106 lines
3.3 KiB
C
106 lines
3.3 KiB
C
/*
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Copyright 2009 Jason Moxham
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This file is part of the MPIR Library.
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The MPIR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published
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by the Free Software Foundation; either version 2.1 of the License, or (at
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your option) any later version.
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The MPIR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the MPIR Library; see the file COPYING.LIB. If not, write
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to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
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Boston, MA 02110-1301, USA.
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*/
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#include "mpir.h"
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#include "gmp-impl.h"
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// could have another parameter to specify what likely means
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// ie for factoring , for RSA
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// or to state that we have allready done trial div
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// could call it mpz_likely_composite_p then when true we could return more info about it , ie a factor
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int
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mpz_likely_prime_p (mpz_srcptr N, gmp_randstate_t STATE, unsigned long td)
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{
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int d, t, r;
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mpz_t base, nm1, x, e, n;
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ALLOC (n) = ALLOC (N);
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SIZ (n) = ABSIZ (N);
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PTR (n) = PTR (N); // fake up an absolute value that we dont have de-allocate
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// algorithm dose not handle small values , get rid of them here
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if (mpz_cmp_ui (n, 2) == 0 || mpz_cmp_ui (n, 3) == 0)
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return 1;
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if (mpz_cmp_ui (n, 5) < 0 || mpz_even_p (n))
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return 0;
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// for factoring purpoises
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// we assume we know nothing about N ie it is a random integer
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// therefore it has a good chance of factoring by small divisiors , so try trial division as its fast and it checks small divisors
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// checking for other divisors is not worth it even if the test is fast as we have random integer so only small divisors are common
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// enough , remember this is not exact so it doesn't matter if we miss a few divisors
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#define LIM 257
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d=mpz_trial_division(n,3,LIM);
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if(d!=0)
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{if(mpz_cmp_ui(n, d) == 0)return 1;
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return 0;}
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if (mpz_cmp_ui (n, LIM * LIM) < 0)
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return 1;
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ASSERT (mpz_odd_p (n));
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ASSERT (mpz_cmp_ui (n, 5) >= 0); // so we can choose a base
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// now do strong pseudoprime test
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// get random base , for now choose any size , later choose a small one
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mpz_init (base);
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mpz_init_set (nm1, n);
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mpz_sub_ui (nm1, nm1, 1);
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do
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{
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mpz_urandomm (base, STATE, nm1);
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}
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while (mpz_cmp_ui (base, 1) <= 0);
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// so base is 2 to n-2 which implys n>=4 , only really want a small base , and ignore the rare base=n-1 condition etc
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//printf("base is ");mpz_out_str(stdout,10,base);printf(" ");
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mpz_init (e);
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mpz_init (x);
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t = mpz_scan1 (nm1, 0); // so 2^t divides nm1
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ASSERT (t > 0);
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mpz_tdiv_q_2exp (e, nm1, t); // so e=nm1/2^t
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mpz_powm (x, base, e, n); // x=base^e mod n
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mpz_clear (e);
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mpz_clear (base);
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if (mpz_cmp_ui (x, 1) == 0)
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{
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mpz_clear (nm1);
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mpz_clear (x);
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return 1;
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}
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if (mpz_cmp (x, nm1) == 0)
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{
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mpz_clear (nm1);
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mpz_clear (x);
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return 1;
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}
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for (r = 0, t = t - 1; t > 0; t--)
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{
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mpz_mul (x, x, x);
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mpz_mod (x, x, n);
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if (mpz_cmp (x, nm1) == 0)
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{
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r = 1;
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break;
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}
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if (mpz_cmp_ui (x, 1) == 0)
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break;
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}
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mpz_clear (nm1);
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mpz_clear (x);
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return r;
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}
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