1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
|
using System;
using Org.BouncyCastle.Math;
using Org.BouncyCastle.Security;
using Org.BouncyCastle.Utilities;
namespace Org.BouncyCastle.Crypto.Generators
{
internal class DHParametersHelper
{
// The primes b/w 2 and ~2^10
/*
3 5 7 11 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
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733
739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863
877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997
1009 1013 1019 1021 1031
*/
// Each list has a product < 2^31
private static readonly int[][] primeLists = new int[][]
{
new int[]{ 3, 5, 7, 11, 13, 17, 19, 23 },
new int[]{ 29, 31, 37, 41, 43 },
new int[]{ 47, 53, 59, 61, 67 },
new int[]{ 71, 73, 79, 83 },
new int[]{ 89, 97, 101, 103 },
new int[]{ 107, 109, 113, 127 },
new int[]{ 131, 137, 139, 149 },
new int[]{ 151, 157, 163, 167 },
new int[]{ 173, 179, 181, 191 },
new int[]{ 193, 197, 199, 211 },
new int[]{ 223, 227, 229 },
new int[]{ 233, 239, 241 },
new int[]{ 251, 257, 263 },
new int[]{ 269, 271, 277 },
new int[]{ 281, 283, 293 },
new int[]{ 307, 311, 313 },
new int[]{ 317, 331, 337 },
new int[]{ 347, 349, 353 },
new int[]{ 359, 367, 373 },
new int[]{ 379, 383, 389 },
new int[]{ 397, 401, 409 },
new int[]{ 419, 421, 431 },
new int[]{ 433, 439, 443 },
new int[]{ 449, 457, 461 },
new int[]{ 463, 467, 479 },
new int[]{ 487, 491, 499 },
new int[]{ 503, 509, 521 },
new int[]{ 523, 541, 547 },
new int[]{ 557, 563, 569 },
new int[]{ 571, 577, 587 },
new int[]{ 593, 599, 601 },
new int[]{ 607, 613, 617 },
new int[]{ 619, 631, 641 },
new int[]{ 643, 647, 653 },
new int[]{ 659, 661, 673 },
new int[]{ 677, 683, 691 },
new int[]{ 701, 709, 719 },
new int[]{ 727, 733, 739 },
new int[]{ 743, 751, 757 },
new int[]{ 761, 769, 773 },
new int[]{ 787, 797, 809 },
new int[]{ 811, 821, 823 },
new int[]{ 827, 829, 839 },
new int[]{ 853, 857, 859 },
new int[]{ 863, 877, 881 },
new int[]{ 883, 887, 907 },
new int[]{ 911, 919, 929 },
new int[]{ 937, 941, 947 },
new int[]{ 953, 967, 971 },
new int[]{ 977, 983, 991 },
new int[]{ 997, 1009, 1013 },
new int[]{ 1019, 1021, 1031 },
};
private static readonly BigInteger Six = BigInteger.ValueOf(6);
private static readonly int[] primeProducts;
private static readonly BigInteger[] PrimeProducts;
static DHParametersHelper()
{
primeProducts = new int[primeLists.Length];
PrimeProducts = new BigInteger[primeLists.Length];
for (int i = 0; i < primeLists.Length; ++i)
{
int[] primeList = primeLists[i];
int product = 1;
for (int j = 0; j < primeList.Length; ++j)
{
product *= primeList[j];
}
primeProducts[i] = product;
PrimeProducts[i] = BigInteger.ValueOf(product);
}
}
/*
* Finds a pair of prime BigInteger's {p, q: p = 2q + 1}
*
* (see: Handbook of Applied Cryptography 4.86)
*/
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
BigInteger p, q;
int qLength = size - 1;
if (size <= 32)
{
for (;;)
{
q = new BigInteger(qLength, 2, random);
p = q.ShiftLeft(1).Add(BigInteger.One);
if (p.IsProbablePrime(certainty)
&& (certainty <= 2 || q.IsProbablePrime(certainty)))
break;
}
}
else
{
// Note: Modified from Java version for speed
for (;;)
{
q = new BigInteger(qLength, 0, random);
retry:
for (int i = 0; i < primeLists.Length; ++i)
{
int test = q.Remainder(PrimeProducts[i]).IntValue;
if (i == 0)
{
int rem3 = test % 3;
if (rem3 != 2)
{
int diff = 2 * rem3 + 2;
q = q.Add(BigInteger.ValueOf(diff));
test = (test + diff) % primeProducts[i];
}
}
int[] primeList = primeLists[i];
for (int j = 0; j < primeList.Length; ++j)
{
int prime = primeList[j];
int qRem = test % prime;
if (qRem == 0 || qRem == (prime >> 1))
{
q = q.Add(Six);
goto retry;
}
}
}
if (q.BitLength != qLength)
continue;
if (!q.RabinMillerTest(2, random))
continue;
p = q.ShiftLeft(1).Add(BigInteger.One);
if (p.RabinMillerTest(certainty, random)
&& (certainty <= 2 || q.RabinMillerTest(certainty - 2, random)))
break;
}
}
return new BigInteger[] { p, q };
}
/*
* Select a high order element of the multiplicative group Zp*
*
* p and q must be s.t. p = 2*q + 1, where p and q are prime (see generateSafePrimes)
*/
internal static BigInteger SelectGenerator(BigInteger p, BigInteger q, SecureRandom random)
{
BigInteger pMinusTwo = p.Subtract(BigInteger.Two);
BigInteger g;
/*
* (see: Handbook of Applied Cryptography 4.80)
*/
// do
// {
// g = BigIntegers.CreateRandomInRange(BigInteger.Two, pMinusTwo, random);
// }
// while (g.ModPow(BigInteger.Two, p).Equals(BigInteger.One)
// || g.ModPow(q, p).Equals(BigInteger.One));
/*
* RFC 2631 2.2.1.2 (and see: Handbook of Applied Cryptography 4.81)
*/
do
{
BigInteger h = BigIntegers.CreateRandomInRange(BigInteger.Two, pMinusTwo, random);
g = h.ModPow(BigInteger.Two, p);
}
while (g.Equals(BigInteger.One));
return g;
}
}
}
|
