probably_prime.c

这是一个同样来自贝尔实验室的和UNIX有着渊源的操作系统, 其简洁的设计和实现易于我们学习和理解

#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;
}