From dd1d7bcb69994d81662e709b0ad838880b943870 Mon Sep 17 00:00:00 2001 From: slontis Date: Wed, 2 Nov 2022 12:01:34 +1000 Subject: Improve FIPS RSA keygen performance. 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 Reviewed-by: Tomas Mraz (Merged from https://github.com/openssl/openssl/pull/19578) --- crypto/bn/bn_gcd.c | 31 +++++++++++++++++++++++++++++++ crypto/bn/bn_rsa_fips186_4.c | 24 +++++++++++++++--------- 2 files changed, 46 insertions(+), 9 deletions(-) (limited to 'crypto/bn') diff --git a/crypto/bn/bn_gcd.c b/crypto/bn/bn_gcd.c index 91ad76a161..519bb4e951 100644 --- a/crypto/bn/bn_gcd.c +++ b/crypto/bn/bn_gcd.c @@ -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 diff --git a/crypto/bn/bn_rsa_fips186_4.c b/crypto/bn/bn_rsa_fips186_4.c index 770ae4d1fa..e3a2ad76af 100644 --- a/crypto/bn/bn_rsa_fips186_4.c +++ b/crypto/bn/bn_rsa_fips186_4.c @@ -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) -- cgit v1.2.3