On Sun, Jun 01, 2014 at 08:14:00PM +0000, Viktor Dukhovni wrote:
>
> The new prime generator does not ensure that generated primes are
> "safe" modulo 2, 3, 5, 7 or 11. In particular (p-1)/2 might not
> be co-prime to 2310.
>
> The patch below my signature addresses this problem.
Oops, previous patch neglected the fact that the multiplier needs to be
a multiple of 4 to ensure that all the residues are 3 mod 4.
Updated fix below (just double the multiplier).
--
Viktor.
diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c
index 2d66b61..e74a98f 100644
--- a/crypto/bn/bn_prime.c
+++ b/crypto/bn/bn_prime.c
@@ -132,48 +132,32 @@ static int probable_prime(BIGNUM *rnd, int bits);
static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
-static const 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 const int prime_offset_count = 480;
-static const int prime_multiplier = 2310;
-static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits|
+/*
+ * Residues $r$ modulo $4620 = 4 \cdot 3 \cdot 5 \cdot 7 \cdot 11$ for which
+ * both $r$ and $r-1$ are co-prime to $2310$.
+ */
+static const int prime_offsets[134] = {
+ 47, 59, 83, 107, 167, 179, 227, 263,
+ 299, 347, 359, 383, 443, 467, 479, 503,
+ 527, 563, 587, 599, 647, 719, 767, 779,
+ 839, 863, 887, 899, 923, 983, 1007, 1019,
+ 1103, 1139, 1187, 1223, 1259, 1283, 1307, 1319,
+ 1367, 1403, 1427, 1439, 1487, 1523, 1559, 1619,
+ 1643, 1679, 1703, 1763, 1787, 1823, 1847, 1907,
+ 1943, 1979, 2027, 2039, 2063, 2099, 2147, 2159,
+ 2183, 2207, 2243, 2279, 2327, 2363, 2447, 2459,
+ 2483, 2543, 2567, 2579, 2603, 2627, 2687, 2699,
+ 2747, 2819, 2867, 2879, 2903, 2939, 2963, 2987,
+ 2999, 3023, 3083, 3107, 3119, 3167, 3203, 3239,
+ 3287, 3299, 3359, 3383, 3407, 3419, 3467, 3503,
+ 3527, 3539, 3623, 3659, 3743, 3779, 3803, 3827,
+ 3863, 3887, 3923, 3947, 3959, 4007, 4043, 4079,
+ 4127, 4139, 4163, 4199, 4223, 4259, 4283, 4307,
+ 4343, 4427, 4463, 4547, 4559, 4583,
+ };
+static const int prime_offset_count = 134;
+static const int prime_multiplier = 4620;
+static const int prime_multiplier_bits = 12; /* 2^|prime_multiplier_bits|
<= |prime_multiplier| */
static const int first_prime_index = 5;
diff --git a/tools/primes.py b/tools/primes.py
index 61de99f..cd4a332 100644
--- a/tools/primes.py
+++ b/tools/primes.py
@@ -1,21 +1,37 @@
-primes = [2, 3, 5, 7, 11]
-safe = False # Not sure if the period's right on safe primes.
+# Odd primes < 13
+#
+primes = [3, 5, 7, 11]
-muliplier = 1 if not safe else 2
+multiplier = 4
for p in primes:
- muliplier *= p
+ multiplier *= p
offsets = []
-for x in range(3, muliplier + 3, 2):
- prime = True
+
+# We only test residues 'r' that are 3 mod 4, since both r and (r-1)/2
+# need to be odd. We don't need to test for divisibility by 2, which
+# is why 2 is not in the prime list.
+#
+for r in range(3, multiplier - 1, 4):
+ coprime = True
for p in primes:
- if not x % p or (safe and not ((x - 1) / 2) % p):
- prime = False
+ if r % p <= 1:
+ coprime = False
break
- if prime:
- offsets.append(x)
+ if coprime:
+ offsets.append(r)
+
+count = len(offsets);
+print "static const int prime_offsets[%d] = {\n\t" % (count),
+for i in range(0, count):
+ print "%4d,%s" % (offsets[i], " " if (i % 8 < 7) else "\n\t"),
+print "\n\t};"
-print(offsets)
-print(len(offsets))
-print(muliplier)
+print "static const int prime_offset_count = %d;\n" % (count),
+print "static const int prime_multiplier = %d;\n" % (multiplier),
+bits = 0;
+while multiplier > 1:
+ multiplier /= 2
+ bits += 1
+print "static const int prime_multiplier_bits = %d;\n" % (bits),
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