blob: 2e750393131bb5989300b1dee4db53cbfec07954 [file] [log] [blame]
 #include "os.h" #include #include /* 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; 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++){ for(;;){ /* find x = random in [2, n-2] */ r = mprand(nbits, prng, nil); mpmod(r, nm1, x); mpfree(r); if(mpcmp(x, mpone) > 0) break; } /* y = x**q mod n */ mpexp(x, q, n, y); if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0) continue; for(j = 1;; j++){ if(j >= k) { isprime = 0; goto done; } mpmul(y, y, x); mpmod(x, n, y); /* y = y*y mod n */ if(mpcmp(y, nm1) == 0) break; if(mpcmp(y, mpone) == 0){ isprime = 0; goto done; } } } isprime = 1; done: mpfree(y); mpfree(x); mpfree(q); mpfree(nm1); return isprime; }