提交 7eccef21 编写于 作者: B Bernd Edlinger

Add a parameter to probable_prime if we look for a safe prime

Currently probable_prime makes sure that p-1 does not have
any prime factors from 3..17863, which is useful for safe primes,
but not necessarily for the general case.

Issue was initially reported here:
MIRONOV, I. Factoring RSA Moduli II.
https://windowsontheory.org/2012/05/17/factoring-rsa-moduli-part-ii/Reviewed-by: NTomas Mraz <tmraz@fedoraproject.org>
(Merged from https://github.com/openssl/openssl/pull/9387)
上级 9e1eaa4a
......@@ -22,11 +22,13 @@
static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
const BIGNUM *a1_odd, int k, BN_CTX *ctx,
BN_MONT_CTX *mont);
static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods);
static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
const BIGNUM *add, const BIGNUM *rem,
BN_CTX *ctx);
#define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))
int BN_GENCB_call(BN_GENCB *cb, int a, int b)
{
/* No callback means continue */
......@@ -87,7 +89,7 @@ int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
loop:
/* make a random number and set the top and bottom bits */
if (add == NULL) {
if (!probable_prime(ret, bits, mods))
if (!probable_prime(ret, bits, safe, mods))
goto err;
} else {
if (safe) {
......@@ -272,17 +274,18 @@ static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
return 1;
}
static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods)
{
int i;
BN_ULONG delta;
BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
char is_single_word = bits <= BN_BITS2;
again:
/* TODO: Not all primes are private */
if (!BN_priv_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
return 0;
if (safe && !BN_set_bit(rnd, 1))
return 0;
/* we now have a random number 'rnd' to test. */
for (i = 1; i < NUMPRIMES; i++) {
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
......@@ -290,61 +293,25 @@ static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
return 0;
mods[i] = (prime_t) mod;
}
/*
* If bits is so small that it fits into a single word then we
* additionally don't want to exceed that many bits.
*/
if (is_single_word) {
BN_ULONG size_limit;
if (bits == BN_BITS2) {
/*
* Shifting by this much has undefined behaviour so we do it a
* different way
*/
size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
} else {
size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
}
if (size_limit < maxdelta)
maxdelta = size_limit;
}
delta = 0;
loop:
if (is_single_word) {
BN_ULONG rnd_word = BN_get_word(rnd);
/*-
* In the case that the candidate prime is a single word then
* we check that:
* 1) It's greater than primes[i] because we shouldn't reject
* 3 as being a prime number because it's a multiple of
* three.
* 2) That it's not a multiple of a known prime. We don't
* check that rnd-1 is also coprime to all the known
* primes because there aren't many small primes where
* that's true.
for (i = 1; i < NUMPRIMES; i++) {
/*
* check that rnd is a prime and also that
* gcd(rnd-1,primes) == 1 (except for 2)
* do the second check only if we are interested in safe primes
* in the case that the candidate prime is a single word then
* we check only the primes up to sqrt(rnd)
*/
for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
if ((mods[i] + delta) % primes[i] == 0) {
delta += 2;
if (delta > maxdelta)
goto again;
goto loop;
}
}
} else {
for (i = 1; i < NUMPRIMES; i++) {
/*
* check that rnd is not a prime and also that gcd(rnd-1,primes)
* == 1 (except for 2)
*/
if (((mods[i] + delta) % primes[i]) <= 1) {
delta += 2;
if (delta > maxdelta)
goto again;
goto loop;
}
if (bits <= 31 && delta <= 0x7fffffff
&& square(primes[i]) > BN_get_word(rnd) + delta)
break;
if (safe ? (mods[i] + delta) % primes[i] <= 1
: (mods[i] + delta) % primes[i] == 0) {
delta += safe ? 4 : 2;
if (delta > maxdelta)
goto again;
goto loop;
}
}
if (!BN_add_word(rnd, delta))
......
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