1/* vi: set sw=4 ts=4: */ 2/* 3 * $RANDOM support. 4 * 5 * Copyright (C) 2009 Denys Vlasenko 6 * 7 * Licensed under GPLv2, see file LICENSE in this source tree. 8 */ 9 10/* For testing against dieharder, you need only random.{c,h} 11 * Howto: 12 * gcc -O2 -Wall -DRANDTEST random.c -o random 13 * ./random | dieharder -g 200 -a 14 */ 15 16#if !defined RANDTEST 17 18# include "libbb.h" 19# include "random.h" 20# define RAND_BASH_MASK 0x7fff 21 22#else 23# include <stdint.h> 24# include <unistd.h> 25# include <stdio.h> 26# include <time.h> 27# define FAST_FUNC /* nothing */ 28# define PUSH_AND_SET_FUNCTION_VISIBILITY_TO_HIDDEN /* nothing */ 29# define POP_SAVED_FUNCTION_VISIBILITY /* nothing */ 30# define monotonic_us() time(NULL) 31# include "random.h" 32# define RAND_BASH_MASK 0xffffffff /* off */ 33#endif 34 35uint32_t FAST_FUNC 36next_random(random_t *rnd) 37{ 38 /* Galois LFSR parameter: 39 * Taps at 32 31 29 1: 40 */ 41 enum { MASK = 0x8000000b }; 42 /* Another example - taps at 32 31 30 10: */ 43 /* enum { MASK = 0x00400007 }; */ 44 45 /* Xorshift parameters: 46 * Choices for a,b,c: 10,13,10; 8,9,22; 2,7,3; 23,3,24 47 * (given by algorithm author) 48 */ 49 enum { 50 a = 2, 51 b = 7, 52 c = 3, 53 }; 54 55 uint32_t t; 56 57 if (UNINITED_RANDOM_T(rnd)) { 58 /* Can use monotonic_ns() for better randomness but for now 59 * it is not used anywhere else in busybox... so avoid bloat 60 */ 61 INIT_RANDOM_T(rnd, getpid(), monotonic_us()); 62 } 63 64 /* LCG: period of 2^32, but quite weak: 65 * bit 0 alternates beetween 0 and 1 (pattern of length 2) 66 * bit 1 has a repeating pattern of length 4 67 * bit 2 has a repeating pattern of length 8 68 * etc... 69 */ 70 rnd->LCG = 1664525 * rnd->LCG + 1013904223; 71 72 /* Galois LFSR: 73 * period of 2^32-1 = 3 * 5 * 17 * 257 * 65537. 74 * Successive values are right-shifted one bit 75 * and possibly xored with a sparse constant. 76 */ 77 t = (rnd->galois_LFSR << 1); 78 if (rnd->galois_LFSR < 0) /* if we just shifted 1 out of msb... */ 79 t ^= MASK; 80 rnd->galois_LFSR = t; 81 82 /* http://en.wikipedia.org/wiki/Xorshift 83 * Moderately good statistical properties: 84 * fails the following "dieharder -g 200 -a" tests: 85 * diehard_operm5| 0 86 * diehard_oqso| 0 87 * diehard_count_1s_byt| 0 88 * diehard_3dsphere| 3 89 * diehard_squeeze| 0 90 * diehard_runs| 0 91 * diehard_runs| 0 92 * diehard_craps| 0 93 * diehard_craps| 0 94 * rgb_minimum_distance| 3 95 * rgb_minimum_distance| 4 96 * rgb_minimum_distance| 5 97 * rgb_permutations| 3 98 * rgb_permutations| 4 99 * rgb_permutations| 5 100 * dab_filltree| 32 101 * dab_filltree| 32 102 * dab_monobit2| 12 103 */ 104 again: 105 t = rnd->xs64_x ^ (rnd->xs64_x << a); 106 rnd->xs64_x = rnd->xs64_y; 107 rnd->xs64_y = rnd->xs64_y ^ (rnd->xs64_y >> c) ^ t ^ (t >> b); 108 /* 109 * Period 2^64-1 = 2^32+1 * 2^32-1 has a common divisor with Galois LFSR. 110 * By skipping two possible states (0x1 and 0x2) we reduce period to 111 * 2^64-3 = 13 * 3889 * 364870227143809 which has no common divisors: 112 */ 113 if (rnd->xs64_y == 0 && rnd->xs64_x <= 2) 114 goto again; 115 116 /* Combined LCG + Galois LFSR rng has 2^32 * 2^32-1 period. 117 * Strength: 118 * individually, both are extremely weak cryptographycally; 119 * when combined, they fail the following "dieharder -g 200 -a" tests: 120 * diehard_rank_6x8| 0 121 * diehard_oqso| 0 122 * diehard_dna| 0 123 * diehard_count_1s_byt| 0 124 * rgb_bitdist| 2 125 * dab_monobit2| 12 126 * 127 * Combining them with xorshift-64 increases period to 128 * 2^32 * 2^32-1 * 2^64-3 129 * which is about 2^128, or in base 10 ~3.40*10^38. 130 * Strength of the combination: 131 * passes all "dieharder -g 200 -a" tests. 132 * 133 * Combining with subtraction and addition is just for fun. 134 * It does not add meaningful strength, could use xor operation instead. 135 */ 136 t = rnd->galois_LFSR - rnd->LCG + rnd->xs64_y; 137 138 /* bash compat $RANDOM range: */ 139 return t & RAND_BASH_MASK; 140} 141 142#ifdef RANDTEST 143static random_t rnd; 144 145int main(int argc, char **argv) 146{ 147 int i; 148 uint32_t buf[4096]; 149 150 for (;;) { 151 for (i = 0; i < sizeof(buf) / sizeof(buf[0]); i++) { 152 buf[i] = next_random(&rnd); 153 } 154 write(1, buf, sizeof(buf)); 155 } 156 157 return 0; 158} 159 160#endif 161