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cryb-to/lib/rsaref/prime.c

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2014-07-04 11:18:53 +00:00
/* PRIME.C - primality-testing routines
*/
/* Copyright (C) RSA Laboratories, a division of RSA Data Security,
Inc., created 1991. All rights reserved.
*/
#include "global.h"
#include "rsaref.h"
#include "r_random.h"
#include "nn.h"
#include "prime.h"
static unsigned int SMALL_PRIMES[] = { 3, 5, 7, 11 };
#define SMALL_PRIME_COUNT 4
static int ProbablePrime PROTO_LIST ((NN_DIGIT *, unsigned int));
static int SmallFactor PROTO_LIST ((NN_DIGIT *, unsigned int));
static int FermatTest PROTO_LIST ((NN_DIGIT *, unsigned int));
/* Generates a probable prime a between b and c such that a-1 is
divisible by d.
Lengths: a[digits], b[digits], c[digits], d[digits].
Assumes b < c, digits < MAX_NN_DIGITS.
Returns RE_NEED_RANDOM if randomStruct not seeded, RE_DATA if
unsuccessful.
*/
int GeneratePrime (a, b, c, d, digits, randomStruct)
NN_DIGIT *a, *b, *c, *d;
unsigned int digits;
R_RANDOM_STRUCT *randomStruct;
{
int status;
unsigned char block[MAX_NN_DIGITS * NN_DIGIT_LEN];
NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS];
/* Generate random number between b and c.
*/
if ((status = R_GenerateBytes (block, digits * NN_DIGIT_LEN, randomStruct)))
return (status);
NN_Decode (a, digits, block, digits * NN_DIGIT_LEN);
NN_Sub (t, c, b, digits);
NN_ASSIGN_DIGIT (u, 1, digits);
NN_Add (t, t, u, digits);
NN_Mod (a, a, digits, t, digits);
NN_Add (a, a, b, digits);
/* Adjust so that a-1 is divisible by d.
*/
NN_Mod (t, a, digits, d, digits);
NN_Sub (a, a, t, digits);
NN_Add (a, a, u, digits);
if (NN_Cmp (a, b, digits) < 0)
NN_Add (a, a, d, digits);
if (NN_Cmp (a, c, digits) > 0)
NN_Sub (a, a, d, digits);
/* Search to c in steps of d.
*/
NN_Assign (t, c, digits);
NN_Sub (t, t, d, digits);
while (! ProbablePrime (a, digits)) {
if (NN_Cmp (a, t, digits) > 0)
return (RE_DATA);
NN_Add (a, a, d, digits);
}
return (0);
}
/* Returns nonzero iff a is a probable prime.
Lengths: a[aDigits].
Assumes aDigits < MAX_NN_DIGITS.
*/
static int ProbablePrime (a, aDigits)
NN_DIGIT *a;
unsigned int aDigits;
{
return (! SmallFactor (a, aDigits) && FermatTest (a, aDigits));
}
/* Returns nonzero iff a has a prime factor in SMALL_PRIMES.
Lengths: a[aDigits].
Assumes aDigits < MAX_NN_DIGITS.
*/
static int SmallFactor (a, aDigits)
NN_DIGIT *a;
unsigned int aDigits;
{
int status;
NN_DIGIT t[1];
unsigned int i;
status = 0;
for (i = 0; i < SMALL_PRIME_COUNT; i++) {
NN_ASSIGN_DIGIT (t, SMALL_PRIMES[i], 1);
if ((aDigits == 1) && ! NN_Cmp (a, t, 1))
break;
NN_Mod (t, a, aDigits, t, 1);
if (NN_Zero (t, 1)) {
status = 1;
break;
}
}
/* Zeroize sensitive information.
*/
i = 0;
R_memset ((POINTER)t, 0, sizeof (t));
return (status);
}
/* Returns nonzero iff a passes Fermat's test for witness 2.
(All primes pass the test, and nearly all composites fail.)
Lengths: a[aDigits].
Assumes aDigits < MAX_NN_DIGITS.
*/
static int FermatTest (a, aDigits)
NN_DIGIT *a;
unsigned int aDigits;
{
int status;
NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS];
NN_ASSIGN_DIGIT (t, 2, aDigits);
NN_ModExp (u, t, a, aDigits, a, aDigits);
status = NN_EQUAL (t, u, aDigits);
/* Zeroize sensitive information.
*/
R_memset ((POINTER)u, 0, sizeof (u));
return (status);
}