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/* PRIME.C - primality-testing routines
*/
/* Copyright (C) 1991-2 RSA Laboratories, a division of RSA Data
Security, Inc. All rights reserved.
*/
#include "global.h"
#include "rsaref.h"
#include "nn.h"
#include "prime.h"
static unsigned int SMALL_PRIMES[] = { 3, 5, 7, 11 };
#define SMALL_PRIME_COUNT 4
static int RSAPrime PROTO_LIST
((NN_DIGIT *, unsigned int, NN_DIGIT *, unsigned int));
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));
static int RelativelyPrime PROTO_LIST
((NN_DIGIT *, unsigned int, NN_DIGIT *, unsigned int));
/* Find a probable prime a between 3*2^(b-2) and 2^b-1, starting at
3*2^(b-2) + (c mod 2^(b-2)), such that gcd (a-1, d) = 1.
Lengths: a[cDigits], c[cDigits], d[dDigits].
Assumes b > 2, b < cDigits * NN_DIGIT_BITS, d is odd,
cDigits < MAX_NN_DIGITS, dDigits < MAX_NN_DIGITS, and a
probable prime can be found.
*/
void FindRSAPrime (a, b, c, cDigits, d, dDigits)
NN_DIGIT *a, *c, *d;
unsigned int b, cDigits, dDigits;
{
NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS], v[MAX_NN_DIGITS],
w[MAX_NN_DIGITS];
/* Compute t = 2^(b-2), u = 3*2^(b-2).
*/
NN_Assign2Exp (t, b-2, cDigits);
NN_Assign2Exp (u, b-1, cDigits);
NN_Add (u, u, t, cDigits);
/* Compute v = 3*2^(b-2) + (c mod 2^(b-2)); add one if even.
*/
NN_Mod (v, c, cDigits, t, cDigits);
NN_Add (v, v, u, cDigits);
if (NN_EVEN (v, cDigits)) {
NN_ASSIGN_DIGIT (w, 1, cDigits);
NN_Add (v, v, w, cDigits);
}
/* Compute w = 2, u = 2^b - 2.
*/
NN_ASSIGN_DIGIT (w, 2, cDigits);
NN_Sub (u, u, w, cDigits);
NN_Add (u, u, t, cDigits);
/* Search to 2^b-1 from starting point, then from 3*2^(b-2)+1.
*/
while (! RSAPrime (v, cDigits, d, dDigits)) {
if (NN_Cmp (v, u, cDigits) > 0)
NN_Sub (v, v, t, cDigits);
NN_Add (v, v, w, cDigits);
}
NN_Assign (a, v, cDigits);
/* Zeroize sensitive information.
*/
R_memset ((POINTER)v, 0, sizeof (v));
}
/* Returns nonzero iff a is a probable prime and GCD (a-1, b) = 1.
Lengths: a[aDigits], b[bDigits].
Assumes aDigits < MAX_NN_DIGITS, bDigits < MAX_NN_DIGITS.
*/
static int RSAPrime (a, aDigits, b, bDigits)
NN_DIGIT *a, *b;
unsigned int aDigits, bDigits;
{
int status;
NN_DIGIT aMinus1[MAX_NN_DIGITS], t[MAX_NN_DIGITS];
NN_ASSIGN_DIGIT (t, 1, aDigits);
NN_Sub (aMinus1, a, t, aDigits);
status = ProbablePrime (a, aDigits) &&
RelativelyPrime (aMinus1, aDigits, b, bDigits);
/* Zeroize sensitive information.
*/
R_memset ((POINTER)aMinus1, 0, sizeof (aMinus1));
return (status);
}
/* 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);
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);
}
/* Returns nonzero iff a and b are relatively prime.
Lengths: a[aDigits], b[bDigits].
Assumes aDigits >= bDigits, aDigits < MAX_NN_DIGITS.
*/
static int RelativelyPrime (a, aDigits, b, bDigits)
NN_DIGIT *a, *b;
unsigned int aDigits, bDigits;
{
int status;
NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS];
NN_AssignZero (t, aDigits);
NN_Assign (t, b, bDigits);
NN_Gcd (t, a, t, aDigits);
NN_ASSIGN_DIGIT (u, 1, aDigits);
status = NN_EQUAL (t, u, aDigits);
/* Zeroize sensitive information.
*/
R_memset ((POINTER)t, 0, sizeof (t));
return (status);
}
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.