New unbiased prime generator function fixes

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New unbiased prime generator function fixes

Viktor Dukhovni

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.

--
        Viktor.

diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c
index 2d66b61..bb36124 100644
--- a/crypto/bn/bn_prime.c
+++ b/crypto/bn/bn_prime.c
@@ -132,46 +132,22 @@ 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;
+/*
+ * Residues $r$ modulo $2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11$ for which
+ * both $r$ and $(r-1)/2$ are co-prime to $2310$.
+ */
+static const int prime_offsets[68] = {
+  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
+ };
+static const int prime_offset_count = 68;
 static const int prime_multiplier = 2310;
 static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits|
  <= |prime_multiplier| */
diff --git a/tools/primes.py b/tools/primes.py
index 61de99f..0cdecb7 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 = 2
 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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Re: New unbiased prime generator function fixes

Viktor Dukhovni
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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Re: New unbiased prime generator function fixes

Ben Laurie-2
You didn't update the test...

On 1 June 2014 21:26, Viktor Dukhovni <[hidden email]> wrote:

> 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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Re: New unbiased prime generator function fixes

Viktor Dukhovni
On Sun, Jun 01, 2014 at 09:45:15PM +0100, Ben Laurie wrote:
> You didn't update the test...

You're right.  The below should take care of that.

--
        Viktor.

diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c
index 2d66b61..df50305 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 $(r-1)/2$ 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/crypto/bn/bntest.c b/crypto/bn/bntest.c
index 697d77a..f17f61b 100644
--- a/crypto/bn/bntest.c
+++ b/crypto/bn/bntest.c
@@ -1944,9 +1944,9 @@ int test_probable_prime_coprime(BIO *bp, BN_CTX *ctx)
 
  for (j = 0; j < 5; j++)
  {
- if (BN_mod_word(&r, primes[j]) == 0)
+ if (BN_mod_word(&r, primes[j]) <= (j ? 1 : 0))
  {
- BIO_printf(bp, "Number generated is not coprime to %ld:\n", primes[j]);
+ BIO_printf(bp, "Number generated is <= %d mod %ld:\n", j ? 1 : 0, primes[j]);
  BN_print_fp(stdout, &r);
  BIO_printf(bp, "\n");
  goto err;
diff --git a/tools/primes.py b/tools/primes.py
index 61de99f..6adac96 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, 13, 17, 19]
 
-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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Re: New unbiased prime generator function fixes

Kurt Roeckx
On Sun, Jun 01, 2014 at 09:04:29PM +0000, Viktor Dukhovni wrote:
> @@ -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, 13, 17, 19]

Maybe the comment is wrong?


Kurt

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Re: New unbiased prime generator function fixes

Viktor Dukhovni
On Sun, Jun 01, 2014 at 11:12:53PM +0200, Kurt Roeckx wrote:
> On Sun, Jun 01, 2014 at 09:04:29PM +0000, Viktor Dukhovni wrote:
> > @@ -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, 13, 17, 19]
>
> Maybe the comment is wrong?

No, the primes are supposed to be < 13, I was playing around with
17 and 19 also, but the dataset is too big that way.

The python code is used only once to generate the table in the C-code,
but it should only be going up to 11. :-)

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        Viktor.
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Re: New unbiased prime generator function fixes

Felix Laurie von Massenbach
Only just joined the list and I see that there's been some follow up
stuff to my contribution, but I submitted a follow up pull request to
some of this stuff on GitHub
(https://github.com/openssl/openssl/pull/118). So probably some
duplication there :).

--
Felix - http://www.erbridge.co.uk/


On 2 June 2014 00:15, Viktor Dukhovni <[hidden email]> wrote:

> On Sun, Jun 01, 2014 at 11:12:53PM +0200, Kurt Roeckx wrote:
>> On Sun, Jun 01, 2014 at 09:04:29PM +0000, Viktor Dukhovni wrote:
>> > @@ -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, 13, 17, 19]
>>
>> Maybe the comment is wrong?
>
> No, the primes are supposed to be < 13, I was playing around with
> 17 and 19 also, but the dataset is too big that way.
>
> The python code is used only once to generate the table in the C-code,
> but it should only be going up to 11. :-)
>
> --
>         Viktor.
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