From 982c42cb20f6a6797ea0ce5c5a8c1a040b170d65 Mon Sep 17 00:00:00 2001 From: Felix Laurie von Massenbach Date: Tue, 27 May 2014 12:55:20 +0100 Subject: [PATCH] Try skipping over the adding and just picking a new random number. Generates a number coprime to 2, 3, 5, 7, 11. Speed: Trial div (add) : trial div (retry) : coprime 1 : 0.42 : 0.84 --- apps/speed.c | 42 +++++++++---- crypto/bn/bn_lcl.h | 4 +- crypto/bn/bn_prime.c | 139 +++++++++++++++++++++++++++++++++---------- tools/primes.py | 6 +- 4 files changed, 145 insertions(+), 46 deletions(-) diff --git a/apps/speed.c b/apps/speed.c index 36e885a594..eec2fd0999 100644 --- a/apps/speed.c +++ b/apps/speed.c @@ -228,7 +228,7 @@ static int do_multi(int multi); #define ALGOR_NUM 30 #define SIZE_NUM 5 -#define PRIME_NUM 2 +#define PRIME_NUM 3 #define RSA_NUM 4 #define DSA_NUM 3 @@ -246,7 +246,7 @@ static const char *names[ALGOR_NUM]={ static double results[ALGOR_NUM][SIZE_NUM]; static int lengths[SIZE_NUM]={16,64,256,1024,8*1024}; static const char *prime_names[PRIME_NUM]={ - "prime trial division", "prime coprime" }; + "prime trial division", "prime trial division retry", "prime coprime" }; #ifndef OPENSSL_NO_RSA static double rsa_results[RSA_NUM][2]; #endif @@ -501,8 +501,9 @@ int MAIN(int argc, char **argv) double d=0.0; long c[ALGOR_NUM][SIZE_NUM]; -#define D_PRIME_TRIAL_DIVISION 0 -#define D_PRIME_COPRIME 1 +#define D_PRIME_TRIAL_DIVISION 0 +#define D_PRIME_TRIAL_DIVISION_RETRY 1 +#define D_PRIME_COPRIME 2 long prime_c[PRIME_NUM]; #define R_DSA_512 0 @@ -1011,8 +1012,12 @@ int MAIN(int argc, char **argv) } else #endif - if (strcmp(*argv,"prime-trial-division") == 0) prime_doit[D_PRIME_TRIAL_DIVISION]=1; - else if (strcmp(*argv,"prime-coprime") == 0) prime_doit[D_PRIME_COPRIME]=1; + if (strcmp(*argv,"prime-trial-division") == 0) + prime_doit[D_PRIME_TRIAL_DIVISION] = 1; + else if (strcmp(*argv,"prime-trial-division-retry") == 0) + prime_doit[D_PRIME_TRIAL_DIVISION_RETRY] = 1; + else if (strcmp(*argv,"prime-coprime") == 0) + prime_doit[D_PRIME_COPRIME] = 1; else { BIO_printf(bio_err,"Error: bad option or value\n"); @@ -1350,6 +1355,7 @@ int MAIN(int argc, char **argv) } prime_c[D_PRIME_TRIAL_DIVISION]=count; + prime_c[D_PRIME_TRIAL_DIVISION_RETRY]=count; prime_c[D_PRIME_COPRIME]=count; #ifndef OPENSSL_NO_RSA @@ -2039,30 +2045,44 @@ int MAIN(int argc, char **argv) BN_CTX_free(ctx); BN_free(add); BN_free(rnd); + } + + if (prime_doit[D_PRIME_TRIAL_DIVISION_RETRY]) + { + BIGNUM *rnd = BN_new(); + BN_CTX *ctx = BN_CTX_new(); + + prime_print_message(prime_names[D_PRIME_TRIAL_DIVISION_RETRY], + prime_c[D_PRIME_TRIAL_DIVISION_RETRY]); + + Time_F(START); + for (count=0, run=1; COND(prime_c[D_PRIME_TRIAL_DIVISION_RETRY]); count++) + bn_probable_prime_dh_retry(rnd, 1024, ctx); + d=Time_F(STOP); + prime_print_result(D_PRIME_TRIAL_DIVISION_RETRY, count, d); + + BN_CTX_free(ctx); + BN_free(rnd); } if (prime_doit[D_PRIME_COPRIME]) { BIGNUM *rnd = BN_new(); - BIGNUM *add = BN_new(); BN_CTX *ctx = BN_CTX_new(); - BN_set_word(add, 2); prime_print_message(prime_names[D_PRIME_COPRIME], prime_c[D_PRIME_COPRIME]); Time_F(START); for (count=0, run=1; COND(prime_c[D_PRIME_COPRIME]); count++) - bn_probable_prime_dh_coprime_safe(rnd, 1024, add, NULL, ctx); + bn_probable_prime_dh_coprime(rnd, 1024, ctx); d=Time_F(STOP); prime_print_result(D_PRIME_COPRIME, count, d); BN_CTX_free(ctx); - BN_free(add); BN_free(rnd); - } RAND_pseudo_bytes(buf,36); diff --git a/crypto/bn/bn_lcl.h b/crypto/bn/bn_lcl.h index f0cfaeaaba..3de1d4cde1 100644 --- a/crypto/bn/bn_lcl.h +++ b/crypto/bn/bn_lcl.h @@ -536,8 +536,8 @@ BIGNUM *int_bn_mod_inverse(BIGNUM *in, int bn_probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); -int bn_probable_prime_dh_coprime_safe(BIGNUM *rnd, int bits, - const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); +int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx); +int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx); #ifdef __cplusplus } diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c index 90f840fdd9..064944c8dd 100644 --- a/crypto/bn/bn_prime.c +++ b/crypto/bn/bn_prime.c @@ -129,15 +129,49 @@ 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); -static int probable_prime_dh(BIGNUM *rnd, const BIGNUM *add, - const BIGNUM *rem, BN_CTX *ctx, int first_prime_index); static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); -static int prime_multiplier = 210; -static int prime_offsets[8] = { 23, 47, 59, 83, 107, 143, 167, 179 }; -static int prime_offset_count = 8; -static int prime_offset_count_exponent = 3; +static int prime_offsets[480] = { + 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, + 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229, 233, 239, + 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293, 299, 307, 311, + 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367, 373, 377, 379, 383, + 389, 391, 397, 401, 403, 409, 419, 421, 431, 433, 437, 439, 443, 449, 457, + 461, 463, 467, 479, 481, 487, 491, 493, 499, 503, 509, 521, 523, 527, 529, + 533, 541, 547, 551, 557, 559, 563, 569, 571, 577, 587, 589, 593, 599, 601, + 607, 611, 613, 617, 619, 629, 631, 641, 643, 647, 653, 659, 661, 667, 673, + 677, 683, 689, 691, 697, 701, 703, 709, 713, 719, 727, 731, 733, 739, 743, + 751, 757, 761, 767, 769, 773, 779, 787, 793, 797, 799, 809, 811, 817, 821, + 823, 827, 829, 839, 841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, + 893, 899, 901, 907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, + 967, 971, 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, + 1031, 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, + 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, + 1151, 1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, + 1213, 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, + 1271, 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, + 1319, 1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, + 1373, 1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, + 1433, 1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, + 1489, 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, + 1549, 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, + 1609, 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, + 1667, 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, + 1721, 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, + 1781, 1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, + 1843, 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, + 1901, 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, + 1951, 1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, + 2017, 2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, + 2071, 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, + 2131, 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, + 2197, 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, + 2249, 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, + 2297, 2309, 2311 }; +static int prime_offset_count = 480; +static int prime_multiplier = 2310; int BN_GENCB_call(BN_GENCB *cb, int a, int b) { @@ -367,35 +401,76 @@ err: return(ret); } -int bn_probable_prime_dh(BIGNUM *rnd, int bits, - const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) +int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx) { - if (!BN_rand(rnd, bits, 0, 1)) return(0); + int i; + BIGNUM *t1; + int ret = 0; - return(probable_prime_dh(rnd, add, rem, ctx, 1)); - } + BN_CTX_start(ctx); + if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; -int bn_probable_prime_dh_coprime_safe(BIGNUM *rnd, int bits, - const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) - { - int i = prime_offset_count; - BIGNUM *offset_index = BN_new(); +loop: + if (!BN_rand(rnd, bits, 0, 1)) goto err; - if (!BN_rand(rnd, bits, 0, 1)) return(0); - - while (i >= prime_offset_count) + /* we now have a random number 'rand' to test. */ + + for (i = 1; i < NUMPRIMES; i++) { - if (!BN_rand(offset_index, prime_offset_count_exponent, -1, -1)) - return(0); - i = BN_get_word(offset_index); + /* check that rnd is a prime */ + if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) + { + /*if (!BN_add(rnd, rnd, add)) goto err;*/ + goto loop; + } } + ret=1; - BN_mul_word(rnd, prime_multiplier); - BN_add_word(rnd, prime_offsets[i]); +err: + BN_CTX_end(ctx); + bn_check_top(rnd); + return(ret); + } + +int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx) + { + int i; + BIGNUM *t1; + BIGNUM *offset_index; + BIGNUM *offset_count; + int ret = 0; - BN_free(offset_index); + BN_CTX_start(ctx); + if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; + if ((offset_index = BN_CTX_get(ctx)) == NULL) goto err; + if ((offset_count = BN_CTX_get(ctx)) == NULL) goto err; + + BN_add_word(offset_count, prime_offset_count); + +loop: + if (!BN_rand(rnd, bits, 0, 1)) goto err; + if (!BN_rand_range(offset_index, offset_count)) goto err; + + BN_mul_word(rnd, prime_multiplier); + BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]); - return(probable_prime_dh(rnd, add, rem, ctx, 4)); + /* we now have a random number 'rand' to test. */ + + /* skip primes 2, 3, 5, 7, 11 */ + for (i = 5; i < NUMPRIMES; i++) + { + /* check that rnd is a prime */ + if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) + { + goto loop; + } + } + ret=1; + +err: + BN_CTX_end(ctx); + bn_check_top(rnd); + return(ret); } static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, @@ -490,8 +565,8 @@ loop: return(1); } -static int probable_prime_dh(BIGNUM *rnd, const BIGNUM *add, - const BIGNUM *rem, BN_CTX *ctx, int first_prime_index) +int bn_probable_prime_dh(BIGNUM *rnd, int bits, + const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) { int i,ret=0; BIGNUM *t1; @@ -499,6 +574,8 @@ static int probable_prime_dh(BIGNUM *rnd, const BIGNUM *add, BN_CTX_start(ctx); if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; + if (!BN_rand(rnd,bits,0,1)) goto err; + /* we need ((rnd-rem) % add) == 0 */ if (!BN_mod(t1,rnd,add,ctx)) goto err; @@ -511,7 +588,7 @@ static int probable_prime_dh(BIGNUM *rnd, const BIGNUM *add, /* we now have a random number 'rand' to test. */ loop: - for (i=first_prime_index; i