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ash,hush: fix a thinko about 2^64-1 factorization

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function                                             old     new   delta
next_random                                          113     119      +6

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
This commit is contained in:
Denys Vlasenko 2014-03-15 09:25:46 +01:00
parent 2bba591991
commit ac03a40cba
1 changed files with 11 additions and 5 deletions
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16
shell/random.c
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@ -80,7 +80,6 @@ next_random(random_t *rnd)
rnd->galois_LFSR = 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
@ -102,11 +101,19 @@ next_random(random_t *rnd)
* 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 have 2^32 * 2^32-1 period.
/* 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:
@ -118,9 +125,8 @@ next_random(random_t *rnd)
* 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.
* 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.
*