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Hakase
2019-10-17 23:54:38 +09:00
parent 41a23ae6f6
commit ee84d0dd84
1357 changed files with 41111 additions and 9603 deletions
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crypto/bn/bn_prime.c
+100 -16
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@@ -10,7 +10,7 @@
#include <stdio.h>
#include <time.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
#include "bn_local.h"
/*
* The quick sieve algorithm approach to weeding out primes is Philip
@@ -24,6 +24,8 @@ static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
const BIGNUM *add, const BIGNUM *rem,
BN_CTX *ctx);
static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
int do_trial_division, BN_GENCB *cb);
#define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))
@@ -65,6 +67,37 @@ const BIGNUM *bn_get0_small_factors(void)
return &_bignum_small_prime_factors;
}
/*
* Calculate the number of trial divisions that gives the best speed in
* combination with Miller-Rabin prime test, based on the sized of the prime.
*/
static int calc_trial_divisions(int bits)
{
if (bits <= 512)
return 64;
else if (bits <= 1024)
return 128;
else if (bits <= 2048)
return 384;
else if (bits <= 4096)
return 1024;
return NUMPRIMES;
}
/*
* Use a minimum of 64 rounds of Miller-Rabin, which should give a false
* positive rate of 2^-128. If the size of the prime is larger than 2048
* the user probably wants a higher security level than 128, so switch
* to 128 rounds giving a false positive rate of 2^-256.
* Returns the number of rounds.
*/
static int bn_mr_min_checks(int bits)
{
if (bits > 2048)
return 128;
return 64;
}
int BN_GENCB_call(BN_GENCB *cb, int a, int b)
{
/* No callback means continue */
@@ -95,7 +128,7 @@ int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
int found = 0;
int i, j, c1 = 0;
prime_t *mods = NULL;
int checks = BN_prime_checks_for_size(bits);
int checks = bn_mr_min_checks(bits);
if (bits < 2) {
/* There are no prime numbers this small. */
@@ -134,7 +167,7 @@ int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
goto err;
if (!safe) {
i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
i = bn_is_prime_int(ret, checks, ctx, 0, cb);
if (i == -1)
goto err;
if (i == 0)
@@ -148,13 +181,13 @@ int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
goto err;
for (i = 0; i < checks; i++) {
j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
j = bn_is_prime_int(ret, 1, ctx, 0, cb);
if (j == -1)
goto err;
if (j == 0)
goto loop;
j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
j = bn_is_prime_int(t, 1, ctx, 0, cb);
if (j == -1)
goto err;
if (j == 0)
@@ -191,15 +224,45 @@ int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
}
#endif
#if !OPENSSL_API_3
int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
BN_GENCB *cb)
{
return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
return bn_check_prime_int(a, checks, ctx_passed, 0, cb);
}
/* See FIPS 186-4 C.3.1 Miller Rabin Probabilistic Primality Test. */
int BN_is_prime_fasttest_ex(const BIGNUM *w, int checks, BN_CTX *ctx,
int do_trial_division, BN_GENCB *cb)
{
return bn_check_prime_int(w, checks, ctx, do_trial_division, cb);
}
#endif
/* Wrapper around bn_is_prime_int that sets the minimum number of checks */
int bn_check_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
int do_trial_division, BN_GENCB *cb)
{
int min_checks = bn_mr_min_checks(BN_num_bits(w));
if (checks < min_checks)
checks = min_checks;
return bn_is_prime_int(w, checks, ctx, do_trial_division, cb);
}
int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb)
{
return bn_check_prime_int(p, 0, ctx, 1, cb);
}
/*
* Tests that |w| is probably prime
* See FIPS 186-4 C.3.1 Miller Rabin Probabilistic Primality Test.
*
* Returns 0 when composite, 1 when probable prime, -1 on error.
*/
static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
int do_trial_division, BN_GENCB *cb)
{
int i, status, ret = -1;
#ifndef FIPS_MODE
@@ -226,7 +289,9 @@ int BN_is_prime_fasttest_ex(const BIGNUM *w, int checks, BN_CTX *ctx,
/* first look for small factors */
if (do_trial_division) {
for (i = 1; i < NUMPRIMES; i++) {
int trial_divisions = calc_trial_divisions(BN_num_bits(w));
for (i = 1; i < trial_divisions; i++) {
BN_ULONG mod = BN_mod_word(w, primes[i]);
if (mod == (BN_ULONG)-1)
return -1;
@@ -313,8 +378,8 @@ int bn_miller_rabin_is_prime(const BIGNUM *w, int iterations, BN_CTX *ctx,
if (mont == NULL || !BN_MONT_CTX_set(mont, w, ctx))
goto err;
if (iterations == BN_prime_checks)
iterations = BN_prime_checks_for_size(BN_num_bits(w));
if (iterations == 0)
iterations = bn_mr_min_checks(BN_num_bits(w));
/* (Step 4) */
for (i = 0; i < iterations; ++i) {
@@ -398,12 +463,22 @@ err:
return ret;
}
/*
* Generate a random number of |bits| bits that is probably prime by sieving.
* If |safe| != 0, it generates a safe prime.
* |mods| is a preallocated array that gets reused when called again.
*
* The probably prime is saved in |rnd|.
*
* Returns 1 on success and 0 on error.
*/
static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
BN_CTX *ctx)
{
int i;
BN_ULONG delta;
BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
int trial_divisions = calc_trial_divisions(bits);
BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
again:
/* TODO: Not all primes are private */
@@ -412,7 +487,7 @@ static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
if (safe && !BN_set_bit(rnd, 1))
return 0;
/* we now have a random number 'rnd' to test. */
for (i = 1; i < NUMPRIMES; i++) {
for (i = 1; i < trial_divisions; i++) {
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
if (mod == (BN_ULONG)-1)
return 0;
@@ -420,7 +495,7 @@ static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
}
delta = 0;
loop:
for (i = 1; i < NUMPRIMES; i++) {
for (i = 1; i < trial_divisions; i++) {
/*
* check that rnd is a prime and also that
* gcd(rnd-1,primes) == 1 (except for 2)
@@ -447,6 +522,14 @@ static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
return 1;
}
/*
* Generate a random number |rnd| of |bits| bits that is probably prime
* and satisfies |rnd| % |add| == |rem| by sieving.
* If |safe| != 0, it generates a safe prime.
* |mods| is a preallocated array that gets reused when called again.
*
* Returns 1 on success and 0 on error.
*/
static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
const BIGNUM *add, const BIGNUM *rem,
BN_CTX *ctx)
@@ -454,7 +537,8 @@ static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
int i, ret = 0;
BIGNUM *t1;
BN_ULONG delta;
BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
int trial_divisions = calc_trial_divisions(bits);
BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
BN_CTX_start(ctx);
if ((t1 = BN_CTX_get(ctx)) == NULL)
@@ -488,7 +572,7 @@ static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
}
/* we now have a random number 'rnd' to test. */
for (i = 1; i < NUMPRIMES; i++) {
for (i = 1; i < trial_divisions; i++) {
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
if (mod == (BN_ULONG)-1)
goto err;
@@ -496,7 +580,7 @@ static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
}
delta = 0;
loop:
for (i = 1; i < NUMPRIMES; i++) {
for (i = 1; i < trial_divisions; i++) {
/* check that rnd is a prime */
if (bits <= 31 && delta <= 0x7fffffff
&& square(primes[i]) > BN_get_word(rnd) + delta)