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Try skipping over the adding and just picking a new random number.

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Generates a number coprime to 2, 3, 5, 7, 11.

Speed:
Trial div (add) : trial div (retry) : coprime
1 : 0.42 : 0.84
This commit is contained in:
Felix Laurie von Massenbach 2014-05-27 12:55:20 +01:00 committed by Ben Laurie
parent 7e965dcc38
commit 982c42cb20
4 changed files with 145 additions and 46 deletions
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42
apps/speed.c
View File

@ -228,7 +228,7 @@ static int do_multi(int multi);
#define ALGOR_NUM 30 #define ALGOR_NUM 30
#define SIZE_NUM 5 #define SIZE_NUM 5
#define PRIME_NUM 2 #define PRIME_NUM 3
#define RSA_NUM 4 #define RSA_NUM 4
#define DSA_NUM 3 #define DSA_NUM 3
@ -246,7 +246,7 @@ static const char *names[ALGOR_NUM]={
static double results[ALGOR_NUM][SIZE_NUM]; static double results[ALGOR_NUM][SIZE_NUM];
static int lengths[SIZE_NUM]={16,64,256,1024,8*1024}; static int lengths[SIZE_NUM]={16,64,256,1024,8*1024};
static const char *prime_names[PRIME_NUM]={ 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 #ifndef OPENSSL_NO_RSA
static double rsa_results[RSA_NUM][2]; static double rsa_results[RSA_NUM][2];
#endif #endif
@ -501,8 +501,9 @@ int MAIN(int argc, char **argv)
double d=0.0; double d=0.0;
long c[ALGOR_NUM][SIZE_NUM]; long c[ALGOR_NUM][SIZE_NUM];
#define D_PRIME_TRIAL_DIVISION 0 #define D_PRIME_TRIAL_DIVISION 0
#define D_PRIME_COPRIME 1 #define D_PRIME_TRIAL_DIVISION_RETRY 1
#define D_PRIME_COPRIME 2
long prime_c[PRIME_NUM]; long prime_c[PRIME_NUM];
#define R_DSA_512 0 #define R_DSA_512 0
@ -1011,8 +1012,12 @@ int MAIN(int argc, char **argv)
} }
else else
#endif #endif
if (strcmp(*argv,"prime-trial-division") == 0) prime_doit[D_PRIME_TRIAL_DIVISION]=1; if (strcmp(*argv,"prime-trial-division") == 0)
else if (strcmp(*argv,"prime-coprime") == 0) prime_doit[D_PRIME_COPRIME]=1; 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 else
{ {
BIO_printf(bio_err,"Error: bad option or value\n"); 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]=count;
prime_c[D_PRIME_TRIAL_DIVISION_RETRY]=count;
prime_c[D_PRIME_COPRIME]=count; prime_c[D_PRIME_COPRIME]=count;
#ifndef OPENSSL_NO_RSA #ifndef OPENSSL_NO_RSA
@ -2039,30 +2045,44 @@ int MAIN(int argc, char **argv)
BN_CTX_free(ctx); BN_CTX_free(ctx);
BN_free(add); BN_free(add);
BN_free(rnd); 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]) if (prime_doit[D_PRIME_COPRIME])
{ {
BIGNUM *rnd = BN_new(); BIGNUM *rnd = BN_new();
BIGNUM *add = BN_new();
BN_CTX *ctx = BN_CTX_new(); BN_CTX *ctx = BN_CTX_new();
BN_set_word(add, 2);
prime_print_message(prime_names[D_PRIME_COPRIME], prime_print_message(prime_names[D_PRIME_COPRIME],
prime_c[D_PRIME_COPRIME]); prime_c[D_PRIME_COPRIME]);
Time_F(START); Time_F(START);
for (count=0, run=1; COND(prime_c[D_PRIME_COPRIME]); count++) 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); d=Time_F(STOP);
prime_print_result(D_PRIME_COPRIME, count, d); prime_print_result(D_PRIME_COPRIME, count, d);
BN_CTX_free(ctx); BN_CTX_free(ctx);
BN_free(add);
BN_free(rnd); BN_free(rnd);
} }
RAND_pseudo_bytes(buf,36); RAND_pseudo_bytes(buf,36);

4
crypto/bn/bn_lcl.h
View File

@ -536,8 +536,8 @@ BIGNUM *int_bn_mod_inverse(BIGNUM *in,
int bn_probable_prime_dh(BIGNUM *rnd, int bits, int bn_probable_prime_dh(BIGNUM *rnd, int bits,
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
int bn_probable_prime_dh_coprime_safe(BIGNUM *rnd, int bits, int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx);
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx);
#ifdef __cplusplus #ifdef __cplusplus
} }

139
crypto/bn/bn_prime.c
View File

@ -129,15 +129,49 @@
static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); 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(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, static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
static int prime_multiplier = 210; static int prime_offsets[480] = {
static int prime_offsets[8] = { 23, 47, 59, 83, 107, 143, 167, 179 }; 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89,
static int prime_offset_count = 8; 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
static int prime_offset_count_exponent = 3; 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) int BN_GENCB_call(BN_GENCB *cb, int a, int b)
{ {
@ -367,35 +401,76 @@ err:
return(ret); return(ret);
} }
int bn_probable_prime_dh(BIGNUM *rnd, int bits, int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
const BIGNUM *add, const BIGNUM *rem, 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;
loop:
if (!BN_rand(rnd, bits, 0, 1)) goto err;
/* we now have a random number 'rand' to test. */
for (i = 1; i < NUMPRIMES; i++)
{
/* 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;
err:
BN_CTX_end(ctx);
bn_check_top(rnd);
return(ret);
} }
int bn_probable_prime_dh_coprime_safe(BIGNUM *rnd, int bits, int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
{ {
int i = prime_offset_count; int i;
BIGNUM *offset_index = BN_new(); BIGNUM *t1;
BIGNUM *offset_index;
if (!BN_rand(rnd, bits, 0, 1)) return(0); BIGNUM *offset_count;
int ret = 0;
while (i >= prime_offset_count) BN_CTX_start(ctx);
{ if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
if (!BN_rand(offset_index, prime_offset_count_exponent, -1, -1)) if ((offset_index = BN_CTX_get(ctx)) == NULL) goto err;
return(0); if ((offset_count = BN_CTX_get(ctx)) == NULL) goto err;
i = BN_get_word(offset_index);
} 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_mul_word(rnd, prime_multiplier);
BN_add_word(rnd, prime_offsets[i]); BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]);
BN_free(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, static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
@ -490,8 +565,8 @@ loop:
return(1); return(1);
} }
static int probable_prime_dh(BIGNUM *rnd, const BIGNUM *add, int bn_probable_prime_dh(BIGNUM *rnd, int bits,
const BIGNUM *rem, BN_CTX *ctx, int first_prime_index) const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
{ {
int i,ret=0; int i,ret=0;
BIGNUM *t1; BIGNUM *t1;
@ -499,6 +574,8 @@ static int probable_prime_dh(BIGNUM *rnd, const BIGNUM *add,
BN_CTX_start(ctx); BN_CTX_start(ctx);
if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
if (!BN_rand(rnd,bits,0,1)) goto err;
/* we need ((rnd-rem) % add) == 0 */ /* we need ((rnd-rem) % add) == 0 */
if (!BN_mod(t1,rnd,add,ctx)) goto err; 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. */ /* we now have a random number 'rand' to test. */
loop: loop:
for (i=first_prime_index; i<NUMPRIMES; i++) for (i=1; i<NUMPRIMES; i++)
{ {
/* check that rnd is a prime */ /* check that rnd is a prime */
if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1) if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
@ -521,6 +598,7 @@ loop:
} }
} }
ret=1; ret=1;
err: err:
BN_CTX_end(ctx); BN_CTX_end(ctx);
bn_check_top(rnd); bn_check_top(rnd);
@ -565,7 +643,7 @@ loop:
/* check that p and q are prime */ /* check that p and q are prime */
/* check that for p and q /* check that for p and q
* gcd(p-1,primes) == 1 (except for 2) */ * gcd(p-1,primes) == 1 (except for 2) */
if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) || if ((BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
(BN_mod_word(q,(BN_ULONG)primes[i]) == 0)) (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
{ {
if (!BN_add(p,p,padd)) goto err; if (!BN_add(p,p,padd)) goto err;
@ -574,6 +652,7 @@ loop:
} }
} }
ret=1; ret=1;
err: err:
BN_CTX_end(ctx); BN_CTX_end(ctx);
bn_check_top(p); bn_check_top(p);

6
tools/primes.py
View File

@ -1,7 +1,7 @@
primes = [2, 3, 5, 7] primes = [2, 3, 5, 7, 11]
safe = True safe = False # Not sure if the period's right on safe primes.
muliplier = 1 muliplier = 1 if not safe else 2
for p in primes: for p in primes:
muliplier *= p muliplier *= p