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1/* $OpenBSD: res_random.c,v 1.17 2008/04/13 00:28:35 djm Exp $ */
2
3/*
4 * Copyright 1997 Niels Provos <provos@physnet.uni-hamburg.de>
5 * Copyright 2008 Damien Miller <djm@openbsd.org>
6 * All rights reserved.
7 *
8 * Theo de Raadt <deraadt@openbsd.org> came up with the idea of using
9 * such a mathematical system to generate more random (yet non-repeating)
10 * ids to solve the resolver/named problem. But Niels designed the
11 * actual system based on the constraints.
12 *
13 * Later modified by Damien Miller to wrap the LCG output in a 15-bit
14 * permutation generator based on a Luby-Rackoff block cipher. This
15 * ensures the output is non-repeating and preserves the MSB twiddle
16 * trick, but makes it more resistant to LCG prediction.
17 *
18 * Redistribution and use in source and binary forms, with or without
19 * modification, are permitted provided that the following conditions
20 * are met:
21 * 1. Redistributions of source code must retain the above copyright
22 * notice, this list of conditions and the following disclaimer.
23 * 2. Redistributions in binary form must reproduce the above copyright
24 * notice, this list of conditions and the following disclaimer in the
25 * documentation and/or other materials provided with the distribution.
26 *
27 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
28 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
29 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
30 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
31 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
32 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
33 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
34 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
35 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
36 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
37 */
38
39/*
40 * seed = random 15bit
41 * n = prime, g0 = generator to n,
42 * j = random so that gcd(j,n-1) == 1
43 * g = g0^j mod n will be a generator again.
44 *
45 * X[0] = random seed.
46 * X[n] = a*X[n-1]+b mod m is a Linear Congruential Generator
47 * with a = 7^(even random) mod m,
48 * b = random with gcd(b,m) == 1
49 * m = 31104 and a maximal period of m-1.
50 *
51 * The transaction id is determined by:
52 * id[n] = seed xor (g^X[n] mod n)
53 *
54 * Effectivly the id is restricted to the lower 15 bits, thus
55 * yielding two different cycles by toggling the msb on and off.
56 * This avoids reuse issues caused by reseeding.
57 *
58 * The output of this generator is then randomly permuted though a
59 * custom 15 bit Luby-Rackoff block cipher.
60 */
61
62#include <sys/types.h>
63#include <netinet/in.h>
64#include <sys/time.h>
65#include <resolv.h>
66
67#include <unistd.h>
68#include <stdlib.h>
69#include <string.h>
70
71#define RU_OUT 180 /* Time after wich will be reseeded */
72#define RU_MAX 30000 /* Uniq cycle, avoid blackjack prediction */
73#define RU_GEN 2 /* Starting generator */
74#define RU_N 32749 /* RU_N-1 = 2*2*3*2729 */
75#define RU_AGEN 7 /* determine ru_a as RU_AGEN^(2*rand) */
76#define RU_M 31104 /* RU_M = 2^7*3^5 - don't change */
77#define RU_ROUNDS 11 /* Number of rounds for permute (odd) */
78
79struct prf_ctx {
80 /* PRF lookup table for odd rounds (7 bits input to 8 bits output) */
81 u_char prf7[(RU_ROUNDS / 2) * (1 << 7)];
82
83 /* PRF lookup table for even rounds (8 bits input to 7 bits output) */
84 u_char prf8[((RU_ROUNDS + 1) / 2) * (1 << 8)];
85};
86
87#define PFAC_N 3
88const static u_int16_t pfacts[PFAC_N] = {
89 2,
90 3,
91 2729
92};
93
94static u_int16_t ru_x;
95static u_int16_t ru_seed, ru_seed2;
96static u_int16_t ru_a, ru_b;
97static u_int16_t ru_g;
98static u_int16_t ru_counter = 0;
99static u_int16_t ru_msb = 0;
100static struct prf_ctx *ru_prf = NULL;
101static long ru_reseed;
102
103static u_int16_t pmod(u_int16_t, u_int16_t, u_int16_t);
104static void res_initid(void);
105
106/*
107 * Do a fast modular exponation, returned value will be in the range
108 * of 0 - (mod-1)
109 */
110static u_int16_t
111pmod(u_int16_t gen, u_int16_t exp, u_int16_t mod)
112{
113 u_int16_t s, t, u;
114
115 s = 1;
116 t = gen;
117 u = exp;
118
119 while (u) {
120 if (u & 1)
121 s = (s * t) % mod;
122 u >>= 1;
123 t = (t * t) % mod;
124 }
125 return (s);
126}
127
128/*
129 * 15-bit permutation based on Luby-Rackoff block cipher
130 */
131u_int
132permute15(u_int in)
133{
134 int i;
135 u_int left, right, tmp;
136
137 if (ru_prf == NULL)
138 return in;
139
140 left = (in >> 8) & 0x7f;
141 right = in & 0xff;
142
143 /*
144 * Each round swaps the width of left and right. Even rounds have
145 * a 7-bit left, odd rounds have an 8-bit left. Since this uses an
146 * odd number of rounds, left is always 8 bits wide at the end.
147 */
148 for (i = 0; i < RU_ROUNDS; i++) {
149 if ((i & 1) == 0)
150 tmp = ru_prf->prf8[(i << (8 - 1)) | right] & 0x7f;
151 else
152 tmp = ru_prf->prf7[((i - 1) << (7 - 1)) | right];
153 tmp ^= left;
154 left = right;
155 right = tmp;
156 }
157
158 return (right << 8) | left;
159}
160
161/*
162 * Initializes the seed and chooses a suitable generator. Also toggles
163 * the msb flag. The msb flag is used to generate two distinct
164 * cycles of random numbers and thus avoiding reuse of ids.
165 *
166 * This function is called from res_randomid() when needed, an
167 * application does not have to worry about it.
168 */
169static void
170res_initid(void)
171{
172 u_int16_t j, i;
173 u_int32_t tmp;
174 int noprime = 1;
175 struct timeval tv;
176
177 ru_x = arc4random_uniform(RU_M);
178
179 /* 15 bits of random seed */
180 tmp = arc4random();
181 ru_seed = (tmp >> 16) & 0x7FFF;
182 ru_seed2 = tmp & 0x7FFF;
183
184 /* Determine the LCG we use */
185 tmp = arc4random();
186 ru_b = (tmp & 0xfffe) | 1;
187 ru_a = pmod(RU_AGEN, (tmp >> 16) & 0xfffe, RU_M);
188 while (ru_b % 3 == 0)
189 ru_b += 2;
190
191 j = arc4random_uniform(RU_N);
192
193 /*
194 * Do a fast gcd(j,RU_N-1), so we can find a j with
195 * gcd(j, RU_N-1) == 1, giving a new generator for
196 * RU_GEN^j mod RU_N
197 */
198
199 while (noprime) {
200 for (i = 0; i < PFAC_N; i++)
201 if (j % pfacts[i] == 0)
202 break;
203
204 if (i >= PFAC_N)
205 noprime = 0;
206 else
207 j = (j + 1) % RU_N;
208 }
209
210 ru_g = pmod(RU_GEN, j, RU_N);
211 ru_counter = 0;
212
213 /* Initialise PRF for Luby-Rackoff permutation */
214 if (ru_prf == NULL)
215 ru_prf = malloc(sizeof(*ru_prf));
216 if (ru_prf != NULL)
217 arc4random_buf(ru_prf, sizeof(*ru_prf));
218
219 gettimeofday(&tv, NULL);
220 ru_reseed = tv.tv_sec + RU_OUT;
221 ru_msb = ru_msb == 0x8000 ? 0 : 0x8000;
222}
223
224u_int
225res_randomid(void)
226{
227 struct timeval tv;
228
229 gettimeofday(&tv, NULL);
230 if (ru_counter >= RU_MAX || tv.tv_sec > ru_reseed)
231 res_initid();
232
233 /* Linear Congruential Generator */
234 ru_x = (ru_a * ru_x + ru_b) % RU_M;
235 ru_counter++;
236
237 return permute15(ru_seed ^ pmod(ru_g, ru_seed2 + ru_x, RU_N)) | ru_msb;
238}
239
240#if 0
241int
242main(int argc, char **argv)
243{
244 int i, n;
245 u_int16_t wert;
246
247 res_initid();
248
249 printf("Generator: %u\n", ru_g);
250 printf("Seed: %u\n", ru_seed);
251 printf("Reseed at %ld\n", ru_reseed);
252 printf("Ru_X: %u\n", ru_x);
253 printf("Ru_A: %u\n", ru_a);
254 printf("Ru_B: %u\n", ru_b);
255
256 n = argc > 1 ? atoi(argv[1]) : 60001;
257 for (i=0;i<n;i++) {
258 wert = res_randomid();
259 printf("%u\n", wert);
260 }
261 return 0;
262}
263#endif
264