1 /* $OpenBSD: random.c,v 1.20 2014/06/13 15:35:34 deraadt Exp $ */ 2 /* 3 * Copyright (c) 1983 Regents of the University of California. 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31 #include <sys/param.h> 32 #include <sys/sysctl.h> 33 #include <sys/time.h> 34 #include <fcntl.h> 35 #include <stdio.h> 36 #include <stdlib.h> 37 #include <unistd.h> 38 39 #include "thread_private.h" 40 41 /* 42 * random.c: 43 * 44 * An improved random number generation package. In addition to the standard 45 * rand()/srand() like interface, this package also has a special state info 46 * interface. The initstate() routine is called with a seed, an array of 47 * bytes, and a count of how many bytes are being passed in; this array is 48 * then initialized to contain information for random number generation with 49 * that much state information. Good sizes for the amount of state 50 * information are 32, 64, 128, and 256 bytes. The state can be switched by 51 * calling the setstate() routine with the same array as was initiallized 52 * with initstate(). By default, the package runs with 128 bytes of state 53 * information and generates far better random numbers than a linear 54 * congruential generator. If the amount of state information is less than 55 * 32 bytes, a simple linear congruential R.N.G. is used. 56 * 57 * Internally, the state information is treated as an array of int32_t; the 58 * zeroeth element of the array is the type of R.N.G. being used (small 59 * integer); the remainder of the array is the state information for the 60 * R.N.G. Thus, 32 bytes of state information will give 7 int32_ts worth of 61 * state information, which will allow a degree seven polynomial. (Note: 62 * the zeroeth word of state information also has some other information 63 * stored in it -- see setstate() for details). 64 * 65 * The random number generation technique is a linear feedback shift register 66 * approach, employing trinomials (since there are fewer terms to sum up that 67 * way). In this approach, the least significant bit of all the numbers in 68 * the state table will act as a linear feedback shift register, and will 69 * have period 2^deg - 1 (where deg is the degree of the polynomial being 70 * used, assuming that the polynomial is irreducible and primitive). The 71 * higher order bits will have longer periods, since their values are also 72 * influenced by pseudo-random carries out of the lower bits. The total 73 * period of the generator is approximately deg*(2**deg - 1); thus doubling 74 * the amount of state information has a vast influence on the period of the 75 * generator. Note: the deg*(2**deg - 1) is an approximation only good for 76 * large deg, when the period of the shift register is the dominant factor. 77 * With deg equal to seven, the period is actually much longer than the 78 * 7*(2**7 - 1) predicted by this formula. 79 */ 80 81 /* 82 * For each of the currently supported random number generators, we have a 83 * break value on the amount of state information (you need at least this 84 * many bytes of state info to support this random number generator), a degree 85 * for the polynomial (actually a trinomial) that the R.N.G. is based on, and 86 * the separation between the two lower order coefficients of the trinomial. 87 */ 88 #define TYPE_0 0 /* linear congruential */ 89 #define BREAK_0 8 90 #define DEG_0 0 91 #define SEP_0 0 92 93 #define TYPE_1 1 /* x**7 + x**3 + 1 */ 94 #define BREAK_1 32 95 #define DEG_1 7 96 #define SEP_1 3 97 98 #define TYPE_2 2 /* x**15 + x + 1 */ 99 #define BREAK_2 64 100 #define DEG_2 15 101 #define SEP_2 1 102 103 #define TYPE_3 3 /* x**31 + x**3 + 1 */ 104 #define BREAK_3 128 105 #define DEG_3 31 106 #define SEP_3 3 107 108 #define TYPE_4 4 /* x**63 + x + 1 */ 109 #define BREAK_4 256 110 #define DEG_4 63 111 #define SEP_4 1 112 113 /* 114 * Array versions of the above information to make code run faster -- 115 * relies on fact that TYPE_i == i. 116 */ 117 #define MAX_TYPES 5 /* max number of types above */ 118 119 static int degrees[MAX_TYPES] = { DEG_0, DEG_1, DEG_2, DEG_3, DEG_4 }; 120 static int seps [MAX_TYPES] = { SEP_0, SEP_1, SEP_2, SEP_3, SEP_4 }; 121 122 /* 123 * Initially, everything is set up as if from: 124 * 125 * initstate(1, &randtbl, 128); 126 * 127 * Note that this initialization takes advantage of the fact that srandom() 128 * advances the front and rear pointers 10*rand_deg times, and hence the 129 * rear pointer which starts at 0 will also end up at zero; thus the zeroeth 130 * element of the state information, which contains info about the current 131 * position of the rear pointer is just 132 * 133 * MAX_TYPES * (rptr - state) + TYPE_3 == TYPE_3. 134 */ 135 136 static int32_t randtbl[DEG_3 + 1] = { 137 TYPE_3, 138 0x991539b1, 0x16a5bce3, 0x6774a4cd, 0x3e01511e, 0x4e508aaa, 0x61048c05, 139 0xf5500617, 0x846b7115, 0x6a19892c, 0x896a97af, 0xdb48f936, 0x14898454, 140 0x37ffd106, 0xb58bff9c, 0x59e17104, 0xcf918a49, 0x09378c83, 0x52c7a471, 141 0x8d293ea9, 0x1f4fc301, 0xc3db71be, 0x39b44e1c, 0xf8a44ef9, 0x4c8b80b1, 142 0x19edc328, 0x87bf4bdd, 0xc9b240e5, 0xe9ee4b1b, 0x4382aee7, 0x535b6b41, 143 0xf3bec5da, 144 }; 145 146 /* 147 * fptr and rptr are two pointers into the state info, a front and a rear 148 * pointer. These two pointers are always rand_sep places aparts, as they 149 * cycle cyclically through the state information. (Yes, this does mean we 150 * could get away with just one pointer, but the code for random() is more 151 * efficient this way). The pointers are left positioned as they would be 152 * from the call 153 * 154 * initstate(1, randtbl, 128); 155 * 156 * (The position of the rear pointer, rptr, is really 0 (as explained above 157 * in the initialization of randtbl) because the state table pointer is set 158 * to point to randtbl[1] (as explained below). 159 */ 160 static int32_t *fptr = &randtbl[SEP_3 + 1]; 161 static int32_t *rptr = &randtbl[1]; 162 163 /* 164 * The following things are the pointer to the state information table, the 165 * type of the current generator, the degree of the current polynomial being 166 * used, and the separation between the two pointers. Note that for efficiency 167 * of random(), we remember the first location of the state information, not 168 * the zeroeth. Hence it is valid to access state[-1], which is used to 169 * store the type of the R.N.G. Also, we remember the last location, since 170 * this is more efficient than indexing every time to find the address of 171 * the last element to see if the front and rear pointers have wrapped. 172 */ 173 static int32_t *state = &randtbl[1]; 174 static int32_t *end_ptr = &randtbl[DEG_3 + 1]; 175 static int rand_type = TYPE_3; 176 static int rand_deg = DEG_3; 177 static int rand_sep = SEP_3; 178 179 _THREAD_PRIVATE_MUTEX(random); 180 static long random_l(void); 181 182 #define LOCK() _THREAD_PRIVATE_MUTEX_LOCK(random) 183 #define UNLOCK() _THREAD_PRIVATE_MUTEX_UNLOCK(random) 184 185 /* 186 * srandom: 187 * 188 * Initialize the random number generator based on the given seed. If the 189 * type is the trivial no-state-information type, just remember the seed. 190 * Otherwise, initializes state[] based on the given "seed" via a linear 191 * congruential generator. Then, the pointers are set to known locations 192 * that are exactly rand_sep places apart. Lastly, it cycles the state 193 * information a given number of times to get rid of any initial dependencies 194 * introduced by the L.C.R.N.G. Note that the initialization of randtbl[] 195 * for default usage relies on values produced by this routine. 196 */ 197 static void 198 srandom_l(unsigned int x) 199 { 200 int i; 201 int32_t test; 202 div_t val; 203 204 if (rand_type == TYPE_0) 205 state[0] = x; 206 else { 207 /* A seed of 0 would result in state[] always being zero. */ 208 state[0] = x ? x : 1; 209 for (i = 1; i < rand_deg; i++) { 210 /* 211 * Implement the following, without overflowing 31 bits: 212 * 213 * state[i] = (16807 * state[i - 1]) % 2147483647; 214 * 215 * 2^31-1 (prime) = 2147483647 = 127773*16807+2836 216 */ 217 val = div(state[i-1], 127773); 218 test = 16807 * val.rem - 2836 * val.quot; 219 state[i] = test + (test < 0 ? 2147483647 : 0); 220 } 221 fptr = &state[rand_sep]; 222 rptr = &state[0]; 223 for (i = 0; i < 10 * rand_deg; i++) 224 (void)random_l(); 225 } 226 } 227 228 void 229 srandom(unsigned int x) 230 { 231 LOCK(); 232 srandom_l(x); 233 UNLOCK(); 234 } 235 236 #if defined(APIWARN) 237 __warn_references(srandom, 238 "warning: srandom() seed choices are invariably poor"); 239 #endif 240 241 /* 242 * srandomdev: 243 * 244 * Many programs choose the seed value in a totally predictable manner. 245 * This often causes problems. We seed the generator using random 246 * data from the kernel. 247 * Note that this particular seeding procedure can generate states 248 * which are impossible to reproduce by calling srandom() with any 249 * value, since the succeeding terms in the state buffer are no longer 250 * derived from the LC algorithm applied to a fixed seed. 251 */ 252 void 253 srandomdev(void) 254 { 255 size_t len; 256 257 LOCK(); 258 if (rand_type == TYPE_0) 259 len = sizeof(state[0]); 260 else 261 len = rand_deg * sizeof(state[0]); 262 263 getentropy(state, len); 264 265 if (rand_type != TYPE_0) { 266 fptr = &state[rand_sep]; 267 rptr = &state[0]; 268 } 269 UNLOCK(); 270 } 271 272 #if defined(APIWARN) 273 __warn_references(srandomdev, 274 "warning: srandomdev() usage; consider switching to arc4random()"); 275 #endif 276 277 /* 278 * initstate: 279 * 280 * Initialize the state information in the given array of n bytes for future 281 * random number generation. Based on the number of bytes we are given, and 282 * the break values for the different R.N.G.'s, we choose the best (largest) 283 * one we can and set things up for it. srandom() is then called to 284 * initialize the state information. 285 * 286 * Note that on return from srandom(), we set state[-1] to be the type 287 * multiplexed with the current value of the rear pointer; this is so 288 * successive calls to initstate() won't lose this information and will be 289 * able to restart with setstate(). 290 * 291 * Note: the first thing we do is save the current state, if any, just like 292 * setstate() so that it doesn't matter when initstate is called. 293 * 294 * Returns a pointer to the old state. 295 */ 296 char * 297 initstate(u_int seed, char *arg_state, size_t n) 298 { 299 char *ostate = (char *)(&state[-1]); 300 301 LOCK(); 302 if (rand_type == TYPE_0) 303 state[-1] = rand_type; 304 else 305 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 306 if (n < BREAK_0) { 307 UNLOCK(); 308 return(NULL); 309 } 310 if (n < BREAK_1) { 311 rand_type = TYPE_0; 312 rand_deg = DEG_0; 313 rand_sep = SEP_0; 314 } else if (n < BREAK_2) { 315 rand_type = TYPE_1; 316 rand_deg = DEG_1; 317 rand_sep = SEP_1; 318 } else if (n < BREAK_3) { 319 rand_type = TYPE_2; 320 rand_deg = DEG_2; 321 rand_sep = SEP_2; 322 } else if (n < BREAK_4) { 323 rand_type = TYPE_3; 324 rand_deg = DEG_3; 325 rand_sep = SEP_3; 326 } else { 327 rand_type = TYPE_4; 328 rand_deg = DEG_4; 329 rand_sep = SEP_4; 330 } 331 state = &(((int32_t *)arg_state)[1]); /* first location */ 332 end_ptr = &state[rand_deg]; /* must set end_ptr before srandom */ 333 srandom_l(seed); 334 if (rand_type == TYPE_0) 335 state[-1] = rand_type; 336 else 337 state[-1] = MAX_TYPES*(rptr - state) + rand_type; 338 UNLOCK(); 339 return(ostate); 340 } 341 342 /* 343 * setstate: 344 * 345 * Restore the state from the given state array. 346 * 347 * Note: it is important that we also remember the locations of the pointers 348 * in the current state information, and restore the locations of the pointers 349 * from the old state information. This is done by multiplexing the pointer 350 * location into the zeroeth word of the state information. 351 * 352 * Note that due to the order in which things are done, it is OK to call 353 * setstate() with the same state as the current state. 354 * 355 * Returns a pointer to the old state information. 356 */ 357 char * 358 setstate(char *arg_state) 359 { 360 int32_t *new_state = (int32_t *)arg_state; 361 int32_t type = new_state[0] % MAX_TYPES; 362 int32_t rear = new_state[0] / MAX_TYPES; 363 char *ostate = (char *)(&state[-1]); 364 365 LOCK(); 366 if (rand_type == TYPE_0) 367 state[-1] = rand_type; 368 else 369 state[-1] = MAX_TYPES * (rptr - state) + rand_type; 370 switch(type) { 371 case TYPE_0: 372 case TYPE_1: 373 case TYPE_2: 374 case TYPE_3: 375 case TYPE_4: 376 rand_type = type; 377 rand_deg = degrees[type]; 378 rand_sep = seps[type]; 379 break; 380 default: 381 UNLOCK(); 382 return(NULL); 383 } 384 state = &new_state[1]; 385 if (rand_type != TYPE_0) { 386 rptr = &state[rear]; 387 fptr = &state[(rear + rand_sep) % rand_deg]; 388 } 389 end_ptr = &state[rand_deg]; /* set end_ptr too */ 390 UNLOCK(); 391 return(ostate); 392 } 393 394 /* 395 * random: 396 * 397 * If we are using the trivial TYPE_0 R.N.G., just do the old linear 398 * congruential bit. Otherwise, we do our fancy trinomial stuff, which is 399 * the same in all the other cases due to all the global variables that have 400 * been set up. The basic operation is to add the number at the rear pointer 401 * into the one at the front pointer. Then both pointers are advanced to 402 * the next location cyclically in the table. The value returned is the sum 403 * generated, reduced to 31 bits by throwing away the "least random" low bit. 404 * 405 * Note: the code takes advantage of the fact that both the front and 406 * rear pointers can't wrap on the same call by not testing the rear 407 * pointer if the front one has wrapped. 408 * 409 * Returns a 31-bit random number. 410 */ 411 static long 412 random_l(void) 413 { 414 int32_t i; 415 416 if (rand_type == TYPE_0) 417 i = state[0] = (state[0] * 1103515245 + 12345) & 0x7fffffff; 418 else { 419 *fptr += *rptr; 420 i = (*fptr >> 1) & 0x7fffffff; /* chucking least random bit */ 421 if (++fptr >= end_ptr) { 422 fptr = state; 423 ++rptr; 424 } else if (++rptr >= end_ptr) 425 rptr = state; 426 } 427 return((long)i); 428 } 429 430 long 431 random(void) 432 { 433 long r; 434 LOCK(); 435 r = random_l(); 436 UNLOCK(); 437 return r; 438 } 439 440 #if defined(APIWARN) 441 __warn_references(random, 442 "warning: random() isn't random; consider using arc4random()"); 443 #endif 444