1) == 0) |
| return 1; |
| if (mpz_cmp_ui (y, 1L) == 0) |
| return 0; |
| } |
| return 0; |
| } |