spisprime.c

大数的计算包括加减乘除

/* spIsPrime.c */

/******************* SHORT COPYRIGHT NOTICE*************************
This source code is part of the BigDigits multiple-precision
arithmetic library Version 1.0 originally written by David Ireland,
copyright (c) 2001 D.I. Management Services Pty Limited, all rights
reserved. It is provided "as is" with no warranties. You may use
this software under the terms of the full copyright notice
"bigdigitsCopyright.txt" that should have been included with
this library. To obtain a copy send an email to
<[e-mail]> or visit <www.di-mgt.com.au/crypto.html>.
This notice must be retained in any copy.
****************** END OF COPYRIGHT NOTICE*************************/

#include <assert.h>
#include "bigdigits.h"

static DIGIT_T SMALL_PRIMES[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
#define N_SMALL_PRIMES sizeof(SMALL_PRIMES)/sizeof(DIGIT_T)

int spIsPrime(DIGIT_T w, unsigned int t)
{	/*	Returns true if w is a probable prime 
		Carries out t iterations
		(Use t = 50 for DSS Standard) 
	*/
	/*	Uses Rabin-Miller Probabilistic Primality Test,
		Ref: FIPS-186-2 Appendix 2.
		Also Schneier 2nd ed p 260 & Knuth Vol 2, p 379.
	*/
	/*	Rabin-Miller Probabilistic Primality Test,
		from FIPS-186-2 Appendix 2.
		Also Schneier 2nd ed p 260 & Knuth Vol 2, p 379.
	*/

	unsigned int i, j;
	DIGIT_T m, a, b, z;
	int failed;

	/*	First check for small primes */
	for (i = 0; i < N_SMALL_PRIMES; i++)
	{
		if (w % SMALL_PRIMES[i] == 0)
			return 0;	/* Failed */
	}

	/*	Now do Rabin-Miller  */
	/*	Step 2. Find a and m where w = 1 + (2^a)m
		m is odd and 2^a is largest power of 2 dividing w - 1 */
	m = w - 1;
	for (a = 0; ISEVEN(m); a++)
		m >>= 1;	/* Divide by 2 until m is odd */

	/*
	assert((1 << a) * m + 1 == w);
	*/

	for (i = 0; i < t; i++)
	{
		failed = 1;	/* Assume fail unless passed in loop */
		/* Step 3. Generate a random integer 1 < b < w */
		b = spPseudoRand(2, w - 1);

		/*
		assert(1 < b && b < w);
		*/

		/* Step 4. Set j = 0 and z = b^m mod w */
		j = 0;
		spModExp(&z, b, m, w);
		do
		{
			/* Step 5. If j = 0 and z = 1, or if z = w - 1 */
			if ((j == 0 && z == 1) || (z == w - 1))
			{	/* Passes on this loop  - go to Step 9 */
				failed = 0;
				break;
			}

			/* Step 6. If j > 0 and z = 1 */
			if (j > 0 && z == 1)
			{	/* Fails - go to Step 8 */
				failed = 1;
				break;
			}

			/* Step 7. j = j + 1. If j < a set z = z^2 mod w */
			j++;
			if (j < a)
				spModMult(&z, z, z, w);
			/* Loop: if j < a go to Step 5 */
		} while (j < a);

		if (failed)
		{	/* Step 8. Not a prime - stop */
			return 0;
		}
	}	/* Step 9. Go to Step 3 until i >= n */
	/* If got here, probably prime => success */
	return 1;
}