1 /* $OpenBSD: ip_id.c,v 1.14 2007/05/27 19:59:11 dlg Exp $ */
2
3 /*
4 * Copyright 1998 Niels Provos <provos@citi.umich.edu>
5 * All rights reserved.
6 *
7 * Theo de Raadt <deraadt@openbsd.org> came up with the idea of using
8 * such a mathematical system to generate more random (yet non-repeating)
9 * ids to solve the resolver/named problem. But Niels designed the
10 * actual system based on the constraints.
11 *
12 * Redistribution and use in source and binary forms, with or without
13 * modification, are permitted provided that the following conditions
14 * are met:
15 * 1. Redistributions of source code must retain the above copyright
16 * notice, this list of conditions and the following disclaimer.
17 * 2. Redistributions in binary form must reproduce the above copyright
18 * notice, this list of conditions and the following disclaimer in the
19 * documentation and/or other materials provided with the distribution.
20 *
21 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
22 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
23 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
24 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
25 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
26 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
27 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
28 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
29 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
30 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
31 */
32
33 /*
34 * seed = random 15bit
35 * n = prime, g0 = generator to n,
36 * j = random so that gcd(j,n-1) == 1
37 * g = g0^j mod n will be a generator again.
38 *
39 * X[0] = random seed.
40 * X[n] = a*X[n-1]+b mod m is a Linear Congruential Generator
41 * with a = 7^(even random) mod m,
42 * b = random with gcd(b,m) == 1
43 * m = 31104 and a maximal period of m-1.
44 *
45 * The transaction id is determined by:
46 * id[n] = seed xor (g^X[n] mod n)
47 *
48 * Effectively the id is restricted to the lower 15 bits, thus
49 * yielding two different cycles by toggling the msb on and off.
50 * This avoids reuse issues caused by reseeding.
51 */
52
53 #include <sys/param.h>
54 #include <sys/kernel.h>
55
56 #include <dev/rndvar.h>
57
58 #define RU_OUT 180 /* Time after wich will be reseeded */
59 #define RU_MAX 30000 /* Uniq cycle, avoid blackjack prediction */
60 #define RU_GEN 2 /* Starting generator */
61 #define RU_N 32749 /* RU_N-1 = 2*2*3*2729 */
62 #define RU_AGEN 7 /* determine ru_a as RU_AGEN^(2*rand) */
63 #define RU_M 31104 /* RU_M = 2^7*3^5 - don't change */
64
65 #define PFAC_N 3
66 const static u_int16_t pfacts[PFAC_N] = {
67 2,
68 3,
69 2729
70 };
71
72 static u_int16_t ru_x;
73 static u_int16_t ru_seed, ru_seed2;
74 static u_int16_t ru_a, ru_b;
75 static u_int16_t ru_g;
76 static u_int16_t ru_counter = 0;
77 static u_int16_t ru_msb = 0;
78 static long ru_reseed;
79 static u_int32_t tmp; /* Storage for unused random */
80
81 u_int16_t pmod(u_int16_t, u_int16_t, u_int16_t);
82 void ip_initid(void);
83 u_int16_t ip_randomid(void);
84
85 /*
86 * Do a fast modular exponation, returned value will be in the range
87 * of 0 - (mod-1)
88 */
89
90 u_int16_t
91 pmod(u_int16_t gen, u_int16_t expo, u_int16_t mod)
92 {
93 u_int16_t s, t, u;
94
95 s = 1;
96 t = gen;
97 u = expo;
98
99 while (u) {
100 if (u & 1)
101 s = (s*t) % mod;
102 u >>= 1;
103 t = (t*t) % mod;
104 }
105 return (s);
106 }
107
108 /*
109 * Initalizes the seed and chooses a suitable generator. Also toggles
110 * the msb flag. The msb flag is used to generate two distinct
111 * cycles of random numbers and thus avoiding reuse of ids.
112 *
113 * This function is called from id_randomid() when needed, an
114 * application does not have to worry about it.
115 */
116 void
117 ip_initid(void)
118 {
119 u_int16_t j, i;
120 int noprime = 1;
121
122 ru_x = ((tmp = arc4random()) & 0xFFFF) % RU_M;
123
124 /* 15 bits of random seed */
125 ru_seed = (tmp >> 16) & 0x7FFF;
126 ru_seed2 = arc4random() & 0x7FFF;
127
128 /* Determine the LCG we use */
129 ru_b = ((tmp = arc4random()) & 0xfffe) | 1;
130 ru_a = pmod(RU_AGEN, (tmp >> 16) & 0xfffe, RU_M);
131 while (ru_b % 3 == 0)
132 ru_b += 2;
133
134 j = (tmp = arc4random()) % RU_N;
135 tmp = tmp >> 16;
136
137 /*
138 * Do a fast gcd(j,RU_N-1), so we can find a j with
139 * gcd(j, RU_N-1) == 1, giving a new generator for
140 * RU_GEN^j mod RU_N
141 */
142
143 while (noprime) {
144 for (i = 0; i < PFAC_N; i++)
145 if (j % pfacts[i] == 0)
146 break;
147
148 if (i >= PFAC_N)
149 noprime = 0;
150 else
151 j = (j+1) % RU_N;
152 }
153
154 ru_g = pmod(RU_GEN,j,RU_N);
155 ru_counter = 0;
156
157 ru_reseed = time_second + RU_OUT;
158 ru_msb = ru_msb == 0x8000 ? 0 : 0x8000;
159 }
160
161 u_int16_t
162 ip_randomid(void)
163 {
164 int i, n;
165
166 if (ru_counter >= RU_MAX || time_second > ru_reseed)
167 ip_initid();
168
169 #if 0
170 if (!tmp)
171 tmp = arc4random();
172
173 /* Skip a random number of ids */
174 n = tmp & 0x3; tmp = tmp >> 2;
175 if (ru_counter + n >= RU_MAX)
176 ip_initid();
177 #else
178 n = 0;
179 #endif
180
181 for (i = 0; i <= n; i++)
182 /* Linear Congruential Generator */
183 ru_x = (ru_a * ru_x + ru_b) % RU_M;
184
185 ru_counter += i;
186
187 return (ru_seed ^ pmod(ru_g,ru_seed2 + ru_x, RU_N)) | ru_msb;
188 }