mirror of
https://github.com/cryb-to/cryb-to.git
synced 2024-11-15 10:15:40 +00:00
143 lines
3.3 KiB
C
143 lines
3.3 KiB
C
/* 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);
|
|
}
|