1 // SPDX-License-Identifier: GPL-2.0
3 * This is a maximally equidistributed combined Tausworthe generator
4 * based on code from GNU Scientific Library 1.5 (30 Jun 2004)
8 * x_n = (s1_n ^ s2_n ^ s3_n ^ s4_n)
10 * s1_{n+1} = (((s1_n & 4294967294) << 18) ^ (((s1_n << 6) ^ s1_n) >> 13))
11 * s2_{n+1} = (((s2_n & 4294967288) << 2) ^ (((s2_n << 2) ^ s2_n) >> 27))
12 * s3_{n+1} = (((s3_n & 4294967280) << 7) ^ (((s3_n << 13) ^ s3_n) >> 21))
13 * s4_{n+1} = (((s4_n & 4294967168) << 13) ^ (((s4_n << 3) ^ s4_n) >> 12))
15 * The period of this generator is about 2^113 (see erratum paper).
17 * From: P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe
18 * Generators", Mathematics of Computation, 65, 213 (1996), 203--213:
19 * http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
20 * ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/tausme.ps
22 * There is an erratum in the paper "Tables of Maximally Equidistributed
23 * Combined LFSR Generators", Mathematics of Computation, 68, 225 (1999),
24 * 261--269: http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
26 * ... the k_j most significant bits of z_j must be non-zero,
27 * for each j. (Note: this restriction also applies to the
28 * computer code given in [4], but was mistakenly not mentioned
31 * This affects the seeding procedure by imposing the requirement
32 * s1 > 1, s2 > 7, s3 > 15, s4 > 127.
35 #include <linux/types.h>
36 #include <linux/percpu.h>
37 #include <linux/export.h>
38 #include <linux/jiffies.h>
39 #include <linux/random.h>
40 #include <linux/sched.h>
41 #include <asm/unaligned.h>
44 * prandom_u32_state - seeded pseudo-random number generator.
45 * @state: pointer to state structure holding seeded state.
47 * This is used for pseudo-randomness with no outside seeding.
48 * For more random results, use prandom_u32().
50 u32
prandom_u32_state(struct rnd_state
*state
)
52 #define TAUSWORTHE(s, a, b, c, d) ((s & c) << d) ^ (((s << a) ^ s) >> b)
53 state
->s1
= TAUSWORTHE(state
->s1
, 6U, 13U, 4294967294U, 18U);
54 state
->s2
= TAUSWORTHE(state
->s2
, 2U, 27U, 4294967288U, 2U);
55 state
->s3
= TAUSWORTHE(state
->s3
, 13U, 21U, 4294967280U, 7U);
56 state
->s4
= TAUSWORTHE(state
->s4
, 3U, 12U, 4294967168U, 13U);
58 return (state
->s1
^ state
->s2
^ state
->s3
^ state
->s4
);
60 EXPORT_SYMBOL(prandom_u32_state
);
63 * prandom_bytes_state - get the requested number of pseudo-random bytes
65 * @state: pointer to state structure holding seeded state.
66 * @buf: where to copy the pseudo-random bytes to
67 * @bytes: the requested number of bytes
69 * This is used for pseudo-randomness with no outside seeding.
70 * For more random results, use prandom_bytes().
72 void prandom_bytes_state(struct rnd_state
*state
, void *buf
, size_t bytes
)
76 while (bytes
>= sizeof(u32
)) {
77 put_unaligned(prandom_u32_state(state
), (u32
*) ptr
);
83 u32 rem
= prandom_u32_state(state
);
87 rem
>>= BITS_PER_BYTE
;
91 EXPORT_SYMBOL(prandom_bytes_state
);
93 static void prandom_warmup(struct rnd_state
*state
)
95 /* Calling RNG ten times to satisfy recurrence condition */
96 prandom_u32_state(state
);
97 prandom_u32_state(state
);
98 prandom_u32_state(state
);
99 prandom_u32_state(state
);
100 prandom_u32_state(state
);
101 prandom_u32_state(state
);
102 prandom_u32_state(state
);
103 prandom_u32_state(state
);
104 prandom_u32_state(state
);
105 prandom_u32_state(state
);
108 void prandom_seed_full_state(struct rnd_state __percpu
*pcpu_state
)
112 for_each_possible_cpu(i
) {
113 struct rnd_state
*state
= per_cpu_ptr(pcpu_state
, i
);
116 get_random_bytes(&seeds
, sizeof(seeds
));
117 state
->s1
= __seed(seeds
[0], 2U);
118 state
->s2
= __seed(seeds
[1], 8U);
119 state
->s3
= __seed(seeds
[2], 16U);
120 state
->s4
= __seed(seeds
[3], 128U);
122 prandom_warmup(state
);
125 EXPORT_SYMBOL(prandom_seed_full_state
);
127 #ifdef CONFIG_RANDOM32_SELFTEST
128 static struct prandom_test1
{
138 static struct prandom_test2
{
143 /* Test cases against taus113 from GSL library. */
144 { 931557656U, 959U, 2975593782U },
145 { 1339693295U, 876U, 3887776532U },
146 { 1545556285U, 961U, 1615538833U },
147 { 601730776U, 723U, 1776162651U },
148 { 1027516047U, 687U, 511983079U },
149 { 416526298U, 700U, 916156552U },
150 { 1395522032U, 652U, 2222063676U },
151 { 366221443U, 617U, 2992857763U },
152 { 1539836965U, 714U, 3783265725U },
153 { 556206671U, 994U, 799626459U },
154 { 684907218U, 799U, 367789491U },
155 { 2121230701U, 931U, 2115467001U },
156 { 1668516451U, 644U, 3620590685U },
157 { 768046066U, 883U, 2034077390U },
158 { 1989159136U, 833U, 1195767305U },
159 { 536585145U, 996U, 3577259204U },
160 { 1008129373U, 642U, 1478080776U },
161 { 1740775604U, 939U, 1264980372U },
162 { 1967883163U, 508U, 10734624U },
163 { 1923019697U, 730U, 3821419629U },
164 { 442079932U, 560U, 3440032343U },
165 { 1961302714U, 845U, 841962572U },
166 { 2030205964U, 962U, 1325144227U },
167 { 1160407529U, 507U, 240940858U },
168 { 635482502U, 779U, 4200489746U },
169 { 1252788931U, 699U, 867195434U },
170 { 1961817131U, 719U, 668237657U },
171 { 1071468216U, 983U, 917876630U },
172 { 1281848367U, 932U, 1003100039U },
173 { 582537119U, 780U, 1127273778U },
174 { 1973672777U, 853U, 1071368872U },
175 { 1896756996U, 762U, 1127851055U },
176 { 847917054U, 500U, 1717499075U },
177 { 1240520510U, 951U, 2849576657U },
178 { 1685071682U, 567U, 1961810396U },
179 { 1516232129U, 557U, 3173877U },
180 { 1208118903U, 612U, 1613145022U },
181 { 1817269927U, 693U, 4279122573U },
182 { 1510091701U, 717U, 638191229U },
183 { 365916850U, 807U, 600424314U },
184 { 399324359U, 702U, 1803598116U },
185 { 1318480274U, 779U, 2074237022U },
186 { 697758115U, 840U, 1483639402U },
187 { 1696507773U, 840U, 577415447U },
188 { 2081979121U, 981U, 3041486449U },
189 { 955646687U, 742U, 3846494357U },
190 { 1250683506U, 749U, 836419859U },
191 { 595003102U, 534U, 366794109U },
192 { 47485338U, 558U, 3521120834U },
193 { 619433479U, 610U, 3991783875U },
194 { 704096520U, 518U, 4139493852U },
195 { 1712224984U, 606U, 2393312003U },
196 { 1318233152U, 922U, 3880361134U },
197 { 855572992U, 761U, 1472974787U },
198 { 64721421U, 703U, 683860550U },
199 { 678931758U, 840U, 380616043U },
200 { 692711973U, 778U, 1382361947U },
201 { 677703619U, 530U, 2826914161U },
202 { 92393223U, 586U, 1522128471U },
203 { 1222592920U, 743U, 3466726667U },
204 { 358288986U, 695U, 1091956998U },
205 { 1935056945U, 958U, 514864477U },
206 { 735675993U, 990U, 1294239989U },
207 { 1560089402U, 897U, 2238551287U },
208 { 70616361U, 829U, 22483098U },
209 { 368234700U, 731U, 2913875084U },
210 { 20221190U, 879U, 1564152970U },
211 { 539444654U, 682U, 1835141259U },
212 { 1314987297U, 840U, 1801114136U },
213 { 2019295544U, 645U, 3286438930U },
214 { 469023838U, 716U, 1637918202U },
215 { 1843754496U, 653U, 2562092152U },
216 { 400672036U, 809U, 4264212785U },
217 { 404722249U, 965U, 2704116999U },
218 { 600702209U, 758U, 584979986U },
219 { 519953954U, 667U, 2574436237U },
220 { 1658071126U, 694U, 2214569490U },
221 { 420480037U, 749U, 3430010866U },
222 { 690103647U, 969U, 3700758083U },
223 { 1029424799U, 937U, 3787746841U },
224 { 2012608669U, 506U, 3362628973U },
225 { 1535432887U, 998U, 42610943U },
226 { 1330635533U, 857U, 3040806504U },
227 { 1223800550U, 539U, 3954229517U },
228 { 1322411537U, 680U, 3223250324U },
229 { 1877847898U, 945U, 2915147143U },
230 { 1646356099U, 874U, 965988280U },
231 { 805687536U, 744U, 4032277920U },
232 { 1948093210U, 633U, 1346597684U },
233 { 392609744U, 783U, 1636083295U },
234 { 690241304U, 770U, 1201031298U },
235 { 1360302965U, 696U, 1665394461U },
236 { 1220090946U, 780U, 1316922812U },
237 { 447092251U, 500U, 3438743375U },
238 { 1613868791U, 592U, 828546883U },
239 { 523430951U, 548U, 2552392304U },
240 { 726692899U, 810U, 1656872867U },
241 { 1364340021U, 836U, 3710513486U },
242 { 1986257729U, 931U, 935013962U },
243 { 407983964U, 921U, 728767059U },
246 static u32
__extract_hwseed(void)
248 unsigned int val
= 0;
250 (void)(arch_get_random_seed_int(&val
) ||
251 arch_get_random_int(&val
));
256 static void prandom_seed_early(struct rnd_state
*state
, u32 seed
,
257 bool mix_with_hwseed
)
259 #define LCG(x) ((x) * 69069U) /* super-duper LCG */
260 #define HWSEED() (mix_with_hwseed ? __extract_hwseed() : 0)
261 state
->s1
= __seed(HWSEED() ^ LCG(seed
), 2U);
262 state
->s2
= __seed(HWSEED() ^ LCG(state
->s1
), 8U);
263 state
->s3
= __seed(HWSEED() ^ LCG(state
->s2
), 16U);
264 state
->s4
= __seed(HWSEED() ^ LCG(state
->s3
), 128U);
267 static int __init
prandom_state_selftest(void)
269 int i
, j
, errors
= 0, runs
= 0;
272 for (i
= 0; i
< ARRAY_SIZE(test1
); i
++) {
273 struct rnd_state state
;
275 prandom_seed_early(&state
, test1
[i
].seed
, false);
276 prandom_warmup(&state
);
278 if (test1
[i
].result
!= prandom_u32_state(&state
))
283 pr_warn("prandom: seed boundary self test failed\n");
285 pr_info("prandom: seed boundary self test passed\n");
287 for (i
= 0; i
< ARRAY_SIZE(test2
); i
++) {
288 struct rnd_state state
;
290 prandom_seed_early(&state
, test2
[i
].seed
, false);
291 prandom_warmup(&state
);
293 for (j
= 0; j
< test2
[i
].iteration
- 1; j
++)
294 prandom_u32_state(&state
);
296 if (test2
[i
].result
!= prandom_u32_state(&state
))
304 pr_warn("prandom: %d/%d self tests failed\n", errors
, runs
);
306 pr_info("prandom: %d self tests passed\n", runs
);
309 core_initcall(prandom_state_selftest
);
313 * The prandom_u32() implementation is now completely separate from the
314 * prandom_state() functions, which are retained (for now) for compatibility.
316 * Because of (ab)use in the networking code for choosing random TCP/UDP port
317 * numbers, which open DoS possibilities if guessable, we want something
318 * stronger than a standard PRNG. But the performance requirements of
319 * the network code do not allow robust crypto for this application.
321 * So this is a homebrew Junior Spaceman implementation, based on the
322 * lowest-latency trustworthy crypto primitive available, SipHash.
323 * (The authors of SipHash have not been consulted about this abuse of
326 * Standard SipHash-2-4 uses 2n+4 rounds to hash n words of input to
327 * one word of output. This abbreviated version uses 2 rounds per word
331 struct siprand_state
{
338 static DEFINE_PER_CPU(struct siprand_state
, net_rand_state
) __latent_entropy
;
341 * This is the core CPRNG function. As "pseudorandom", this is not used
342 * for truly valuable things, just intended to be a PITA to guess.
343 * For maximum speed, we do just two SipHash rounds per word. This is
344 * the same rate as 4 rounds per 64 bits that SipHash normally uses,
345 * so hopefully it's reasonably secure.
347 * There are two changes from the official SipHash finalization:
348 * - We omit some constants XORed with v2 in the SipHash spec as irrelevant;
349 * they are there only to make the output rounds distinct from the input
350 * rounds, and this application has no input rounds.
351 * - Rather than returning v0^v1^v2^v3, return v1+v3.
352 * If you look at the SipHash round, the last operation on v3 is
353 * "v3 ^= v0", so "v0 ^ v3" just undoes that, a waste of time.
354 * Likewise "v1 ^= v2". (The rotate of v2 makes a difference, but
355 * it still cancels out half of the bits in v2 for no benefit.)
356 * Second, since the last combining operation was xor, continue the
357 * pattern of alternating xor/add for a tiny bit of extra non-linearity.
359 static inline u32
siprand_u32(struct siprand_state
*s
)
361 unsigned long v0
= s
->v0
, v1
= s
->v1
, v2
= s
->v2
, v3
= s
->v3
;
363 PRND_SIPROUND(v0
, v1
, v2
, v3
);
364 PRND_SIPROUND(v0
, v1
, v2
, v3
);
365 s
->v0
= v0
; s
->v1
= v1
; s
->v2
= v2
; s
->v3
= v3
;
371 * prandom_u32 - pseudo random number generator
373 * A 32 bit pseudo-random number is generated using a fast
374 * algorithm suitable for simulation. This algorithm is NOT
375 * considered safe for cryptographic use.
377 u32
prandom_u32(void)
379 struct siprand_state
*state
= get_cpu_ptr(&net_rand_state
);
380 u32 res
= siprand_u32(state
);
382 put_cpu_ptr(&net_rand_state
);
385 EXPORT_SYMBOL(prandom_u32
);
388 * prandom_bytes - get the requested number of pseudo-random bytes
389 * @buf: where to copy the pseudo-random bytes to
390 * @bytes: the requested number of bytes
392 void prandom_bytes(void *buf
, size_t bytes
)
394 struct siprand_state
*state
= get_cpu_ptr(&net_rand_state
);
397 while (bytes
>= sizeof(u32
)) {
398 put_unaligned(siprand_u32(state
), (u32
*)ptr
);
400 bytes
-= sizeof(u32
);
404 u32 rem
= siprand_u32(state
);
408 rem
>>= BITS_PER_BYTE
;
409 } while (--bytes
> 0);
411 put_cpu_ptr(&net_rand_state
);
413 EXPORT_SYMBOL(prandom_bytes
);
416 * prandom_seed - add entropy to pseudo random number generator
417 * @entropy: entropy value
419 * Add some additional seed material to the prandom pool.
420 * The "entropy" is actually our IP address (the only caller is
421 * the network code), not for unpredictability, but to ensure that
422 * different machines are initialized differently.
424 void prandom_seed(u32 entropy
)
428 add_device_randomness(&entropy
, sizeof(entropy
));
430 for_each_possible_cpu(i
) {
431 struct siprand_state
*state
= per_cpu_ptr(&net_rand_state
, i
);
432 unsigned long v0
= state
->v0
, v1
= state
->v1
;
433 unsigned long v2
= state
->v2
, v3
= state
->v3
;
437 PRND_SIPROUND(v0
, v1
, v2
, v3
);
438 PRND_SIPROUND(v0
, v1
, v2
, v3
);
440 } while (unlikely(!v0
|| !v1
|| !v2
|| !v3
));
442 WRITE_ONCE(state
->v0
, v0
);
443 WRITE_ONCE(state
->v1
, v1
);
444 WRITE_ONCE(state
->v2
, v2
);
445 WRITE_ONCE(state
->v3
, v3
);
448 EXPORT_SYMBOL(prandom_seed
);
451 * Generate some initially weak seeding values to allow
452 * the prandom_u32() engine to be started.
454 static int __init
prandom_init_early(void)
457 unsigned long v0
, v1
, v2
, v3
;
459 if (!arch_get_random_long(&v0
))
461 if (!arch_get_random_long(&v1
))
462 v1
= random_get_entropy();
466 for_each_possible_cpu(i
) {
467 struct siprand_state
*state
;
470 PRND_SIPROUND(v0
, v1
, v2
, v3
);
471 PRND_SIPROUND(v0
, v1
, v2
, v3
);
474 state
= per_cpu_ptr(&net_rand_state
, i
);
475 state
->v0
= v0
; state
->v1
= v1
;
476 state
->v2
= v2
; state
->v3
= v3
;
481 core_initcall(prandom_init_early
);
484 /* Stronger reseeding when available, and periodically thereafter. */
485 static void prandom_reseed(unsigned long dontcare
);
487 static DEFINE_TIMER(seed_timer
, prandom_reseed
, 0, 0);
489 static void prandom_reseed(unsigned long dontcare
)
491 unsigned long expires
;
495 * Reinitialize each CPU's PRNG with 128 bits of key.
496 * No locking on the CPUs, but then somewhat random results are,
499 for_each_possible_cpu(i
) {
500 struct siprand_state
*state
;
501 unsigned long v0
= get_random_long(), v2
= v0
^ PRND_K0
;
502 unsigned long v1
= get_random_long(), v3
= v1
^ PRND_K1
;
503 #if BITS_PER_LONG == 32
507 * On 32-bit machines, hash in two extra words to
508 * approximate 128-bit key length. Not that the hash
509 * has that much security, but this prevents a trivial
510 * 64-bit brute force.
512 for (j
= 0; j
< 2; j
++) {
513 unsigned long m
= get_random_long();
516 PRND_SIPROUND(v0
, v1
, v2
, v3
);
517 PRND_SIPROUND(v0
, v1
, v2
, v3
);
522 * Probably impossible in practice, but there is a
523 * theoretical risk that a race between this reseeding
524 * and the target CPU writing its state back could
525 * create the all-zero SipHash fixed point.
527 * To ensure that never happens, ensure the state
528 * we write contains no zero words.
530 state
= per_cpu_ptr(&net_rand_state
, i
);
531 WRITE_ONCE(state
->v0
, v0
? v0
: -1ul);
532 WRITE_ONCE(state
->v1
, v1
? v1
: -1ul);
533 WRITE_ONCE(state
->v2
, v2
? v2
: -1ul);
534 WRITE_ONCE(state
->v3
, v3
? v3
: -1ul);
537 /* reseed every ~60 seconds, in [40 .. 80) interval with slack */
538 expires
= round_jiffies(jiffies
+ 40 * HZ
+ prandom_u32_max(40 * HZ
));
539 mod_timer(&seed_timer
, expires
);
543 * The random ready callback can be called from almost any interrupt.
544 * To avoid worrying about whether it's safe to delay that interrupt
545 * long enough to seed all CPUs, just schedule an immediate timer event.
547 static void prandom_timer_start(struct random_ready_callback
*unused
)
549 mod_timer(&seed_timer
, jiffies
);
553 * Start periodic full reseeding as soon as strong
554 * random numbers are available.
556 static int __init
prandom_init_late(void)
558 static struct random_ready_callback random_ready
= {
559 .func
= prandom_timer_start
561 int ret
= add_random_ready_callback(&random_ready
);
563 if (ret
== -EALREADY
) {
564 prandom_timer_start(&random_ready
);
569 late_initcall(prandom_init_late
);