2 * This is a maximally equidistributed combined Tausworthe generator
3 * based on code from GNU Scientific Library 1.5 (30 Jun 2004)
7 * x_n = (s1_n ^ s2_n ^ s3_n ^ s4_n)
9 * s1_{n+1} = (((s1_n & 4294967294) << 18) ^ (((s1_n << 6) ^ s1_n) >> 13))
10 * s2_{n+1} = (((s2_n & 4294967288) << 2) ^ (((s2_n << 2) ^ s2_n) >> 27))
11 * s3_{n+1} = (((s3_n & 4294967280) << 7) ^ (((s3_n << 13) ^ s3_n) >> 21))
12 * s4_{n+1} = (((s4_n & 4294967168) << 13) ^ (((s4_n << 3) ^ s4_n) >> 12))
14 * The period of this generator is about 2^113 (see erratum paper).
16 * From: P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe
17 * Generators", Mathematics of Computation, 65, 213 (1996), 203--213:
18 * http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
19 * ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/tausme.ps
21 * There is an erratum in the paper "Tables of Maximally Equidistributed
22 * Combined LFSR Generators", Mathematics of Computation, 68, 225 (1999),
23 * 261--269: http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
25 * ... the k_j most significant bits of z_j must be non-zero,
26 * for each j. (Note: this restriction also applies to the
27 * computer code given in [4], but was mistakenly not mentioned
30 * This affects the seeding procedure by imposing the requirement
31 * s1 > 1, s2 > 7, s3 > 15, s4 > 127.
34 #include <linux/types.h>
35 #include <linux/percpu.h>
36 #include <linux/export.h>
37 #include <linux/jiffies.h>
38 #include <linux/random.h>
39 #include <linux/sched.h>
41 #ifdef CONFIG_RANDOM32_SELFTEST
42 static void __init
prandom_state_selftest(void);
45 static DEFINE_PER_CPU(struct rnd_state
, net_rand_state
);
48 * prandom_u32_state - seeded pseudo-random number generator.
49 * @state: pointer to state structure holding seeded state.
51 * This is used for pseudo-randomness with no outside seeding.
52 * For more random results, use prandom_u32().
54 u32
prandom_u32_state(struct rnd_state
*state
)
56 #define TAUSWORTHE(s,a,b,c,d) ((s&c)<<d) ^ (((s <<a) ^ s)>>b)
58 state
->s1
= TAUSWORTHE(state
->s1
, 6U, 13U, 4294967294U, 18U);
59 state
->s2
= TAUSWORTHE(state
->s2
, 2U, 27U, 4294967288U, 2U);
60 state
->s3
= TAUSWORTHE(state
->s3
, 13U, 21U, 4294967280U, 7U);
61 state
->s4
= TAUSWORTHE(state
->s4
, 3U, 12U, 4294967168U, 13U);
63 return (state
->s1
^ state
->s2
^ state
->s3
^ state
->s4
);
65 EXPORT_SYMBOL(prandom_u32_state
);
68 * prandom_u32 - pseudo random number generator
70 * A 32 bit pseudo-random number is generated using a fast
71 * algorithm suitable for simulation. This algorithm is NOT
72 * considered safe for cryptographic use.
76 struct rnd_state
*state
= &get_cpu_var(net_rand_state
);
79 res
= prandom_u32_state(state
);
84 EXPORT_SYMBOL(prandom_u32
);
87 * prandom_bytes_state - get the requested number of pseudo-random bytes
89 * @state: pointer to state structure holding seeded state.
90 * @buf: where to copy the pseudo-random bytes to
91 * @bytes: the requested number of bytes
93 * This is used for pseudo-randomness with no outside seeding.
94 * For more random results, use prandom_bytes().
96 void prandom_bytes_state(struct rnd_state
*state
, void *buf
, int bytes
)
98 unsigned char *p
= buf
;
101 for (i
= 0; i
< round_down(bytes
, sizeof(u32
)); i
+= sizeof(u32
)) {
102 u32 random
= prandom_u32_state(state
);
105 for (j
= 0; j
< sizeof(u32
); j
++) {
107 random
>>= BITS_PER_BYTE
;
111 u32 random
= prandom_u32_state(state
);
113 for (; i
< bytes
; i
++) {
115 random
>>= BITS_PER_BYTE
;
119 EXPORT_SYMBOL(prandom_bytes_state
);
122 * prandom_bytes - get the requested number of pseudo-random bytes
123 * @buf: where to copy the pseudo-random bytes to
124 * @bytes: the requested number of bytes
126 void prandom_bytes(void *buf
, int bytes
)
128 struct rnd_state
*state
= &get_cpu_var(net_rand_state
);
130 prandom_bytes_state(state
, buf
, bytes
);
133 EXPORT_SYMBOL(prandom_bytes
);
135 static void prandom_warmup(struct rnd_state
*state
)
137 /* Calling RNG ten times to satify recurrence condition */
138 prandom_u32_state(state
);
139 prandom_u32_state(state
);
140 prandom_u32_state(state
);
141 prandom_u32_state(state
);
142 prandom_u32_state(state
);
143 prandom_u32_state(state
);
144 prandom_u32_state(state
);
145 prandom_u32_state(state
);
146 prandom_u32_state(state
);
147 prandom_u32_state(state
);
150 static void prandom_seed_very_weak(struct rnd_state
*state
, u32 seed
)
152 /* Note: This sort of seeding is ONLY used in test cases and
153 * during boot at the time from core_initcall until late_initcall
154 * as we don't have a stronger entropy source available yet.
155 * After late_initcall, we reseed entire state, we have to (!),
156 * otherwise an attacker just needs to search 32 bit space to
157 * probe for our internal 128 bit state if he knows a couple
158 * of prandom32 outputs!
160 #define LCG(x) ((x) * 69069U) /* super-duper LCG */
161 state
->s1
= __seed(LCG(seed
), 2U);
162 state
->s2
= __seed(LCG(state
->s1
), 8U);
163 state
->s3
= __seed(LCG(state
->s2
), 16U);
164 state
->s4
= __seed(LCG(state
->s3
), 128U);
168 * prandom_seed - add entropy to pseudo random number generator
171 * Add some additional seeding to the prandom pool.
173 void prandom_seed(u32 entropy
)
177 * No locking on the CPUs, but then somewhat random results are, well,
180 for_each_possible_cpu (i
) {
181 struct rnd_state
*state
= &per_cpu(net_rand_state
, i
);
183 state
->s1
= __seed(state
->s1
^ entropy
, 2U);
184 prandom_warmup(state
);
187 EXPORT_SYMBOL(prandom_seed
);
190 * Generate some initially weak seeding values to allow
191 * to start the prandom_u32() engine.
193 static int __init
prandom_init(void)
197 #ifdef CONFIG_RANDOM32_SELFTEST
198 prandom_state_selftest();
201 for_each_possible_cpu(i
) {
202 struct rnd_state
*state
= &per_cpu(net_rand_state
,i
);
204 prandom_seed_very_weak(state
, (i
+ jiffies
) ^ random_get_entropy());
205 prandom_warmup(state
);
210 core_initcall(prandom_init
);
212 static void __prandom_timer(unsigned long dontcare
);
213 static DEFINE_TIMER(seed_timer
, __prandom_timer
, 0, 0);
215 static void __prandom_timer(unsigned long dontcare
)
218 unsigned long expires
;
220 get_random_bytes(&entropy
, sizeof(entropy
));
221 prandom_seed(entropy
);
223 /* reseed every ~60 seconds, in [40 .. 80) interval with slack */
224 expires
= 40 + (prandom_u32() % 40);
225 seed_timer
.expires
= jiffies
+ msecs_to_jiffies(expires
* MSEC_PER_SEC
);
227 add_timer(&seed_timer
);
230 static void __init
__prandom_start_seed_timer(void)
232 set_timer_slack(&seed_timer
, HZ
);
233 seed_timer
.expires
= jiffies
+ msecs_to_jiffies(40 * MSEC_PER_SEC
);
234 add_timer(&seed_timer
);
238 * Generate better values after random number generator
239 * is fully initialized.
241 static void __prandom_reseed(bool late
)
245 static bool latch
= false;
246 static DEFINE_SPINLOCK(lock
);
248 /* Asking for random bytes might result in bytes getting
249 * moved into the nonblocking pool and thus marking it
250 * as initialized. In this case we would double back into
251 * this function and attempt to do a late reseed.
252 * Ignore the pointless attempt to reseed again if we're
253 * already waiting for bytes when the nonblocking pool
257 /* only allow initial seeding (late == false) once */
258 if (!spin_trylock_irqsave(&lock
, flags
))
266 for_each_possible_cpu(i
) {
267 struct rnd_state
*state
= &per_cpu(net_rand_state
,i
);
270 get_random_bytes(&seeds
, sizeof(seeds
));
271 state
->s1
= __seed(seeds
[0], 2U);
272 state
->s2
= __seed(seeds
[1], 8U);
273 state
->s3
= __seed(seeds
[2], 16U);
274 state
->s4
= __seed(seeds
[3], 128U);
276 prandom_warmup(state
);
279 spin_unlock_irqrestore(&lock
, flags
);
282 void prandom_reseed_late(void)
284 __prandom_reseed(true);
287 static int __init
prandom_reseed(void)
289 __prandom_reseed(false);
290 __prandom_start_seed_timer();
293 late_initcall(prandom_reseed
);
295 #ifdef CONFIG_RANDOM32_SELFTEST
296 static struct prandom_test1
{
306 static struct prandom_test2
{
311 /* Test cases against taus113 from GSL library. */
312 { 931557656U, 959U, 2975593782U },
313 { 1339693295U, 876U, 3887776532U },
314 { 1545556285U, 961U, 1615538833U },
315 { 601730776U, 723U, 1776162651U },
316 { 1027516047U, 687U, 511983079U },
317 { 416526298U, 700U, 916156552U },
318 { 1395522032U, 652U, 2222063676U },
319 { 366221443U, 617U, 2992857763U },
320 { 1539836965U, 714U, 3783265725U },
321 { 556206671U, 994U, 799626459U },
322 { 684907218U, 799U, 367789491U },
323 { 2121230701U, 931U, 2115467001U },
324 { 1668516451U, 644U, 3620590685U },
325 { 768046066U, 883U, 2034077390U },
326 { 1989159136U, 833U, 1195767305U },
327 { 536585145U, 996U, 3577259204U },
328 { 1008129373U, 642U, 1478080776U },
329 { 1740775604U, 939U, 1264980372U },
330 { 1967883163U, 508U, 10734624U },
331 { 1923019697U, 730U, 3821419629U },
332 { 442079932U, 560U, 3440032343U },
333 { 1961302714U, 845U, 841962572U },
334 { 2030205964U, 962U, 1325144227U },
335 { 1160407529U, 507U, 240940858U },
336 { 635482502U, 779U, 4200489746U },
337 { 1252788931U, 699U, 867195434U },
338 { 1961817131U, 719U, 668237657U },
339 { 1071468216U, 983U, 917876630U },
340 { 1281848367U, 932U, 1003100039U },
341 { 582537119U, 780U, 1127273778U },
342 { 1973672777U, 853U, 1071368872U },
343 { 1896756996U, 762U, 1127851055U },
344 { 847917054U, 500U, 1717499075U },
345 { 1240520510U, 951U, 2849576657U },
346 { 1685071682U, 567U, 1961810396U },
347 { 1516232129U, 557U, 3173877U },
348 { 1208118903U, 612U, 1613145022U },
349 { 1817269927U, 693U, 4279122573U },
350 { 1510091701U, 717U, 638191229U },
351 { 365916850U, 807U, 600424314U },
352 { 399324359U, 702U, 1803598116U },
353 { 1318480274U, 779U, 2074237022U },
354 { 697758115U, 840U, 1483639402U },
355 { 1696507773U, 840U, 577415447U },
356 { 2081979121U, 981U, 3041486449U },
357 { 955646687U, 742U, 3846494357U },
358 { 1250683506U, 749U, 836419859U },
359 { 595003102U, 534U, 366794109U },
360 { 47485338U, 558U, 3521120834U },
361 { 619433479U, 610U, 3991783875U },
362 { 704096520U, 518U, 4139493852U },
363 { 1712224984U, 606U, 2393312003U },
364 { 1318233152U, 922U, 3880361134U },
365 { 855572992U, 761U, 1472974787U },
366 { 64721421U, 703U, 683860550U },
367 { 678931758U, 840U, 380616043U },
368 { 692711973U, 778U, 1382361947U },
369 { 677703619U, 530U, 2826914161U },
370 { 92393223U, 586U, 1522128471U },
371 { 1222592920U, 743U, 3466726667U },
372 { 358288986U, 695U, 1091956998U },
373 { 1935056945U, 958U, 514864477U },
374 { 735675993U, 990U, 1294239989U },
375 { 1560089402U, 897U, 2238551287U },
376 { 70616361U, 829U, 22483098U },
377 { 368234700U, 731U, 2913875084U },
378 { 20221190U, 879U, 1564152970U },
379 { 539444654U, 682U, 1835141259U },
380 { 1314987297U, 840U, 1801114136U },
381 { 2019295544U, 645U, 3286438930U },
382 { 469023838U, 716U, 1637918202U },
383 { 1843754496U, 653U, 2562092152U },
384 { 400672036U, 809U, 4264212785U },
385 { 404722249U, 965U, 2704116999U },
386 { 600702209U, 758U, 584979986U },
387 { 519953954U, 667U, 2574436237U },
388 { 1658071126U, 694U, 2214569490U },
389 { 420480037U, 749U, 3430010866U },
390 { 690103647U, 969U, 3700758083U },
391 { 1029424799U, 937U, 3787746841U },
392 { 2012608669U, 506U, 3362628973U },
393 { 1535432887U, 998U, 42610943U },
394 { 1330635533U, 857U, 3040806504U },
395 { 1223800550U, 539U, 3954229517U },
396 { 1322411537U, 680U, 3223250324U },
397 { 1877847898U, 945U, 2915147143U },
398 { 1646356099U, 874U, 965988280U },
399 { 805687536U, 744U, 4032277920U },
400 { 1948093210U, 633U, 1346597684U },
401 { 392609744U, 783U, 1636083295U },
402 { 690241304U, 770U, 1201031298U },
403 { 1360302965U, 696U, 1665394461U },
404 { 1220090946U, 780U, 1316922812U },
405 { 447092251U, 500U, 3438743375U },
406 { 1613868791U, 592U, 828546883U },
407 { 523430951U, 548U, 2552392304U },
408 { 726692899U, 810U, 1656872867U },
409 { 1364340021U, 836U, 3710513486U },
410 { 1986257729U, 931U, 935013962U },
411 { 407983964U, 921U, 728767059U },
414 static void __init
prandom_state_selftest(void)
416 int i
, j
, errors
= 0, runs
= 0;
419 for (i
= 0; i
< ARRAY_SIZE(test1
); i
++) {
420 struct rnd_state state
;
422 prandom_seed_very_weak(&state
, test1
[i
].seed
);
423 prandom_warmup(&state
);
425 if (test1
[i
].result
!= prandom_u32_state(&state
))
430 pr_warn("prandom: seed boundary self test failed\n");
432 pr_info("prandom: seed boundary self test passed\n");
434 for (i
= 0; i
< ARRAY_SIZE(test2
); i
++) {
435 struct rnd_state state
;
437 prandom_seed_very_weak(&state
, test2
[i
].seed
);
438 prandom_warmup(&state
);
440 for (j
= 0; j
< test2
[i
].iteration
- 1; j
++)
441 prandom_u32_state(&state
);
443 if (test2
[i
].result
!= prandom_u32_state(&state
))
451 pr_warn("prandom: %d/%d self tests failed\n", errors
, runs
);
453 pr_info("prandom: %d self tests passed\n", runs
);
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