1 0fc65b37 2004-03-21 devnull #include "os.h"
 2 0fc65b37 2004-03-21 devnull #include <mp.h>
 3 0fc65b37 2004-03-21 devnull #include <libsec.h>
 4 0fc65b37 2004-03-21 devnull 
 5 0fc65b37 2004-03-21 devnull // Miller-Rabin probabilistic primality testing
 6 0fc65b37 2004-03-21 devnull //	Knuth (1981) Seminumerical Algorithms, p.379
 7 0fc65b37 2004-03-21 devnull //	Menezes et al () Handbook, p.39
 8 0fc65b37 2004-03-21 devnull // 0 if composite; 1 if almost surely prime, Pr(err)<1/4**nrep
 9 0fc65b37 2004-03-21 devnull int
10 0fc65b37 2004-03-21 devnull probably_prime(mpint *n, int nrep)
11 0fc65b37 2004-03-21 devnull {
12 0fc65b37 2004-03-21 devnull 	int j, k, rep, nbits, isprime = 1;
13 0fc65b37 2004-03-21 devnull 	mpint *nm1, *q, *x, *y, *r;
14 0fc65b37 2004-03-21 devnull 
15 0fc65b37 2004-03-21 devnull 	if(n->sign < 0)
16 0fc65b37 2004-03-21 devnull 		sysfatal("negative prime candidate");
17 0fc65b37 2004-03-21 devnull 
18 0fc65b37 2004-03-21 devnull 	if(nrep <= 0)
19 0fc65b37 2004-03-21 devnull 		nrep = 18;
20 0fc65b37 2004-03-21 devnull 
21 0fc65b37 2004-03-21 devnull 	k = mptoi(n);
22 0fc65b37 2004-03-21 devnull 	if(k == 2)		// 2 is prime
23 0fc65b37 2004-03-21 devnull 		return 1;
24 0fc65b37 2004-03-21 devnull 	if(k < 2)		// 1 is not prime
25 0fc65b37 2004-03-21 devnull 		return 0;
26 0fc65b37 2004-03-21 devnull 	if((n->p[0] & 1) == 0)	// even is not prime
27 0fc65b37 2004-03-21 devnull 		return 0;
28 0fc65b37 2004-03-21 devnull 
29 0fc65b37 2004-03-21 devnull 	// test against small prime numbers
30 0fc65b37 2004-03-21 devnull 	if(smallprimetest(n) < 0)
31 0fc65b37 2004-03-21 devnull 		return 0;
32 0fc65b37 2004-03-21 devnull 
33 0fc65b37 2004-03-21 devnull 	// fermat test, 2^n mod n == 2 if p is prime
34 0fc65b37 2004-03-21 devnull 	x = uitomp(2, nil);
35 0fc65b37 2004-03-21 devnull 	y = mpnew(0);
36 0fc65b37 2004-03-21 devnull 	mpexp(x, n, n, y);
37 0fc65b37 2004-03-21 devnull 	k = mptoi(y);
38 0fc65b37 2004-03-21 devnull 	if(k != 2){
39 0fc65b37 2004-03-21 devnull 		mpfree(x);
40 0fc65b37 2004-03-21 devnull 		mpfree(y);
41 0fc65b37 2004-03-21 devnull 		return 0;
42 0fc65b37 2004-03-21 devnull 	}
43 0fc65b37 2004-03-21 devnull 
44 0fc65b37 2004-03-21 devnull 	nbits = mpsignif(n);
45 0fc65b37 2004-03-21 devnull 	nm1 = mpnew(nbits);
46 0fc65b37 2004-03-21 devnull 	mpsub(n, mpone, nm1);	// nm1 = n - 1 */
47 0fc65b37 2004-03-21 devnull 	k = mplowbits0(nm1);
48 0fc65b37 2004-03-21 devnull 	q = mpnew(0);
49 0fc65b37 2004-03-21 devnull 	mpright(nm1, k, q);	// q = (n-1)/2**k
50 0fc65b37 2004-03-21 devnull 
51 0fc65b37 2004-03-21 devnull 	for(rep = 0; rep < nrep; rep++){
52 0fc65b37 2004-03-21 devnull 		
53 0fc65b37 2004-03-21 devnull 		// x = random in [2, n-2]
54 0fc65b37 2004-03-21 devnull 		r = mprand(nbits, prng, nil);
55 0fc65b37 2004-03-21 devnull 		mpmod(r, nm1, x);
56 0fc65b37 2004-03-21 devnull 		mpfree(r);
57 0fc65b37 2004-03-21 devnull 		if(mpcmp(x, mpone) <= 0)
58 0fc65b37 2004-03-21 devnull 			continue;
59 0fc65b37 2004-03-21 devnull 
60 0fc65b37 2004-03-21 devnull 		// y = x**q mod n
61 0fc65b37 2004-03-21 devnull 		mpexp(x, q, n, y);
62 0fc65b37 2004-03-21 devnull 
63 0fc65b37 2004-03-21 devnull 		if(mpcmp(y, mpone) == 0 || mpcmp(y, nm1) == 0)
64 0fc65b37 2004-03-21 devnull 			goto done;
65 0fc65b37 2004-03-21 devnull 
66 0fc65b37 2004-03-21 devnull 		for(j = 1; j < k; j++){
67 0fc65b37 2004-03-21 devnull 			mpmul(y, y, x);
68 0fc65b37 2004-03-21 devnull 			mpmod(x, n, y);	// y = y*y mod n
69 0fc65b37 2004-03-21 devnull 			if(mpcmp(y, nm1) == 0)
70 0fc65b37 2004-03-21 devnull 				goto done;
71 0fc65b37 2004-03-21 devnull 			if(mpcmp(y, mpone) == 0){
72 0fc65b37 2004-03-21 devnull 				isprime = 0;
73 0fc65b37 2004-03-21 devnull 				goto done;
74 0fc65b37 2004-03-21 devnull 			}
75 0fc65b37 2004-03-21 devnull 		}
76 0fc65b37 2004-03-21 devnull 		isprime = 0;
77 0fc65b37 2004-03-21 devnull 	}
78 0fc65b37 2004-03-21 devnull done:
79 0fc65b37 2004-03-21 devnull 	mpfree(y);
80 0fc65b37 2004-03-21 devnull 	mpfree(x);
81 0fc65b37 2004-03-21 devnull 	mpfree(q);
82 0fc65b37 2004-03-21 devnull 	mpfree(nm1);
83 0fc65b37 2004-03-21 devnull 	return isprime;
84 0fc65b37 2004-03-21 devnull }