From b2bc1712a5578ef8f4a644b5a1f35c41fa5c9f2c Mon Sep 17 00:00:00 2001 From: Gilles Peskine Date: Fri, 8 Feb 2019 17:27:11 +0100 Subject: [PATCH 1/2] Reduce the size of the small primes table used by primality testing Signed-off-by: Gilles Peskine --- library/bignum.c | 62 ++++++++++++++++++++++++------------------------ 1 file changed, 31 insertions(+), 31 deletions(-) diff --git a/library/bignum.c b/library/bignum.c index d559c9e76..f84b2e7ce 100644 --- a/library/bignum.c +++ b/library/bignum.c @@ -2171,29 +2171,29 @@ cleanup: #if defined(MBEDTLS_GENPRIME) -static const int small_prime[] = -{ - 3, 5, 7, 11, 13, 17, 19, 23, - 29, 31, 37, 41, 43, 47, 53, 59, - 61, 67, 71, 73, 79, 83, 89, 97, - 101, 103, 107, 109, 113, 127, 131, 137, - 139, 149, 151, 157, 163, 167, 173, 179, - 181, 191, 193, 197, 199, 211, 223, 227, - 229, 233, 239, 241, 251, 257, 263, 269, - 271, 277, 281, 283, 293, 307, 311, 313, - 317, 331, 337, 347, 349, 353, 359, 367, - 373, 379, 383, 389, 397, 401, 409, 419, - 421, 431, 433, 439, 443, 449, 457, 461, - 463, 467, 479, 487, 491, 499, 503, 509, - 521, 523, 541, 547, 557, 563, 569, 571, - 577, 587, 593, 599, 601, 607, 613, 617, - 619, 631, 641, 643, 647, 653, 659, 661, - 673, 677, 683, 691, 701, 709, 719, 727, - 733, 739, 743, 751, 757, 761, 769, 773, - 787, 797, 809, 811, 821, 823, 827, 829, - 839, 853, 857, 859, 863, 877, 881, 883, - 887, 907, 911, 919, 929, 937, 941, 947, - 953, 967, 971, 977, 983, 991, 997, -103 +/* Gaps between primes, starting at 3. https://oeis.org/A001223 */ +static const unsigned char small_prime_gaps[] = { + 2, 2, 4, 2, 4, 2, 4, 6, + 2, 6, 4, 2, 4, 6, 6, 2, + 6, 4, 2, 6, 4, 6, 8, 4, + 2, 4, 2, 4, 14, 4, 6, 2, + 10, 2, 6, 6, 4, 6, 6, 2, + 10, 2, 4, 2, 12, 12, 4, 2, + 4, 6, 2, 10, 6, 6, 6, 2, + 6, 4, 2, 10, 14, 4, 2, 4, + 14, 6, 10, 2, 4, 6, 8, 6, + 6, 4, 6, 8, 4, 8, 10, 2, + 10, 2, 6, 4, 6, 8, 4, 2, + 4, 12, 8, 4, 8, 4, 6, 12, + 2, 18, 6, 10, 6, 6, 2, 6, + 10, 6, 6, 2, 6, 6, 4, 2, + 12, 10, 2, 4, 6, 6, 2, 12, + 4, 6, 8, 10, 8, 10, 8, 6, + 6, 4, 8, 6, 4, 8, 4, 14, + 10, 12, 2, 10, 2, 4, 2, 10, + 14, 4, 2, 4, 14, 4, 2, 4, + 20, 4, 8, 10, 8, 4, 6, 6, + 14, 4, 6, 6, 8, 6, /*reaches 997*/ }; /* @@ -2210,20 +2210,20 @@ static int mpi_check_small_factors(const mbedtls_mpi *X) int ret = 0; size_t i; mbedtls_mpi_uint r; + unsigned p = 3; /* The first odd prime */ if ((X->p[0] & 1) == 0) { return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; } - for (i = 0; small_prime[i] > 0; i++) { - if (mbedtls_mpi_cmp_int(X, small_prime[i]) <= 0) { - return 1; - } - - MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, small_prime[i])); - + for (i = 0; i < sizeof(small_prime_gaps); p += small_prime_gaps[i], i++) { + MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, p)); if (r == 0) { - return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + if (mbedtls_mpi_cmp_int(X, p) == 0) { + return 1; + } else { + return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + } } } From 30b0378008895e5d9c938761aca424dd28b04e0b Mon Sep 17 00:00:00 2001 From: Gilles Peskine Date: Tue, 22 Aug 2023 11:06:47 +0200 Subject: [PATCH 2/2] Fix off-by-one error The value of p after adding the last entry in the gap table is not used. Signed-off-by: Gilles Peskine --- library/bignum.c | 1 + 1 file changed, 1 insertion(+) diff --git a/library/bignum.c b/library/bignum.c index f84b2e7ce..3724571b2 100644 --- a/library/bignum.c +++ b/library/bignum.c @@ -2194,6 +2194,7 @@ static const unsigned char small_prime_gaps[] = { 14, 4, 2, 4, 14, 4, 2, 4, 20, 4, 8, 10, 8, 4, 6, 6, 14, 4, 6, 6, 8, 6, /*reaches 997*/ + 0 /* the last entry is effectively unused */ }; /*