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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
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@erbridge @benlaurie
erbridge authored and benlaurie committed Jun 1, 2014
1 parent 7e965dc commit 982c42c
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Showing 4 changed files with 145 additions and 46 deletions.
42 changes: 31 additions & 11 deletions apps/speed.c
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Original file line number Diff line number Diff line change
Expand Up @@ -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

Expand All @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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");
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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);
Expand Down
4 changes: 2 additions & 2 deletions crypto/bn/bn_lcl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -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
}
Expand Down
139 changes: 109 additions & 30 deletions crypto/bn/bn_prime.c
View file
Original file line number Diff line number Diff line change
Expand Up @@ -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)
{
Expand Down Expand Up @@ -367,35 +401,76 @@ int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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,
Expand Down Expand Up @@ -490,15 +565,17 @@ static int probable_prime(BIGNUM *rnd, int bits)
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;

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;
Expand All @@ -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<NUMPRIMES; i++)
for (i=1; i<NUMPRIMES; i++)
{
/* check that rnd is a prime */
if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
Expand All @@ -521,6 +598,7 @@ static int probable_prime_dh(BIGNUM *rnd, const BIGNUM *add,
}
}
ret=1;

err:
BN_CTX_end(ctx);
bn_check_top(rnd);
Expand Down Expand Up @@ -565,7 +643,7 @@ static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
/* check that p and q are prime */
/* check that for p and q
* 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))
{
if (!BN_add(p,p,padd)) goto err;
Expand All @@ -574,6 +652,7 @@ static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
}
}
ret=1;

err:
BN_CTX_end(ctx);
bn_check_top(p);
Expand Down
6 changes: 3 additions & 3 deletions tools/primes.py
View file
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
primes = [2, 3, 5, 7]
safe = True
primes = [2, 3, 5, 7, 11]
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:
muliplier *= p

Expand Down

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