ash,hush: improve randomness of $RANDOM, add easy-ish way to test it
function old new delta next_random 68 113 +45 change_random 103 121 +18 Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
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Denys Vlasenko
parent
69f9567de2
commit
fb183076a3
132
shell/random.c
132
shell/random.c
@ -6,17 +6,51 @@
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*
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* Licensed under GPLv2, see file LICENSE in this source tree.
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*/
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/* For testing against dieharder, you need only random.{c,h}
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* Howto:
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* gcc -O2 -Wall -DRANDTEST random.c -o random
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* ./random | dieharder -g 200 -a
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*/
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#if !defined RANDTEST
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# include "libbb.h"
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# include "random.h"
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# define RAND_BASH_MASK 0x7fff
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#else
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# include <stdint.h>
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# include <unistd.h>
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# include <stdio.h>
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# include <time.h>
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# define RAND_BASH_MASK 0xffffffff /* off */
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# define FAST_FUNC /* nothing */
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# define PUSH_AND_SET_FUNCTION_VISIBILITY_TO_HIDDEN /* nothing */
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# define POP_SAVED_FUNCTION_VISIBILITY /* nothing */
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# define monotonic_us() time(NULL)
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# include "random.h"
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#endif
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uint32_t FAST_FUNC
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next_random(random_t *rnd)
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{
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/* Galois LFSR parameter */
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/* Taps at 32 31 29 1: */
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/* Galois LFSR parameter:
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* Taps at 32 31 29 1:
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*/
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enum { MASK = 0x8000000b };
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/* Another example - taps at 32 31 30 10: */
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/* MASK = 0x00400007 */
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/* enum { MASK = 0x00400007 }; */
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/* Xorshift parameters:
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* Choices for a,b,c: 10,13,10; 8,9,22; 2,7,3; 23,3,24
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* (given by algorithm author)
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*/
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enum {
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a = 2,
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b = 7,
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c = 3,
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};
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uint32_t t;
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@ -27,18 +61,94 @@ next_random(random_t *rnd)
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INIT_RANDOM_T(rnd, getpid(), monotonic_us());
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}
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/* LCG has period of 2^32 and alternating lowest bit */
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/* LCG: period of 2^32, but quite weak:
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* bit 0 alternates beetween 0 and 1 (pattern of length 2)
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* bit 1 has a repeating pattern of length 4
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* bit 2 has a repeating pattern of length 8
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* etc...
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*/
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rnd->LCG = 1664525 * rnd->LCG + 1013904223;
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/* Galois LFSR has period of 2^32-1 = 3 * 5 * 17 * 257 * 65537 */
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/* Galois LFSR:
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* period of 2^32-1 = 3 * 5 * 17 * 257 * 65537.
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* Successive values are right-shifted one bit
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* and possibly xored with a sparse constant.
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*/
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t = (rnd->galois_LFSR << 1);
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if (rnd->galois_LFSR < 0) /* if we just shifted 1 out of msb... */
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t ^= MASK;
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rnd->galois_LFSR = t;
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/* Both are weak, combining them gives better randomness
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* and ~2^64 period. & 0x7fff is probably bash compat
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* for $RANDOM range. Combining with subtraction is
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* just for fun. + and ^ would work equally well. */
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t = (t - rnd->LCG) & 0x7fff;
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return t;
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/* http://en.wikipedia.org/wiki/Xorshift
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* Period 2^64-1 = 3 * 715827883 * 2147483647
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* Moderately good statistical properties:
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* fails the following "dieharder -g 200 -a" tests:
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* diehard_operm5| 0
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* diehard_oqso| 0
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* diehard_count_1s_byt| 0
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* diehard_3dsphere| 3
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* diehard_squeeze| 0
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* diehard_runs| 0
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* diehard_runs| 0
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* diehard_craps| 0
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* diehard_craps| 0
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* rgb_minimum_distance| 3
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* rgb_minimum_distance| 4
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* rgb_minimum_distance| 5
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* rgb_permutations| 3
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* rgb_permutations| 4
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* rgb_permutations| 5
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* dab_filltree| 32
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* dab_filltree| 32
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* dab_monobit2| 12
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*/
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t = rnd->xs64_x ^ (rnd->xs64_x << a);
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rnd->xs64_x = rnd->xs64_y;
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rnd->xs64_y = rnd->xs64_y ^ (rnd->xs64_y >> c) ^ t ^ (t >> b);
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/* Combined LCG + Galois LFSR have 2^32 * 2^32-1 period.
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* Strength:
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* individually, both are extremely weak cryptographycally;
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* when combined, they fail the following "dieharder -g 200 -a" tests:
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* diehard_rank_6x8| 0
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* diehard_oqso| 0
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* diehard_dna| 0
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* diehard_count_1s_byt| 0
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* rgb_bitdist| 2
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* dab_monobit2| 12
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*
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* Combining them with xorshift-64 increases period to
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* 2^32 * 2^32-1 * 2^64-1 / 3
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* (2^32-1 and 2^64-1 have one common divisor 3, hence "/ 3" part),
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* which is about 2^128 / 3, or in base 10 ~1.13*10^38.
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* Strength of the combination:
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* passes all "dieharder -g 200 -a" tests.
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*
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* Combining with subtraction and addition is just for fun.
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* It does not add meaningful strength, could use xor operation instead.
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*/
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t = rnd->galois_LFSR - rnd->LCG + rnd->xs64_y;
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/* bash compat $RANDOM range: */
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return t & RAND_BASH_MASK;
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}
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#ifdef RANDTEST
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static random_t rnd;
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int main(int argc, char **argv)
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{
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int i;
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int buf[4096];
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for (;;) {
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for (i = 0; i < sizeof(buf) / sizeof(buf[0]); i++) {
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buf[i] = next_random(&rnd);
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}
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write(1, buf, sizeof(buf));
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}
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return 0;
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}
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#endif
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@ -12,16 +12,24 @@
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PUSH_AND_SET_FUNCTION_VISIBILITY_TO_HIDDEN
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typedef struct random_t {
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/* Random number generators */
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int32_t galois_LFSR; /* Galois LFSR (fast but weak). signed! */
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uint32_t LCG; /* LCG (fast but weak) */
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/* State of random number generators: */
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/* Galois LFSR (fast but weak) */
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int32_t galois_LFSR; /* must be signed! */
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/* LCG (fast but weak) */
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uint32_t LCG;
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/* 64-bit xorshift (fast, moderate strength) */
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uint32_t xs64_x;
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uint32_t xs64_y;
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} random_t;
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#define UNINITED_RANDOM_T(rnd) \
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((rnd)->galois_LFSR == 0)
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#define INIT_RANDOM_T(rnd, nonzero, v) \
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((rnd)->galois_LFSR = (nonzero), (rnd)->LCG = (v))
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((rnd)->galois_LFSR = (rnd)->xs64_x = (nonzero), (rnd)->LCG = (rnd)->xs64_y = (v))
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#define CLEAR_RANDOM_T(rnd) \
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((rnd)->galois_LFSR = 0)
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