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Improve FIPS RSA keygen performance.

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FIPS 186-4 has 5 different algorithms for key generation,
and all of them rely on testing GCD(a,n) == 1 many times.

Cachegrind was showing that during a RSA keygen operation,
the function BN_gcd() was taking a considerable percentage
of the total cycles.

The default provider uses multiprime keygen, which seemed to
be much faster. This is because it uses BN_mod_inverse()
instead.

For a 4096 bit key, the entropy of a key that was taking a
long time to generate was recorded and fed back into subsequent
runs. Roughly 40% of the cycle time was BN_gcd() with most of the
remainder in the prime testing. Changing to use the inverse
resulted in the cycle count being 96% in the prime testing.

Reviewed-by: Paul Dale <pauli@openssl.org>
Reviewed-by: Tomas Mraz <tomas@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/19578)
This commit is contained in:
slontis
2022-11-02 12:01:34 +10:00
committed by Tomas Mraz
parent 88113f5dc6
commit dd1d7bcb69
6 changed files with 85 additions and 12 deletions
Download Patch File Download Diff File Expand all files Collapse all files

31
crypto/bn/bn_gcd.c
View File

@@ -534,6 +534,37 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
return rv;
}
/*
* The numbers a and b are coprime if the only positive integer that is a
* divisor of both of them is 1.
* i.e. gcd(a,b) = 1.
*
* Coprimes have the property: b has a multiplicative inverse modulo a
* i.e there is some value x such that bx = 1 (mod a).
*
* Testing the modulo inverse is currently much faster than the constant
* time version of BN_gcd().
*/
int BN_are_coprime(BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = 0;
BIGNUM *tmp;
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
if (tmp == NULL)
goto end;
ERR_set_mark();
BN_set_flags(a, BN_FLG_CONSTTIME);
ret = (BN_mod_inverse(tmp, a, b, ctx) != NULL);
/* Clear any errors (an error is returned if there is no inverse) */
ERR_pop_to_mark();
end:
BN_CTX_end(ctx);
return ret;
}
/*-
* This function is based on the constant-time GCD work by Bernstein and Yang:
* https://eprint.iacr.org/2019/266

24
crypto/bn/bn_rsa_fips186_4.c
View File

@@ -286,14 +286,20 @@ int ossl_bn_rsa_fips186_4_derive_prime(BIGNUM *Y, BIGNUM *X, const BIGNUM *Xin,
goto err;
}
/*
* (Step 1) GCD(2r1, r2) = 1.
* Note: This algorithm was doing a gcd(2r1, r2)=1 test before doing an
* mod_inverse(2r1, r2) which are effectively the same operation.
* (The algorithm assumed that the gcd test would be faster). Since the
* mod_inverse is currently faster than calling the constant time
* BN_gcd(), the call to BN_gcd() has been omitted. The inverse result
* is used further down.
*/
if (!(BN_lshift1(r1x2, r1)
/* (Step 1) GCD(2r1, r2) = 1 */
&& BN_gcd(tmp, r1x2, r2, ctx)
&& BN_is_one(tmp)
&& (BN_mod_inverse(tmp, r1x2, r2, ctx) != NULL)
/* (Step 2) R = ((r2^-1 mod 2r1) * r2) - ((2r1^-1 mod r2)*2r1) */
&& BN_mod_inverse(R, r2, r1x2, ctx)
&& (BN_mod_inverse(R, r2, r1x2, ctx) != NULL)
&& BN_mul(R, R, r2, ctx) /* R = (r2^-1 mod 2r1) * r2 */
&& BN_mod_inverse(tmp, r1x2, r2, ctx)
&& BN_mul(tmp, tmp, r1x2, ctx) /* tmp = (2r1^-1 mod r2)*2r1 */
&& BN_sub(R, R, tmp)
/* Calculate 2r1r2 */
@@ -305,7 +311,8 @@ int ossl_bn_rsa_fips186_4_derive_prime(BIGNUM *Y, BIGNUM *X, const BIGNUM *Xin,
/*
* In FIPS 186-4 imax was set to 5 * nlen/2.
* Analysis by Allen Roginsky (See https://csrc.nist.gov/CSRC/media/Publications/fips/186/4/final/documents/comments-received-fips186-4-december-2015.pdf
* Analysis by Allen Roginsky
* (See https://csrc.nist.gov/CSRC/media/Publications/fips/186/4/final/documents/comments-received-fips186-4-december-2015.pdf
* page 68) indicates this has a 1 in 2 million chance of failure.
* The number has been updated to 20 * nlen/2 as used in
* FIPS186-5 Appendix B.9 Step 9.
@@ -337,10 +344,9 @@ int ossl_bn_rsa_fips186_4_derive_prime(BIGNUM *Y, BIGNUM *X, const BIGNUM *Xin,
/* (Step 7) If GCD(Y-1) == 1 & Y is probably prime then return Y */
if (BN_copy(y1, Y) == NULL
|| !BN_sub_word(y1, 1)
|| !BN_gcd(tmp, y1, e, ctx))
|| !BN_sub_word(y1, 1))
goto err;
if (BN_is_one(tmp)) {
if (BN_are_coprime(y1, e, ctx)) {
int rv = BN_check_prime(Y, ctx, cb);
if (rv > 0)

14
doc/man3/BN_cmp.pod
View File

@@ -2,7 +2,8 @@
=head1 NAME
BN_cmp, BN_ucmp, BN_is_zero, BN_is_one, BN_is_word, BN_abs_is_word, BN_is_odd - BIGNUM comparison and test functions
BN_cmp, BN_ucmp, BN_is_zero, BN_is_one, BN_is_word, BN_abs_is_word, BN_is_odd, BN_are_coprime
- BIGNUM comparison and test functions
=head1 SYNOPSIS
@@ -17,6 +18,8 @@ BN_cmp, BN_ucmp, BN_is_zero, BN_is_one, BN_is_word, BN_abs_is_word, BN_is_odd -
int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w);
int BN_is_odd(const BIGNUM *a);
int BN_are_coprime(BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
=head1 DESCRIPTION
BN_cmp() compares the numbers I<a> and I<b>. BN_ucmp() compares their
@@ -26,6 +29,10 @@ BN_is_zero(), BN_is_one(), BN_is_word() and BN_abs_is_word() test if
I<a> equals 0, 1, I<w>, or E<verbar>I<w>E<verbar> respectively.
BN_is_odd() tests if I<a> is odd.
BN_are_coprime() determines if B<a> and B<b> are coprime.
B<ctx> is used internally for storing temporary variables.
The values of B<a> and B<b> and B<ctx> must not be NULL.
=head1 RETURN VALUES
BN_cmp() returns -1 if I<a> E<lt> I<b>, 0 if I<a> == I<b> and 1 if
@@ -35,11 +42,16 @@ of I<a> and I<b>.
BN_is_zero(), BN_is_one() BN_is_word(), BN_abs_is_word() and
BN_is_odd() return 1 if the condition is true, 0 otherwise.
BN_are_coprime() returns 1 if the B<BIGNUM>'s are coprime, otherwise it
returns 0.
=head1 HISTORY
Prior to OpenSSL 1.1.0, BN_is_zero(), BN_is_one(), BN_is_word(),
BN_abs_is_word() and BN_is_odd() were macros.
The function BN_are_coprime() was added in OpenSSL 3.1.
=head1 COPYRIGHT
Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved.

1
include/openssl/bn.h
View File

@@ -350,6 +350,7 @@ int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
int BN_kronecker(const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); /* returns
* -2 for
* error */
int BN_are_coprime(BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
BIGNUM *BN_mod_inverse(BIGNUM *ret,
const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
BIGNUM *BN_mod_sqrt(BIGNUM *ret,

26
test/bntest.c
View File

@@ -41,6 +41,7 @@ typedef struct mpitest_st {
static const int NUM0 = 100; /* number of tests */
static const int NUM1 = 50; /* additional tests for some functions */
static const int NUM_PRIME_TESTS = 20;
static BN_CTX *ctx;
/*
@@ -2722,6 +2723,25 @@ static int test_ctx_consttime_flag(void)
return st;
}
static int test_coprime(void)
{
BIGNUM *a = NULL, *b = NULL;
int ret = 0;
ret = TEST_ptr(a = BN_new())
&& TEST_ptr(b = BN_new())
&& TEST_true(BN_set_word(a, 66))
&& TEST_true(BN_set_word(b, 99))
&& TEST_int_eq(BN_are_coprime(a, b, ctx), 0)
&& TEST_int_eq(BN_are_coprime(b, a, ctx), 0)
&& TEST_true(BN_set_word(a, 67))
&& TEST_int_eq(BN_are_coprime(a, b, ctx), 1)
&& TEST_int_eq(BN_are_coprime(b, a, ctx), 1);
BN_free(a);
BN_free(b);
return ret;
}
static int test_gcd_prime(void)
{
BIGNUM *a = NULL, *b = NULL, *gcd = NULL;
@@ -2734,11 +2754,12 @@ static int test_gcd_prime(void)
if (!TEST_true(BN_generate_prime_ex(a, 1024, 0, NULL, NULL, NULL)))
goto err;
for (i = 0; i < NUM0; i++) {
for (i = 0; i < NUM_PRIME_TESTS; i++) {
if (!TEST_true(BN_generate_prime_ex(b, 1024, 0,
NULL, NULL, NULL))
|| !TEST_true(BN_gcd(gcd, a, b, ctx))
|| !TEST_true(BN_is_one(gcd)))
|| !TEST_true(BN_is_one(gcd))
|| !TEST_true(BN_are_coprime(a, b, ctx)))
goto err;
}
@@ -3216,6 +3237,7 @@ int setup_tests(void)
ADD_ALL_TESTS(test_is_prime, (int)OSSL_NELEM(primes));
ADD_ALL_TESTS(test_not_prime, (int)OSSL_NELEM(not_primes));
ADD_TEST(test_gcd_prime);
ADD_TEST(test_coprime);
ADD_ALL_TESTS(test_mod_exp, (int)OSSL_NELEM(ModExpTests));
ADD_ALL_TESTS(test_mod_exp_consttime, (int)OSSL_NELEM(ModExpTests));
ADD_TEST(test_mod_exp2_mont);

1
util/libcrypto.num
View File

@@ -5430,6 +5430,7 @@ OPENSSL_strncasecmp 5557 3_0_3 EXIST::FUNCTION:
EVP_RAND_CTX_up_ref ? 3_1_0 EXIST::FUNCTION:
RAND_set0_public ? 3_1_0 EXIST::FUNCTION:
RAND_set0_private ? 3_1_0 EXIST::FUNCTION:
BN_are_coprime ? 3_1_0 EXIST::FUNCTION:
X509_PUBKEY_set0_public_key ? 3_2_0 EXIST::FUNCTION:
OSSL_STACK_OF_X509_free ? 3_2_0 EXIST::FUNCTION:
EVP_MD_CTX_dup ? 3_2_0 EXIST::FUNCTION: