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
|
/* $OpenBSD: ip_id.c,v 1.10 2003/12/12 02:50:44 itojun Exp $ */
/*
* Copyright 1998 Niels Provos <provos@citi.umich.edu>
* All rights reserved.
*
* Theo de Raadt <deraadt@openbsd.org> came up with the idea of using
* such a mathematical system to generate more random (yet non-repeating)
* ids to solve the resolver/named problem. But Niels designed the
* actual system based on the constraints.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by Niels Provos.
* 4. The name of the author may not be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* seed = random 15bit
* n = prime, g0 = generator to n,
* j = random so that gcd(j,n-1) == 1
* g = g0^j mod n will be a generator again.
*
* X[0] = random seed.
* X[n] = a*X[n-1]+b mod m is a Linear Congruential Generator
* with a = 7^(even random) mod m,
* b = random with gcd(b,m) == 1
* m = 31104 and a maximal period of m-1.
*
* The transaction id is determined by:
* id[n] = seed xor (g^X[n] mod n)
*
* Effectivly the id is restricted to the lower 15 bits, thus
* yielding two different cycles by toggling the msb on and off.
* This avoids reuse issues caused by reseeding.
*/
#include <sys/param.h>
#include <sys/kernel.h>
#include <dev/rndvar.h>
#define RU_OUT 180 /* Time after wich will be reseeded */
#define RU_MAX 30000 /* Uniq cycle, avoid blackjack prediction */
#define RU_GEN 2 /* Starting generator */
#define RU_N 32749 /* RU_N-1 = 2*2*3*2729 */
#define RU_AGEN 7 /* determine ru_a as RU_AGEN^(2*rand) */
#define RU_M 31104 /* RU_M = 2^7*3^5 - don't change */
#define PFAC_N 3
const static u_int16_t pfacts[PFAC_N] = {
2,
3,
2729
};
static u_int16_t ru_x;
static u_int16_t ru_seed, ru_seed2;
static u_int16_t ru_a, ru_b;
static u_int16_t ru_g;
static u_int16_t ru_counter = 0;
static u_int16_t ru_msb = 0;
static long ru_reseed;
static u_int32_t tmp; /* Storage for unused random */
static u_int16_t pmod(u_int16_t, u_int16_t, u_int16_t);
static void ip_initid(void);
u_int16_t ip_randomid(void);
/*
* Do a fast modular exponation, returned value will be in the range
* of 0 - (mod-1)
*/
static u_int16_t
pmod(u_int16_t gen, u_int16_t expo, u_int16_t mod)
{
u_int16_t s, t, u;
s = 1;
t = gen;
u = expo;
while (u) {
if (u & 1)
s = (s*t) % mod;
u >>= 1;
t = (t*t) % mod;
}
return (s);
}
/*
* Initalizes the seed and chooses a suitable generator. Also toggles
* the msb flag. The msb flag is used to generate two distinct
* cycles of random numbers and thus avoiding reuse of ids.
*
* This function is called from id_randomid() when needed, an
* application does not have to worry about it.
*/
static void
ip_initid(void)
{
u_int16_t j, i;
int noprime = 1;
ru_x = ((tmp = arc4random()) & 0xFFFF) % RU_M;
/* 15 bits of random seed */
ru_seed = (tmp >> 16) & 0x7FFF;
ru_seed2 = arc4random() & 0x7FFF;
/* Determine the LCG we use */
ru_b = ((tmp = arc4random()) & 0xfffe) | 1;
ru_a = pmod(RU_AGEN, (tmp >> 16) & 0xfffe, RU_M);
while (ru_b % 3 == 0)
ru_b += 2;
j = (tmp = arc4random()) % RU_N;
tmp = tmp >> 16;
/*
* Do a fast gcd(j,RU_N-1), so we can find a j with
* gcd(j, RU_N-1) == 1, giving a new generator for
* RU_GEN^j mod RU_N
*/
while (noprime) {
for (i = 0; i < PFAC_N; i++)
if (j % pfacts[i] == 0)
break;
if (i >= PFAC_N)
noprime = 0;
else
j = (j+1) % RU_N;
}
ru_g = pmod(RU_GEN,j,RU_N);
ru_counter = 0;
ru_reseed = time.tv_sec + RU_OUT;
ru_msb = ru_msb == 0x8000 ? 0 : 0x8000;
}
u_int16_t
ip_randomid(void)
{
int i, n;
if (ru_counter >= RU_MAX || time.tv_sec > ru_reseed)
ip_initid();
#if 0
if (!tmp)
tmp = arc4random();
/* Skip a random number of ids */
n = tmp & 0x3; tmp = tmp >> 2;
if (ru_counter + n >= RU_MAX)
ip_initid();
#else
n = 0;
#endif
for (i = 0; i <= n; i++)
/* Linear Congruential Generator */
ru_x = (ru_a * ru_x + ru_b) % RU_M;
ru_counter += i;
return (ru_seed ^ pmod(ru_g,ru_seed2 + ru_x, RU_N)) | ru_msb;
}
|
