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