We generated a battery of 100 test cases from GSL taus113 implemention
and compare the results from a particular seed and a particular
iteration with our implementation in the kernel. We have verified on
32 and 64 bit machines that our taus113 kernel implementation gives
same results as GSL taus113 implementation:

  [    0.147370] prandom: seed boundary self test passed
  [    0.148078] prandom: 100 self tests passed

This is a Kconfig option that is disabled on default, just like the
crc32 init selftests in order to not unnecessary slow down boot process.
We also refactored out prandom_seed_very_weak() as it's now used in
multiple places in order to reduce redundant code.

GSL code we used for generating test cases:

  int i, j;
  srand(time(NULL));
  for (i = 0; i < 100; ++i) {
    int iteration = 500 + (rand() % 500);
    gsl_rng_default_seed = rand() + 1;
    gsl_rng *r = gsl_rng_alloc(gsl_rng_taus113);
    printf("\t{ %lu, ", gsl_rng_default_seed);
    for (j = 0; j < iteration - 1; ++j)
      gsl_rng_get(r);
    printf("%u, %lu },\n", iteration, gsl_rng_get(r));
    gsl_rng_free(r);
  }

Joint work with Hannes Frederic Sowa.

Cc: Florian Weimer <fweimer@redhat.com>
Cc: Theodore Ts'o <tytso@mit.edu>
Signed-off-by: NDaniel Borkmann <dborkman@redhat.com>
Signed-off-by: NHannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>

Since we use prandom*() functions quite often in networking code
i.e. in UDP port selection, netfilter code, etc, upgrade the PRNG
from Pierre L'Ecuyer's original paper "Maximally Equidistributed
Combined Tausworthe Generators", Mathematics of Computation, 65,
213 (1996), 203--213 to the version published in his errata paper [1].

The Tausworthe generator is a maximally-equidistributed generator,
that is fast and has good statistical properties [1].

The version presented there upgrades the 3 state LFSR to a 4 state
LFSR with increased periodicity from about 2^88 to 2^113. The
algorithm is presented in [1] by the very same author who also
designed the original algorithm in [2].

Also, by increasing the state, we make it a bit harder for attackers
to "guess" the PRNGs internal state. See also discussion in [3].

Now, as we use this sort of weak initialization discussed in [3]
only between core_initcall() until late_initcall() time [*] for
prandom32*() users, namely in prandom_init(), it is less relevant
from late_initcall() onwards as we overwrite seeds through
prandom_reseed() anyways with a seed source of higher entropy, that
is, get_random_bytes(). In other words, a exhaustive keysearch of
96 bit would be needed. Now, with the help of this patch, this
state-search increases further to 128 bit. Initialization needs
to make sure that s1 > 1, s2 > 7, s3 > 15, s4 > 127.

taus88 and taus113 algorithm is also part of GSL. I added a test
case in the next patch to verify internal behaviour of this patch
with GSL and ran tests with the dieharder 3.31.1 RNG test suite:

$ dieharder -g 052 -a -m 10 -s 1 -S 4137730333 #taus88
$ dieharder -g 054 -a -m 10 -s 1 -S 4137730333 #taus113

With this seed configuration, in order to compare both, we get
the following differences:

algorithm                 taus88           taus113
rands/second [**]         1.61e+08         1.37e+08
sts_serial(4, 1st run)    WEAK             PASSED
sts_serial(9, 2nd run)    WEAK             PASSED
rgb_lagged_sum(31)        WEAK             PASSED

We took out diehard_sums test as according to the authors it is
considered broken and unusable [4]. Despite that and the slight
decrease in performance (which is acceptable), taus113 here passes
all 113 tests (only rgb_minimum_distance_5 in WEAK, the rest PASSED).
In general, taus/taus113 is considered "very good" by the authors
of dieharder [5].

The papers [1][2] states a single warm-up step is sufficient by
running quicktaus once on each state to ensure proper initialization
of ~s_{0}:

Our selection of (s) according to Table 1 of [1] row 1 holds the
condition L - k <= r - s, that is,

  (32 32 32 32) - (31 29 28 25) <= (25 27 15 22) - (18 2 7 13)

with r = k - q and q = (6 2 13 3) as also stated by the paper.
So according to [2] we are safe with one round of quicktaus for
initialization. However we decided to include the warm-up phase
of the PRNG as done in GSL in every case as a safety net. We also
use the warm up phase to make the output of the RNG easier to
verify by the GSL output.

In prandom_init(), we also mix random_get_entropy() into it, just
like drivers/char/random.c does it, jiffies ^ random_get_entropy().
random-get_entropy() is get_cycles(). xor is entropy preserving so
it is fine if it is not implemented by some architectures.

Note, this PRNG is *not* used for cryptography in the kernel, but
rather as a fast PRNG for various randomizations i.e. in the
networking code, or elsewhere for debugging purposes, for example.

[*]: In order to generate some "sort of pseduo-randomness", since
get_random_bytes() is not yet available for us, we use jiffies and
initialize states s1 - s3 with a simple linear congruential generator
(LCG), that is x <- x * 69069; and derive s2, s3, from the 32bit
initialization from s1. So the above quote from [3] accounts only
for the time from core to late initcall, not afterwards.
[**] Single threaded run on MacBook Air w/ Intel Core i5-3317U

 [1] http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
 [2] http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
 [3] http://thread.gmane.org/gmane.comp.encryption.general/12103/
 [4] http://code.google.com/p/dieharder/source/browse/trunk/libdieharder/diehard_sums.c?spec=svn490&r=490#20
 [5] http://www.phy.duke.edu/~rgb/General/dieharder.php

Joint work with Hannes Frederic Sowa.

Cc: Florian Weimer <fweimer@redhat.com>
Cc: Theodore Ts'o <tytso@mit.edu>
Signed-off-by: NDaniel Borkmann <dborkman@redhat.com>
Signed-off-by: NHannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>

The Tausworthe PRNG is initialized at late_initcall time. At that time the
entropy pool serving get_random_bytes is not filled sufficiently. This
patch adds an additional reseeding step as soon as the nonblocking pool
gets marked as initialized.

On some machines it might be possible that late_initcall gets called after
the pool has been initialized. In this situation we won't reseed again.

(A call to prandom_seed_late blocks later invocations of early reseed
attempts.)

Joint work with Daniel Borkmann.

Cc: Eric Dumazet <eric.dumazet@gmail.com>
Cc: Theodore Ts'o <tytso@mit.edu>
Signed-off-by: NHannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: NDaniel Borkmann <dborkman@redhat.com>
Acked-by: N"Theodore Ts'o" <tytso@mit.edu>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>

The current Tausworthe PRNG is never reseeded with truly random data after
the first attempt in late_initcall. As this PRNG is used for some critical
random data as e.g. UDP port randomization we should try better and reseed
the PRNG once in a while with truly random data from get_random_bytes().

When we reseed with prandom_seed we now make also sure to throw the first
output away. This suffices the reseeding procedure.

The delay calculation is based on a proposal from Eric Dumazet.

Joint work with Daniel Borkmann.

Cc: Eric Dumazet <eric.dumazet@gmail.com>
Cc: Theodore Ts'o <tytso@mit.edu>
Signed-off-by: NHannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: NDaniel Borkmann <dborkman@redhat.com>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>

For properly initialising the Tausworthe generator [1], we have
a strict seeding requirement, that is, s1 > 1, s2 > 7, s3 > 15.

Commit 697f8d03 ("random32: seeding improvement") introduced
a __seed() function that imposes boundary checks proposed by the
errata paper [2] to properly ensure above conditions.

However, we're off by one, as the function is implemented as:
"return (x < m) ? x + m : x;", and called with __seed(X, 1),
__seed(X, 7), __seed(X, 15). Thus, an unwanted seed of 1, 7, 15
would be possible, whereas the lower boundary should actually
be of at least 2, 8, 16, just as GSL does. Fix this, as otherwise
an initialization with an unwanted seed could have the effect
that Tausworthe's PRNG properties cannot not be ensured.

Note that this PRNG is *not* used for cryptography in the kernel.

 [1] http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
 [2] http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps

Joint work with Hannes Frederic Sowa.

Fixes: 697f8d03 ("random32: seeding improvement")
Cc: Stephen Hemminger <stephen@networkplumber.org>
Cc: Florian Weimer <fweimer@redhat.com>
Cc: Theodore Ts'o <tytso@mit.edu>
Signed-off-by: NDaniel Borkmann <dborkman@redhat.com>
Signed-off-by: NHannes Frederic Sowa <hannes@stressinduktion.org>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>

Add functions to get the requested number of pseudo-random bytes.

The difference from get_random_bytes() is that it generates pseudo-random
numbers by prandom_u32().  It doesn't consume the entropy pool, and the
sequence is reproducible if the same rnd_state is used.  So it is suitable
for generating random bytes for testing.
Signed-off-by: NAkinobu Mita <akinobu.mita@gmail.com>
Cc: "Theodore Ts'o" <tytso@mit.edu>
Cc: Artem Bityutskiy <dedekind1@gmail.com>
Cc: Adrian Hunter <adrian.hunter@intel.com>
Cc: David Woodhouse <dwmw2@infradead.org>
Cc: Eilon Greenstein <eilong@broadcom.com>
Cc: David Laight <david.laight@aculab.com>
Cc: Michel Lespinasse <walken@google.com>
Cc: Robert Love <robert.w.love@intel.com>
Cc: Valdis Kletnieks <valdis.kletnieks@vt.edu>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

This renames all random32 functions to have 'prandom_' prefix as follows:

  void prandom_seed(u32 seed);	/* rename from srandom32() */
  u32 prandom_u32(void);		/* rename from random32() */
  void prandom_seed_state(struct rnd_state *state, u64 seed);
  				/* rename from prandom32_seed() */
  u32 prandom_u32_state(struct rnd_state *state);
  				/* rename from prandom32() */

The purpose of this renaming is to prevent some kernel developers from
assuming that prandom32() and random32() might imply that only
prandom32() was the one using a pseudo-random number generator by
prandom32's "p", and the result may be a very embarassing security
exposure.  This concern was expressed by Theodore Ts'o.

And furthermore, I'm going to introduce new functions for getting the
requested number of pseudo-random bytes.  If I continue to use both
prandom32 and random32 prefixes for these functions, the confusion
is getting worse.

As a result of this renaming, "prandom_" is the common prefix for
pseudo-random number library.

Currently, srandom32() and random32() are preserved because it is
difficult to rename too many users at once.
Signed-off-by: NAkinobu Mita <akinobu.mita@gmail.com>
Cc: "Theodore Ts'o" <tytso@mit.edu>
Cc: Robert Love <robert.w.love@intel.com>
Cc: Michel Lespinasse <walken@google.com>
Cc: Valdis Kletnieks <valdis.kletnieks@vt.edu>
Cc: David Laight <david.laight@aculab.com>
Cc: Adrian Hunter <adrian.hunter@intel.com>
Cc: Artem Bityutskiy <dedekind1@gmail.com>
Cc: David Woodhouse <dwmw2@infradead.org>
Cc: Eilon Greenstein <eilong@broadcom.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

For files only using THIS_MODULE and/or EXPORT_SYMBOL, map
them onto including export.h -- or if the file isn't even
using those, then just delete the include.  Fix up any implicit
include dependencies that were being masked by module.h along
the way.
Signed-off-by: NPaul Gortmaker <paul.gortmaker@windriver.com>

Signed-off-by: NUwe Kleine-König <u.kleine-koenig@pengutronix.de>
Signed-off-by: NJiri Kosina <jkosina@suse.cz>

This patch moves the definition of struct rnd_state and the inline
__seed() function to linux/random.h.  It renames the static __random32()
function to prandom32() and exports it for use in modules.

prandom32() is useful as a privately-seeded pseudo random number generator
that can give the same result every time it is initialized.

For FCoE FC-BB-6 VN2VN mode self-selected unique FC address generation, we
need an pseudo-random number generator seeded with the 64-bit world-wide
port name.  A truly random generator or one seeded with randomness won't
do because the same sequence of numbers should be generated each time we
boot or the link comes up.

A prandom32_seed() inline function is added to the header file.  It is
inlined not for speed, but so the function won't be expanded in the base
kernel, but only in the module that uses it.
Signed-off-by: NJoe Eykholt <jeykholt@cisco.com>
Acked-by: NMatt Mackall <mpm@selenic.com>
Cc: Theodore Ts'o <tytso@mit.edu>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>

The rationale is:
   * use u32 consistently
   * no need to do LCG on values from (better) get_random_bytes
   * use more data from get_random_bytes for secondary seeding
   * don't reduce state space on srandom32()
   * enforce state variable initialization restrictions

Note: the second paper has a version of random32() with even longer period
and a version of random64() if needed.
Signed-off-by: NStephen Hemminger <shemminger@vyatta.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>

- Let it update the state of all CPUs. The network stack goes
into pains to feed the current IP addresses in, but it is not very
effective if that is only done for some random CPU instead of all.
So change it to feed bits into all CPUs.  I decided to do that lockless 
because well somewhat random results are ok.

v2: Drop rename so that this patch doesn't depend on x86 maintainers
Signed-off-by: NAndi Kleen <ak@suse.de>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>

Signed-off-by: NAl Viro <viro@zeniv.linux.org.uk>

Make net_random() more widely available by calling it random32

akpm: hopefully this will permit the removal of carta_random32.  That needs
confirmation from Stephane - this code looks somewhat more computationally
expensive, and has a different (ie: callee-stateful) interface.

[akpm@osdl.org: lots of build fixes, cleanups]
Signed-off-by: NStephen Hemminger <shemminger@osdl.org>
Signed-off-by: NDavid S. Miller <davem@davemloft.net>
Cc: Stephane Eranian <eranian@hpl.hp.com>
Signed-off-by: NAndrew Morton <akpm@osdl.org>
Signed-off-by: NLinus Torvalds <torvalds@osdl.org>