The current Linux PRNG is based on LFSR113, which means:
- needs some warmup rounds to yield better statistical properties
- seeds/initial states must be of certain structure
- does not pass L’Ecuyer's BigCrush in TestU01
While of course, there is no clear "best" PRNG, replace with
Xoshiro256++, which seams to be a sensible replacement, from
todays point of view:
- only needs one bit set to 1 in the seed, needs no warmup, when
seeded with splitmix64.
- Also has statistical evaluation, like LFSR113.
- Passes BigCrush in TestU01.
The code got smaller, because some edge cases are ruled out now.
I kept the test vectors and adapted them to this RNG.
Signed-off-by: Markus Theil <theil.markus@xxxxxxxxx>
---
include/linux/prandom.h | 28 +---
lib/random32.c | 347 +++++++++++++++++++---------------------
2 files changed, 173 insertions(+), 202 deletions(-)
diff --git a/include/linux/prandom.h b/include/linux/prandom.h
index 63d1fe4b30c8..0a5c12bee5e1 100644
--- a/include/linux/prandom.h
+++ b/include/linux/prandom.h
@@ -14,39 +14,19 @@
#include <linux/random.h>
struct rnd_state {
- __u32 s1, s2, s3, s4;
+ __u64 s[4];
};
/* WARNING: this API MUST NOT be used for cryptographic purposes! */
u32 prandom_u32_state(struct rnd_state *state);
/* WARNING: this API MUST NOT be used for cryptographic purposes! */
+u64 prandom_u64_state(struct rnd_state *state);
void prandom_bytes_state(struct rnd_state *state, void *buf, size_t nbytes);
+
+void prandom_seed_state(struct rnd_state *state, u64 seed);
void prandom_seed_full_state(struct rnd_state __percpu *pcpu_state);
#define prandom_init_once(pcpu_state) \
DO_ONCE(prandom_seed_full_state, (pcpu_state))
-/*
- * Handle minimum values for seeds
- */
-static inline u32 __seed(u32 x, u32 m)
-{
- return (x < m) ? x + m : x;
-}
-
-/**
- * prandom_seed_state - set seed for prandom_u32_state().
- * @state: pointer to state structure to receive the seed.
- * @seed: arbitrary 64-bit value to use as a seed.
- */
-static inline void prandom_seed_state(struct rnd_state *state, u64 seed)
-{
- u32 i = ((seed >> 32) ^ (seed << 10) ^ seed) & 0xffffffffUL;
-
- state->s1 = __seed(i, 2U);
- state->s2 = __seed(i, 8U);
- state->s3 = __seed(i, 16U);
- state->s4 = __seed(i, 128U);
-}
-
#endif
diff --git a/lib/random32.c b/lib/random32.c
index c808745a4b53..50cbff0b995e 100644
--- a/lib/random32.c
+++ b/lib/random32.c
@@ -2,36 +2,18 @@
/*
* WARNING: this API MUST NOT be used for cryptographic purposes!
*
- * This is a maximally equidistributed combined Tausworthe generator
- * based on code from GNU Scientific Library 1.5 (30 Jun 2004)
+ * xoshiro256++ is a high-quality non-cryptographic
+ * pseudorandom number generator (PRNG).
*
- * lfsr113 version:
+ * For a more detailed description, see:
+ * https://vigna.di.unimi.it/ftp/papers/ScrambledLinear.pdf
*
- * x_n = (s1_n ^ s2_n ^ s3_n ^ s4_n)
+ * Usage Advice: As the cryptographic random subsystem is really fast these days,
+ * you should come up with a good reason, to introduce PRNG usage into new code.
+ * Consider its usage, when a predictable/repeatable sequence is needed for
+ * testing purposes. Prefer to use get_random_32(), when possible.
*
- * s1_{n+1} = (((s1_n & 4294967294) << 18) ^ (((s1_n << 6) ^ s1_n) >> 13))
- * s2_{n+1} = (((s2_n & 4294967288) << 2) ^ (((s2_n << 2) ^ s2_n) >> 27))
- * s3_{n+1} = (((s3_n & 4294967280) << 7) ^ (((s3_n << 13) ^ s3_n) >> 21))
- * s4_{n+1} = (((s4_n & 4294967168) << 13) ^ (((s4_n << 3) ^ s4_n) >> 12))
- *
- * The period of this generator is about 2^113 (see erratum paper).
- *
- * From: P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe
- * Generators", Mathematics of Computation, 65, 213 (1996), 203--213:
- * http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
- * ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/tausme.ps
- *
- * There is an erratum in the paper "Tables of Maximally Equidistributed
- * Combined LFSR Generators", Mathematics of Computation, 68, 225 (1999),
- * 261--269: http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
- *
- * ... the k_j most significant bits of z_j must be non-zero,
- * for each j. (Note: this restriction also applies to the
- * computer code given in [4], but was mistakenly not mentioned
- * in that paper.)
- *
- * This affects the seeding procedure by imposing the requirement
- * s1 > 1, s2 > 7, s3 > 15, s4 > 127.
+ * Based on: https://prng.di.unimi.it/xoshiro256plusplus.c
*/
#include <linux/types.h>
@@ -44,6 +26,33 @@
#include <linux/slab.h>
#include <linux/unaligned.h>
+/**
+ * prandom_u64_state - seeded pseudo-random number generator.
+ * @state: pointer to state structure holding seeded state.
+ *
+ * This is used for pseudo-randomness with no outside seeding.
+ * For more random results, use get_random_u64().
+ *
+ * WARNING: this API MUST NOT be used for cryptographic purposes!
+ */
+u64 prandom_u64_state(struct rnd_state *state)
+{
+ const u64 result = rol64(state->s[0] + state->s[3], 23) + state->s[0];
+ const u64 t = state->s[1] << 17;
+
+ state->s[2] ^= state->s[0];
+ state->s[3] ^= state->s[1];
+ state->s[1] ^= state->s[2];
+ state->s[0] ^= state->s[3];
+
+ state->s[2] ^= t;
+
+ state->s[3] = rol64(state->s[3], 45);
+
+ return result;
+}
+EXPORT_SYMBOL(prandom_u64_state);
+
/**
* prandom_u32_state - seeded pseudo-random number generator.
* @state: pointer to state structure holding seeded state.
@@ -55,13 +64,7 @@
*/
u32 prandom_u32_state(struct rnd_state *state)
{
-#define TAUSWORTHE(s, a, b, c, d) ((s & c) << d) ^ (((s << a) ^ s) >> b)
- state->s1 = TAUSWORTHE(state->s1, 6U, 13U, 4294967294U, 18U);
- state->s2 = TAUSWORTHE(state->s2, 2U, 27U, 4294967288U, 2U);
- state->s3 = TAUSWORTHE(state->s3, 13U, 21U, 4294967280U, 7U);
- state->s4 = TAUSWORTHE(state->s4, 3U, 12U, 4294967168U, 13U);
-
- return (state->s1 ^ state->s2 ^ state->s3 ^ state->s4);
+ return (u32) prandom_u64_state(state);
}
EXPORT_SYMBOL(prandom_u32_state);
@@ -81,14 +84,14 @@ void prandom_bytes_state(struct rnd_state *state, void *buf, size_t bytes)
{
u8 *ptr = buf;
- while (bytes >= sizeof(u32)) {
- put_unaligned(prandom_u32_state(state), (u32 *) ptr);
- ptr += sizeof(u32);
- bytes -= sizeof(u32);
+ while (bytes >= sizeof(u64)) {
+ put_unaligned(prandom_u64_state(state), (u64 *) ptr);
+ ptr += sizeof(u64);
+ bytes -= sizeof(u64);
}
if (bytes > 0) {
- u32 rem = prandom_u32_state(state);
+ u64 rem = prandom_u64_state(state);
do {
*ptr++ = (u8) rem;
bytes--;
@@ -98,20 +101,27 @@ void prandom_bytes_state(struct rnd_state *state, void *buf, size_t bytes)
}
EXPORT_SYMBOL(prandom_bytes_state);
-static void prandom_warmup(struct rnd_state *state)
+/**
+ * prandom_seed_state - set seed for prandom_u32_state().
+ * @state: pointer to state structure to receive the seed.
+ * @seed: arbitrary 64-bit value to use as a seed.
+ *
+ * splitmix64 init as suggested for xoshiro256++
+ * See: https://prng.di.unimi.it/splitmix64.c
+ */
+void prandom_seed_state(struct rnd_state *state, u64 seed)
{
- /* Calling RNG ten times to satisfy recurrence condition */
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
- prandom_u32_state(state);
+ int i;
+
+ for (i = 0; i < ARRAY_SIZE(state->s); ++i) {
+ seed += 0x9e3779b97f4a7c15;
+ u64 z = seed;
+ z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
+ z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
+ state->s[i] = z ^ (z >> 31);
+ }
}
+EXPORT_SYMBOL(prandom_seed_state);
void prandom_seed_full_state(struct rnd_state __percpu *pcpu_state)
{
@@ -119,15 +129,7 @@ void prandom_seed_full_state(struct rnd_state __percpu *pcpu_state)
for_each_possible_cpu(i) {
struct rnd_state *state = per_cpu_ptr(pcpu_state, i);
- u32 seeds[4];
-
- get_random_bytes(&seeds, sizeof(seeds));
- state->s1 = __seed(seeds[0], 2U);
- state->s2 = __seed(seeds[1], 8U);
- state->s3 = __seed(seeds[2], 16U);
- state->s4 = __seed(seeds[3], 128U);
-
- prandom_warmup(state);
+ get_random_bytes(&state->s, sizeof(state->s));
}
}
EXPORT_SYMBOL(prandom_seed_full_state);
@@ -137,10 +139,10 @@ static struct prandom_test1 {
u32 seed;
u32 result;
} test1[] = {
- { 1U, 3484351685U },
- { 2U, 2623130059U },
- { 3U, 3125133893U },
- { 4U, 984847254U },
+ { 1U, 1862517403U },
+ { 2U, 3049585706U },
+ { 3U, 3105450281U },
+ { 4U, 2527704881U },
};
static struct prandom_test2 {
@@ -148,118 +150,109 @@ static struct prandom_test2 {
u32 iteration;
u32 result;
} test2[] = {
- /* Test cases against taus113 from GSL library. */
- { 931557656U, 959U, 2975593782U },
- { 1339693295U, 876U, 3887776532U },
- { 1545556285U, 961U, 1615538833U },
- { 601730776U, 723U, 1776162651U },
- { 1027516047U, 687U, 511983079U },
- { 416526298U, 700U, 916156552U },
- { 1395522032U, 652U, 2222063676U },
- { 366221443U, 617U, 2992857763U },
- { 1539836965U, 714U, 3783265725U },
- { 556206671U, 994U, 799626459U },
- { 684907218U, 799U, 367789491U },
- { 2121230701U, 931U, 2115467001U },
- { 1668516451U, 644U, 3620590685U },
- { 768046066U, 883U, 2034077390U },
- { 1989159136U, 833U, 1195767305U },
- { 536585145U, 996U, 3577259204U },
- { 1008129373U, 642U, 1478080776U },
- { 1740775604U, 939U, 1264980372U },
- { 1967883163U, 508U, 10734624U },
- { 1923019697U, 730U, 3821419629U },
- { 442079932U, 560U, 3440032343U },
- { 1961302714U, 845U, 841962572U },
- { 2030205964U, 962U, 1325144227U },
- { 1160407529U, 507U, 240940858U },
- { 635482502U, 779U, 4200489746U },
- { 1252788931U, 699U, 867195434U },
- { 1961817131U, 719U, 668237657U },
- { 1071468216U, 983U, 917876630U },
- { 1281848367U, 932U, 1003100039U },
- { 582537119U, 780U, 1127273778U },
- { 1973672777U, 853U, 1071368872U },
- { 1896756996U, 762U, 1127851055U },
- { 847917054U, 500U, 1717499075U },
- { 1240520510U, 951U, 2849576657U },
- { 1685071682U, 567U, 1961810396U },
- { 1516232129U, 557U, 3173877U },
- { 1208118903U, 612U, 1613145022U },
- { 1817269927U, 693U, 4279122573U },
- { 1510091701U, 717U, 638191229U },
- { 365916850U, 807U, 600424314U },
- { 399324359U, 702U, 1803598116U },
- { 1318480274U, 779U, 2074237022U },
- { 697758115U, 840U, 1483639402U },
- { 1696507773U, 840U, 577415447U },
- { 2081979121U, 981U, 3041486449U },
- { 955646687U, 742U, 3846494357U },
- { 1250683506U, 749U, 836419859U },
- { 595003102U, 534U, 366794109U },
- { 47485338U, 558U, 3521120834U },
- { 619433479U, 610U, 3991783875U },
- { 704096520U, 518U, 4139493852U },
- { 1712224984U, 606U, 2393312003U },
- { 1318233152U, 922U, 3880361134U },
- { 855572992U, 761U, 1472974787U },
- { 64721421U, 703U, 683860550U },
- { 678931758U, 840U, 380616043U },
- { 692711973U, 778U, 1382361947U },
- { 677703619U, 530U, 2826914161U },
- { 92393223U, 586U, 1522128471U },
- { 1222592920U, 743U, 3466726667U },
- { 358288986U, 695U, 1091956998U },
- { 1935056945U, 958U, 514864477U },
- { 735675993U, 990U, 1294239989U },
- { 1560089402U, 897U, 2238551287U },
- { 70616361U, 829U, 22483098U },
- { 368234700U, 731U, 2913875084U },
- { 20221190U, 879U, 1564152970U },
- { 539444654U, 682U, 1835141259U },
- { 1314987297U, 840U, 1801114136U },
- { 2019295544U, 645U, 3286438930U },
- { 469023838U, 716U, 1637918202U },
- { 1843754496U, 653U, 2562092152U },
- { 400672036U, 809U, 4264212785U },
- { 404722249U, 965U, 2704116999U },
- { 600702209U, 758U, 584979986U },
- { 519953954U, 667U, 2574436237U },
- { 1658071126U, 694U, 2214569490U },
- { 420480037U, 749U, 3430010866U },
- { 690103647U, 969U, 3700758083U },
- { 1029424799U, 937U, 3787746841U },
- { 2012608669U, 506U, 3362628973U },
- { 1535432887U, 998U, 42610943U },
- { 1330635533U, 857U, 3040806504U },
- { 1223800550U, 539U, 3954229517U },
- { 1322411537U, 680U, 3223250324U },
- { 1877847898U, 945U, 2915147143U },
- { 1646356099U, 874U, 965988280U },
- { 805687536U, 744U, 4032277920U },
- { 1948093210U, 633U, 1346597684U },
- { 392609744U, 783U, 1636083295U },
- { 690241304U, 770U, 1201031298U },
- { 1360302965U, 696U, 1665394461U },
- { 1220090946U, 780U, 1316922812U },
- { 447092251U, 500U, 3438743375U },
- { 1613868791U, 592U, 828546883U },
- { 523430951U, 548U, 2552392304U },
- { 726692899U, 810U, 1656872867U },
- { 1364340021U, 836U, 3710513486U },
- { 1986257729U, 931U, 935013962U },
- { 407983964U, 921U, 728767059U },
+ /* Test cases against Xoshiro256++, generated with reference impl. */
+ { 931557656U, 959U, 2221272722U },
+ { 1339693295U, 876U, 12322103U },
+ { 1545556285U, 961U, 2793306339U },
+ { 601730776U, 723U, 186699327U },
+ { 1027516047U, 687U, 3385354088U },
+ { 416526298U, 700U, 3047662436U },
+ { 1395522032U, 652U, 370169503U },
+ { 366221443U, 617U, 2468792816U },
+ { 1539836965U, 714U, 4178175423U },
+ { 556206671U, 994U, 1935910425U },
+ { 684907218U, 799U, 2892366361U },
+ { 2121230701U, 931U, 2395880533U },
+ { 1668516451U, 644U, 659315062U },
+ { 768046066U, 883U, 729262650U },
+ { 1989159136U, 833U, 44268867U },
+ { 536585145U, 996U, 3734292685U },
+ { 1008129373U, 642U, 3779097844U },
+ { 1740775604U, 939U, 958440770U },
+ { 1967883163U, 508U, 2766790334U },
+ { 1923019697U, 730U, 4188718967U },
+ { 442079932U, 560U, 2658351430U },
+ { 1961302714U, 845U, 418725413U },
+ { 2030205964U, 962U, 3541720353U },
+ { 1160407529U, 507U, 155686916U },
+ { 635482502U, 779U, 2954399934U },
+ { 1252788931U, 699U, 3195364074U },
+ { 1961817131U, 719U, 3860285454U },
+ { 1071468216U, 983U, 2558711391U },
+ { 1281848367U, 932U, 2429019683U },
+ { 582537119U, 780U, 2251637575U },
+ { 1973672777U, 853U, 2686341687U },
+ { 1896756996U, 762U, 3853948474U },
+ { 847917054U, 500U, 1352384361U },
+ { 1240520510U, 951U, 424294678U },
+ { 1685071682U, 567U, 1127358663U },
+ { 1516232129U, 557U, 2438163725U },
+ { 1208118903U, 612U, 494560814U },
+ { 1817269927U, 693U, 2296243096U },
+ { 1510091701U, 717U, 2522390997U },
+ { 365916850U, 807U, 1704622356U },
+ { 399324359U, 702U, 1692076319U },
+ { 1318480274U, 779U, 3132074148U },
+ { 697758115U, 840U, 2298934293U },
+ { 1696507773U, 840U, 460426950U },
+ { 2081979121U, 981U, 2030259222U },
+ { 955646687U, 742U, 849374769U },
+ { 1250683506U, 749U, 3793648395U },
+ { 595003102U, 534U, 312261219U },
+ { 47485338U, 558U, 1498074521U },
+ { 619433479U, 610U, 3298978919U },
+ { 704096520U, 518U, 1859635041U },
+ { 1712224984U, 606U, 2636341373U },
+ { 1318233152U, 922U, 4294083073U },
+ { 855572992U, 761U, 1398432208U },
+ { 64721421U, 703U, 2917659579U },
+ { 678931758U, 840U, 2610263429U },
+ { 692711973U, 778U, 2364471195U },
+ { 677703619U, 530U, 4293322414U },
+ { 92393223U, 586U, 2200038234U },
+ { 1222592920U, 743U, 3902404436U },
+ { 358288986U, 695U, 4187968216U },
+ { 1935056945U, 958U, 2216763617U },
+ { 735675993U, 990U, 3851267177U },
+ { 1560089402U, 897U, 3110095036U },
+ { 70616361U, 829U, 2727884311U },
+ { 368234700U, 731U, 1394533121U },
+ { 20221190U, 879U, 2426527948U },
+ { 539444654U, 682U, 3323050847U },
+ { 1314987297U, 840U, 1532766257U },
+ { 2019295544U, 645U, 2824742190U },
+ { 469023838U, 716U, 2626662944U },
+ { 1843754496U, 653U, 3912965452U },
+ { 400672036U, 809U, 794673667U },
+ { 404722249U, 965U, 2590267245U },
+ { 600702209U, 758U, 3742697327U },
+ { 519953954U, 667U, 909153960U },
+ { 1658071126U, 694U, 1016441204U },
+ { 420480037U, 749U, 4007274669U },
+ { 690103647U, 969U, 2262636339U },
+ { 1029424799U, 937U, 1940659603U },
+ { 2012608669U, 506U, 239338087U },
+ { 1535432887U, 998U, 1889887018U },
+ { 1330635533U, 857U, 4029849650U },
+ { 1223800550U, 539U, 678829248U },
+ { 1322411537U, 680U, 2745139632U },
+ { 1877847898U, 945U, 153715577U },
+ { 1646356099U, 874U, 525516737U },
+ { 805687536U, 744U, 1564399105U },
+ { 1948093210U, 633U, 507042967U },
+ { 392609744U, 783U, 33573161U },
+ { 690241304U, 770U, 1551691277U },
+ { 1360302965U, 696U, 391079011U },
+ { 1220090946U, 780U, 2587343386U },
+ { 447092251U, 500U, 3335665101U },
+ { 1613868791U, 592U, 131974931U },
+ { 523430951U, 548U, 3871675719U },
+ { 726692899U, 810U, 2919536533U },
+ { 1364340021U, 836U, 1695810824U },
+ { 1986257729U, 931U, 550308813U },
+ { 407983964U, 921U, 360202562U }
};
-static void prandom_state_selftest_seed(struct rnd_state *state, u32 seed)
-{
-#define LCG(x) ((x) * 69069U) /* super-duper LCG */
- state->s1 = __seed(LCG(seed), 2U);
- state->s2 = __seed(LCG(state->s1), 8U);
- state->s3 = __seed(LCG(state->s2), 16U);
- state->s4 = __seed(LCG(state->s3), 128U);
-}
-
static int __init prandom_state_selftest(void)
{
int i, j, errors = 0, runs = 0;
@@ -268,8 +261,7 @@ static int __init prandom_state_selftest(void)
for (i = 0; i < ARRAY_SIZE(test1); i++) {
struct rnd_state state;
- prandom_state_selftest_seed(&state, test1[i].seed);
- prandom_warmup(&state);
+ prandom_seed_state(&state, test1[i].seed);
if (test1[i].result != prandom_u32_state(&state))
error = true;
@@ -283,8 +275,7 @@ static int __init prandom_state_selftest(void)
for (i = 0; i < ARRAY_SIZE(test2); i++) {
struct rnd_state state;
- prandom_state_selftest_seed(&state, test2[i].seed);
- prandom_warmup(&state);
+ prandom_seed_state(&state, test2[i].seed);
for (j = 0; j < test2[i].iteration - 1; j++)
prandom_u32_state(&state);
--
2.47.2
