ref: 14564d23d2114ecff20ab73ff26db5d5db5c0320
dir: /libsec/probably_prime.c/
#include "os.h" #include <mp.h> #include <libsec.h> // Miller-Rabin probabilistic primality testing // Knuth (1981) Seminumerical Algorithms, p.379 // Menezes et al () Handbook, p.39 // 0 if composite; 1 if almost surely prime, Pr(err)<1/4**nrep int probably_prime(mpint *n, int nrep) { int j, k, rep, nbits, isprime = 1; mpint *nm1, *q, *x, *y, *r; if(n->sign < 0) sysfatal("negative prime candidate"); if(nrep <= 0) nrep = 18; k = mptoi(n); if(k == 2) // 2 is prime return 1; if(k < 2) // 1 is not prime return 0; if((n->p[0] & 1) == 0) // even is not prime return 0; // test against small prime numbers if(smallprimetest(n) < 0) return 0; // fermat test, 2^n mod n == 2 if p is prime x = uitomp(2, nil); y = mpnew(0); mpexp(x, n, n, y); k = mptoi(y); if(k != 2){ mpfree(x); mpfree(y); return 0; } nbits = mpsignif(n); nm1 = mpnew(nbits); mpsub(n, mpone, nm1); // nm1 = n - 1 */ k = mplowbits0(nm1); q = mpnew(0); mpright(nm1, k, q); // q = (n-1)/2**k for(rep = 0; rep < nrep; rep++){ // x = random in [2, n-2] r = mprand(nbits, prng, nil); mpmod(r, nm1, x); mpfree(r); if(mpcmp(x, mpone) <= 0) continue; // y = x**q mod n mpexp(x, q, n, y); if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0) goto done; for(j = 1; j < k; j++){ mpmul(y, y, x); mpmod(x, n, y); // y = y*y mod n if(mpcmp(y, nm1) == 0) goto done; if(mpcmp(y, mpone) == 0){ isprime = 0; goto done; } } isprime = 0; } done: mpfree(y); mpfree(x); mpfree(q); mpfree(nm1); return isprime; }