1 /* $OpenBSD: res_random.c,v 1.2 1997/04/19 09:53:25 provos Exp $ */ 2 3 /* 4 * Copyright 1997 Niels Provos <provos@physnet.uni-hamburg.de> 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 * 3. All advertising materials mentioning features or use of this software 21 * must display the following acknowledgement: 22 * This product includes software developed by Niels Provos. 23 * 4. The name of the author may not be used to endorse or promote products 24 * derived from this software without specific prior written permission. 25 * 26 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 27 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 28 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 29 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 30 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 31 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 32 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 33 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 34 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 35 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 36 */ 37 38 /* 39 * seed = random 15bit 40 * n = prime, g0 = generator to n, 41 * j = random so that gcd(j,n-1) == 1 42 * g = g0^j mod n will be a generator again. 43 * 44 * X[0] = random seed. 45 * X[n] = a*X[n-1]+b mod m is a Linear Congruential Generator 46 * with a = 7^(even random) mod m, 47 * b = random with gcd(b,m) == 1 48 * m = 31104 and a maximal period of m-1. 49 * 50 * The transaction id is determined by: 51 * id[n] = seed xor (g^X[n] mod n) 52 * 53 * Effectivly the id is restricted to the lower 15 bits, thus 54 * yielding two different cycles by toggling the msb on and off. 55 * This avoids reuse issues caused by reseeding. 56 * 57 * The 16 bit space is very small and brute force attempts are 58 * entirly feasible, we skip a random number of transaction ids 59 * so that an attacker will not get sequential ids. 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 #include <time.h> 71 72 #define RU_OUT 180 /* Time after wich will be reseeded */ 73 #define RU_MAX 30000 /* Uniq cycle, avoid blackjack prediction */ 74 #define RU_GEN 2 /* Starting generator */ 75 #define RU_N 32749 /* RU_N-1 = 2*2*3*2729 */ 76 #define RU_AGEN 7 /* determine ru_a as RU_AGEN^(2*rand) */ 77 #define RU_M 31104 /* RU_M = 2^7*3^5 - don't change */ 78 79 #define PFAC_N 3 80 const static u_int16_t pfacts[PFAC_N] = { 81 2, 82 3, 83 2729 84 }; 85 86 static u_int16_t ru_x; 87 static u_int16_t ru_seed; 88 static u_int16_t ru_a, ru_b; 89 static u_int16_t ru_g; 90 static u_int16_t ru_counter = 0; 91 static u_int16_t ru_msb = 0; 92 static time_t ru_reseed; 93 static u_int32_t tmp; /* Storage for unused random */ 94 95 static u_int32_t pmod __P((u_int32_t, u_int32_t, u_int32_t)); 96 static void res_initid __P((void)); 97 98 /* 99 * Do a fast modular exponation, returned value will be in the range 100 * of 0 - (mod-1) 101 */ 102 103 static u_int32_t 104 pmod(gen, exp, mod) 105 u_int32_t gen, exp, mod; 106 { 107 u_int32_t s, t, u; 108 109 s = 1; 110 t = gen; 111 u = exp; 112 113 while (u) { 114 if (u & 1) 115 s = (s*t) % mod; 116 u >>= 1; 117 t = (t*t) % mod; 118 } 119 return (s); 120 } 121 122 /* 123 * Initalizes the seed and chooses a suitable generator. Also toggles 124 * the msb flag. The msb flag is used to generate two distinct 125 * cycles of random numbers and thus avoiding reuse of ids. 126 * 127 * This function is called from res_randomid() when needed, an 128 * application does not have to worry about it. 129 */ 130 static void 131 res_initid() 132 { 133 u_int16_t j, i; 134 int noprime = 1; 135 136 tmp = arc4random(); 137 ru_x = (tmp & 0xFFFF) % RU_M; 138 139 /* 15 bits of random seed */ 140 ru_seed = (tmp >> 16) & 0x7FFF; 141 142 tmp = arc4random(); 143 144 /* Determine the LCG we use */ 145 ru_b = (tmp & 0xfffe) | 1; 146 ru_a = pmod(RU_AGEN, (tmp >> 16) & 0xfffe, RU_M); 147 while (ru_b % 3 == 0) 148 ru_b += 2; 149 150 tmp = arc4random(); 151 j = tmp % RU_N; 152 tmp = tmp >> 16; 153 154 /* 155 * Do a fast gcd(j,RU_N-1), so we can find a j with 156 * gcd(j, RU_N-1) == 1, giving a new generator for 157 * RU_GEN^j mod RU_N 158 */ 159 160 while (noprime) { 161 for (i=0; i<PFAC_N; i++) 162 if (j%pfacts[i] == 0) 163 break; 164 165 if (i>=PFAC_N) 166 noprime = 0; 167 else 168 j = (j+1) % RU_N; 169 } 170 171 ru_g = pmod(RU_GEN,j,RU_N); 172 ru_counter = 0; 173 174 ru_reseed = time(NULL) + RU_OUT; 175 ru_msb = ru_msb == 0x8000 ? 0 : 0x8000; 176 } 177 178 u_int 179 res_randomid() 180 { 181 int i, n; 182 183 if (ru_counter >= RU_MAX || time(NULL) > ru_reseed) 184 res_initid(); 185 186 if (!tmp) 187 tmp = arc4random(); 188 189 /* Skip a random number of ids */ 190 n = tmp & 0x2f; tmp = tmp >> 6; 191 if (ru_counter + n >= RU_MAX) 192 res_initid(); 193 194 for (i=0; i<=n; i++) 195 /* Linear Congruential Generator */ 196 ru_x = (ru_a*ru_x + ru_b) % RU_M; 197 198 ru_counter += i; 199 200 return (ru_seed ^ pmod(ru_g,ru_x,RU_N)) | ru_msb; 201 } 202 203 #if 0 204 void 205 main(int argc, char **argv) 206 { 207 int i, n; 208 u_int16_t wert; 209 210 res_initid(); 211 212 printf("Generator: %d\n", ru_g); 213 printf("Seed: %d\n", ru_seed); 214 printf("Ru_X: %d\n", ru_x); 215 printf("Ru_A: %d\n", ru_a); 216 printf("Ru_B: %d\n", ru_b); 217 218 n = atoi(argv[1]); 219 for (i=0;i<n;i++) { 220 wert = res_randomid(); 221 printf("%06d\n", wert); 222 } 223 } 224 #endif 225 226