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 
35 uint32_t FAST_FUNC
next_random(random_t * rnd)36 next_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
143 static random_t rnd;
144 
main(int argc,char ** argv)145 int 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