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1/* $OpenBSD: res_random.c,v 1.20 2013/11/12 07:00:24 deraadt 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#include "thread_private.h"
72
73#define RU_OUT 180 /* Time after wich will be reseeded */
74#define RU_MAX 30000 /* Uniq cycle, avoid blackjack prediction */
75#define RU_GEN 2 /* Starting generator */
76#define RU_N 32749 /* RU_N-1 = 2*2*3*2729 */
77#define RU_AGEN 7 /* determine ru_a as RU_AGEN^(2*rand) */
78#define RU_M 31104 /* RU_M = 2^7*3^5 - don't change */
79#define RU_ROUNDS 11 /* Number of rounds for permute (odd) */
80
81struct prf_ctx {
82 /* PRF lookup table for odd rounds (7 bits input to 8 bits output) */
83 u_char prf7[(RU_ROUNDS / 2) * (1 << 7)];
84
85 /* PRF lookup table for even rounds (8 bits input to 7 bits output) */
86 u_char prf8[((RU_ROUNDS + 1) / 2) * (1 << 8)];
87};
88
89#define PFAC_N 3
90const static u_int16_t pfacts[PFAC_N] = {
91 2,
92 3,
93 2729
94};
95
96static u_int16_t ru_x;
97static u_int16_t ru_seed, ru_seed2;
98static u_int16_t ru_a, ru_b;
99static u_int16_t ru_g;
100static u_int16_t ru_counter = 0;
101static u_int16_t ru_msb = 0;
102static struct prf_ctx *ru_prf = NULL;
103static time_t ru_reseed;
104
105static u_int16_t pmod(u_int16_t, u_int16_t, u_int16_t);
106static void res_initid(void);
107
108/*
109 * Do a fast modular exponation, returned value will be in the range
110 * of 0 - (mod-1)
111 */
112static u_int16_t
113pmod(u_int16_t gen, u_int16_t exp, u_int16_t mod)
114{
115 u_int16_t s, t, u;
116
117 s = 1;
118 t = gen;
119 u = exp;
120
121 while (u) {
122 if (u & 1)
123 s = (s * t) % mod;
124 u >>= 1;
125 t = (t * t) % mod;
126 }
127 return (s);
128}
129
130/*
131 * 15-bit permutation based on Luby-Rackoff block cipher
132 */
133static u_int
134permute15(u_int in)
135{
136 int i;
137 u_int left, right, tmp;
138
139 if (ru_prf == NULL)
140 return in;
141
142 left = (in >> 8) & 0x7f;
143 right = in & 0xff;
144
145 /*
146 * Each round swaps the width of left and right. Even rounds have
147 * a 7-bit left, odd rounds have an 8-bit left. Since this uses an
148 * odd number of rounds, left is always 8 bits wide at the end.
149 */
150 for (i = 0; i < RU_ROUNDS; i++) {
151 if ((i & 1) == 0)
152 tmp = ru_prf->prf8[(i << (8 - 1)) | right] & 0x7f;
153 else
154 tmp = ru_prf->prf7[((i - 1) << (7 - 1)) | right];
155 tmp ^= left;
156 left = right;
157 right = tmp;
158 }
159
160 return (right << 8) | left;
161}
162
163/*
164 * Initializes the seed and chooses a suitable generator. Also toggles
165 * the msb flag. The msb flag is used to generate two distinct
166 * cycles of random numbers and thus avoiding reuse of ids.
167 *
168 * This function is called from res_randomid() when needed, an
169 * application does not have to worry about it.
170 */
171static void
172res_initid(void)
173{
174 u_int16_t j, i;
175 u_int32_t tmp;
176 int noprime = 1;
177 struct timespec ts;
178
179 ru_x = arc4random_uniform(RU_M);
180
181 /* 15 bits of random seed */
182 tmp = arc4random();
183 ru_seed = (tmp >> 16) & 0x7FFF;
184 ru_seed2 = tmp & 0x7FFF;
185
186 /* Determine the LCG we use */
187 tmp = arc4random();
188 ru_b = (tmp & 0xfffe) | 1;
189 ru_a = pmod(RU_AGEN, (tmp >> 16) & 0xfffe, RU_M);
190 while (ru_b % 3 == 0)
191 ru_b += 2;
192
193 j = arc4random_uniform(RU_N);
194
195 /*
196 * Do a fast gcd(j,RU_N-1), so we can find a j with
197 * gcd(j, RU_N-1) == 1, giving a new generator for
198 * RU_GEN^j mod RU_N
199 */
200
201 while (noprime) {
202 for (i = 0; i < PFAC_N; i++)
203 if (j % pfacts[i] == 0)
204 break;
205
206 if (i >= PFAC_N)
207 noprime = 0;
208 else
209 j = (j + 1) % RU_N;
210 }
211
212 ru_g = pmod(RU_GEN, j, RU_N);
213 ru_counter = 0;
214
215 /* Initialise PRF for Luby-Rackoff permutation */
216 if (ru_prf == NULL)
217 ru_prf = malloc(sizeof(*ru_prf));
218 if (ru_prf != NULL)
219 arc4random_buf(ru_prf, sizeof(*ru_prf));
220
221 clock_gettime(CLOCK_MONOTONIC, &ts);
222 ru_reseed = ts.tv_sec + RU_OUT;
223 ru_msb = ru_msb == 0x8000 ? 0 : 0x8000;
224}
225
226u_int
227res_randomid(void)
228{
229 struct timespec ts;
230 u_int r;
231 _THREAD_PRIVATE_MUTEX(random);
232
233 clock_gettime(CLOCK_MONOTONIC, &ts);
234
235 _THREAD_PRIVATE_MUTEX_LOCK(random);
236
237 if (ru_counter >= RU_MAX || ts.tv_sec > ru_reseed)
238 res_initid();
239
240 /* Linear Congruential Generator */
241 ru_x = (ru_a * ru_x + ru_b) % RU_M;
242 ru_counter++;
243
244 r = permute15(ru_seed ^ pmod(ru_g, ru_seed2 + ru_x, RU_N)) | ru_msb;
245
246 _THREAD_PRIVATE_MUTEX_UNLOCK(random);
247
248 return (r);
249}
250
251#if 0
252int
253main(int argc, char **argv)
254{
255 int i, n;
256 u_int16_t wert;
257
258 res_initid();
259
260 printf("Generator: %u\n", ru_g);
261 printf("Seed: %u\n", ru_seed);
262 printf("Reseed at %ld\n", ru_reseed);
263 printf("Ru_X: %u\n", ru_x);
264 printf("Ru_A: %u\n", ru_a);
265 printf("Ru_B: %u\n", ru_b);
266
267 n = argc > 1 ? atoi(argv[1]) : 60001;
268 for (i=0;i<n;i++) {
269 wert = res_randomid();
270 printf("%u\n", wert);
271 }
272 return 0;
273}
274#endif
275