1 #include "os.h" 2 #include <mp.h> 3 #include <libsec.h> 4 5 // Miller-Rabin probabilistic primality testing 6 // Knuth (1981) Seminumerical Algorithms, p.379 7 // Menezes et al () Handbook, p.39 8 // 0 if composite; 1 if almost surely prime, Pr(err)<1/4**nrep 9 int 10 probably_prime(mpint *n, int nrep) 11 { 12 int j, k, rep, nbits, isprime = 1; 13 mpint *nm1, *q, *x, *y, *r; 14 15 if(n->sign < 0) 16 sysfatal("negative prime candidate"); 17 18 if(nrep <= 0) 19 nrep = 18; 20 21 k = mptoi(n); 22 if(k == 2) // 2 is prime 23 return 1; 24 if(k < 2) // 1 is not prime 25 return 0; 26 if((n->p[0] & 1) == 0) // even is not prime 27 return 0; 28 29 // test against small prime numbers 30 if(smallprimetest(n) < 0) 31 return 0; 32 33 // fermat test, 2^n mod n == 2 if p is prime 34 x = uitomp(2, nil); 35 y = mpnew(0); 36 mpexp(x, n, n, y); 37 k = mptoi(y); 38 if(k != 2){ 39 mpfree(x); 40 mpfree(y); 41 return 0; 42 } 43 44 nbits = mpsignif(n); 45 nm1 = mpnew(nbits); 46 mpsub(n, mpone, nm1); // nm1 = n - 1 */ 47 k = mplowbits0(nm1); 48 q = mpnew(0); 49 mpright(nm1, k, q); // q = (n-1)/2**k 50 51 for(rep = 0; rep < nrep; rep++){ 52 53 // x = random in [2, n-2] 54 r = mprand(nbits, prng, nil); 55 mpmod(r, nm1, x); 56 mpfree(r); 57 if(mpcmp(x, mpone) <= 0) 58 continue; 59 60 // y = x**q mod n 61 mpexp(x, q, n, y); 62 63 if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0) 64 goto done; 65 66 for(j = 1; j < k; j++){ 67 mpmul(y, y, x); 68 mpmod(x, n, y); // y = y*y mod n 69 if(mpcmp(y, nm1) == 0) 70 goto done; 71 if(mpcmp(y, mpone) == 0){ 72 isprime = 0; 73 goto done; 74 } 75 } 76 isprime = 0; 77 } 78 done: 79 mpfree(y); 80 mpfree(x); 81 mpfree(q); 82 mpfree(nm1); 83 return isprime; 84 } 85