/*
* $RANDOM support.
*
- * Copyright (C) 2008 Denys Vlasenko
+ * Copyright (C) 2009 Denys Vlasenko
*
- * Licensed under GPLv2, see file LICENSE in this tarball for details.
+ * 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 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"
+# define RAND_BASH_MASK 0xffffffff /* off */
+#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;
- /* LCG has period of 2^32 and alternating lowest bit */
+ if (UNINITED_RANDOM_T(rnd)) {
+ /* Can use monotonic_ns() for better randomness but for now
+ * it is not used anywhere else in busybox... so avoid bloat
+ */
+ INIT_RANDOM_T(rnd, getpid(), monotonic_us());
+ }
+
+ /* 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
+ * 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
+ */
+ again:
+ 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);
+ /*
+ * Period 2^64-1 = 2^32+1 * 2^32-1 has a common divisor with Galois LFSR.
+ * By skipping two possible states (0x1 and 0x2) we reduce period to
+ * 2^64-3 = 13 * 3889 * 364870227143809 which has no common divisors:
+ */
+ if (rnd->xs64_y == 0 && rnd->xs64_x <= 2)
+ goto again;
+
+ /* Combined LCG + Galois LFSR rng has 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 * 2^64-3
+ * which is about 2^128, or in base 10 ~3.40*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;
+ uint32_t 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