diff options
| -rw-r--r-- | shell/random.c | 136 | ||||
| -rw-r--r-- | shell/random.h | 16 |
2 files changed, 135 insertions, 17 deletions
diff --git a/shell/random.c b/shell/random.c index 853ab085a..9a64f54b0 100644 --- a/shell/random.c +++ b/shell/random.c @@ -6,17 +6,51 @@ * * Licensed under GPLv2, see file LICENSE in this source tree. */ -#include "libbb.h" -#include "random.h" + +/* For testing against dieharder, you need only random.{c,h} + * Howto: + * gcc -O2 -Wall -DRANDTEST random.c -o random + * ./random | dieharder -g 200 -a + */ + +#if !defined RANDTEST + +# include "libbb.h" +# include "random.h" +# define RAND_BASH_MASK 0x7fff + +#else +# include <stdint.h> +# include <unistd.h> +# include <stdio.h> +# include <time.h> +# define RAND_BASH_MASK 0xffffffff /* off */ +# define FAST_FUNC /* nothing */ +# define PUSH_AND_SET_FUNCTION_VISIBILITY_TO_HIDDEN /* nothing */ +# define POP_SAVED_FUNCTION_VISIBILITY /* nothing */ +# define monotonic_us() time(NULL) +# include "random.h" +#endif uint32_t FAST_FUNC next_random(random_t *rnd) { - /* Galois LFSR parameter */ - /* Taps at 32 31 29 1: */ + /* Galois LFSR parameter: + * Taps at 32 31 29 1: + */ enum { MASK = 0x8000000b }; /* Another example - taps at 32 31 30 10: */ - /* MASK = 0x00400007 */ + /* enum { MASK = 0x00400007 }; */ + + /* Xorshift parameters: + * Choices for a,b,c: 10,13,10; 8,9,22; 2,7,3; 23,3,24 + * (given by algorithm author) + */ + enum { + a = 2, + b = 7, + c = 3, + }; uint32_t t; @@ -27,18 +61,94 @@ next_random(random_t *rnd) INIT_RANDOM_T(rnd, getpid(), monotonic_us()); } - /* LCG has period of 2^32 and alternating lowest bit */ + /* LCG: period of 2^32, but quite weak: + * bit 0 alternates beetween 0 and 1 (pattern of length 2) + * bit 1 has a repeating pattern of length 4 + * bit 2 has a repeating pattern of length 8 + * etc... + */ rnd->LCG = 1664525 * rnd->LCG + 1013904223; - /* Galois LFSR has period of 2^32-1 = 3 * 5 * 17 * 257 * 65537 */ + + /* Galois LFSR: + * period of 2^32-1 = 3 * 5 * 17 * 257 * 65537. + * Successive values are right-shifted one bit + * and possibly xored with a sparse constant. + */ t = (rnd->galois_LFSR << 1); if (rnd->galois_LFSR < 0) /* if we just shifted 1 out of msb... */ t ^= MASK; rnd->galois_LFSR = t; - /* Both are weak, combining them gives better randomness - * and ~2^64 period. & 0x7fff is probably bash compat - * for $RANDOM range. Combining with subtraction is - * just for fun. + and ^ would work equally well. */ - t = (t - rnd->LCG) & 0x7fff; - return t; + /* http://en.wikipedia.org/wiki/Xorshift + * Period 2^64-1 = 3 * 715827883 * 2147483647 + * Moderately good statistical properties: + * fails the following "dieharder -g 200 -a" tests: + * diehard_operm5| 0 + * diehard_oqso| 0 + * diehard_count_1s_byt| 0 + * diehard_3dsphere| 3 + * diehard_squeeze| 0 + * diehard_runs| 0 + * diehard_runs| 0 + * diehard_craps| 0 + * diehard_craps| 0 + * rgb_minimum_distance| 3 + * rgb_minimum_distance| 4 + * rgb_minimum_distance| 5 + * rgb_permutations| 3 + * rgb_permutations| 4 + * rgb_permutations| 5 + * dab_filltree| 32 + * dab_filltree| 32 + * dab_monobit2| 12 + */ + t = rnd->xs64_x ^ (rnd->xs64_x << a); + rnd->xs64_x = rnd->xs64_y; + rnd->xs64_y = rnd->xs64_y ^ (rnd->xs64_y >> c) ^ t ^ (t >> b); + + /* Combined LCG + Galois LFSR have 2^32 * 2^32-1 period. + * Strength: + * individually, both are extremely weak cryptographycally; + * when combined, they fail the following "dieharder -g 200 -a" tests: + * diehard_rank_6x8| 0 + * diehard_oqso| 0 + * diehard_dna| 0 + * diehard_count_1s_byt| 0 + * rgb_bitdist| 2 + * dab_monobit2| 12 + * + * Combining them with xorshift-64 increases period to + * 2^32 * 2^32-1 * 2^64-1 / 3 + * (2^32-1 and 2^64-1 have one common divisor 3, hence "/ 3" part), + * which is about 2^128 / 3, or in base 10 ~1.13*10^38. + * Strength of the combination: + * passes all "dieharder -g 200 -a" tests. + * + * Combining with subtraction and addition is just for fun. + * It does not add meaningful strength, could use xor operation instead. + */ + t = rnd->galois_LFSR - rnd->LCG + rnd->xs64_y; + + /* bash compat $RANDOM range: */ + return t & RAND_BASH_MASK; } + +#ifdef RANDTEST +static random_t rnd; + +int main(int argc, char **argv) +{ + int i; + int buf[4096]; + + for (;;) { + for (i = 0; i < sizeof(buf) / sizeof(buf[0]); i++) { + buf[i] = next_random(&rnd); + } + write(1, buf, sizeof(buf)); + } + + return 0; +} + +#endif diff --git a/shell/random.h b/shell/random.h index 180c48abb..c4eb44c13 100644 --- a/shell/random.h +++ b/shell/random.h @@ -12,16 +12,24 @@ PUSH_AND_SET_FUNCTION_VISIBILITY_TO_HIDDEN typedef struct random_t { - /* Random number generators */ - int32_t galois_LFSR; /* Galois LFSR (fast but weak). signed! */ - uint32_t LCG; /* LCG (fast but weak) */ + /* State of random number generators: */ + + /* Galois LFSR (fast but weak) */ + int32_t galois_LFSR; /* must be signed! */ + + /* LCG (fast but weak) */ + uint32_t LCG; + + /* 64-bit xorshift (fast, moderate strength) */ + uint32_t xs64_x; + uint32_t xs64_y; } random_t; #define UNINITED_RANDOM_T(rnd) \ ((rnd)->galois_LFSR == 0) #define INIT_RANDOM_T(rnd, nonzero, v) \ - ((rnd)->galois_LFSR = (nonzero), (rnd)->LCG = (v)) + ((rnd)->galois_LFSR = (rnd)->xs64_x = (nonzero), (rnd)->LCG = (rnd)->xs64_y = (v)) #define CLEAR_RANDOM_T(rnd) \ ((rnd)->galois_LFSR = 0) |