random: account for entropy loss due to overwrites

When we write entropy into a non-empty pool, we currently don't
account at all for the fact that we will probabilistically overwrite
some of the entropy in that pool.  This means that unless the pool is
fully empty, we are currently *guaranteed* to overestimate the amount
of entropy in the pool!

Assuming Shannon entropy with zero correlations we end up with an
exponentally decaying value of new entropy added:

	entropy <- entropy + (pool_size - entropy) *
		(1 - exp(-add_entropy/pool_size))

However, calculations involving fractional exponentials are not
practical in the kernel, so apply a piecewise linearization:

	  For add_entropy <= pool_size/2 then

	  (1 - exp(-add_entropy/pool_size)) >= (add_entropy/pool_size)*0.7869...

	  ... so we can approximate the exponential with
	  3/4*add_entropy/pool_size and still be on the
	  safe side by adding at most pool_size/2 at a time.

In order for the loop not to take arbitrary amounts of time if a bad
ioctl is received, terminate if we are within one bit of full.  This
way the loop is guaranteed to terminate after no more than
log2(poolsize) iterations, no matter what the input value is.  The
vast majority of the time the loop will be executed exactly once.

The piecewise linearization is very conservative, approaching 3/4 of
the usable input value for small inputs, however, our entropy
estimation is pretty weak at best, especially for small values; we
have no handle on correlation; and the Shannon entropy measure (Rényi
entropy of order 1) is not the correct one to use in the first place,
but rather the correct entropy measure is the min-entropy, the Rényi
entropy of infinite order.

As such, this conservatism seems more than justified.

This does introduce fractional bit values.  I have left it to have 3
bits of fraction, so that with a pool of 2^12 bits the multiply in
credit_entropy_bits() can still fit into an int, as 2*(3+12) < 31.  It
is definitely possible to allow for more fractional accounting, but
that multiply then would have to be turned into a 32*32 -> 64 multiply.

Signed-off-by: H. Peter Anvin <hpa@linux.intel.com>
Signed-off-by: Theodore Ts'o <tytso@mit.edu>
Cc: DJ Johnston <dj.johnston@intel.com>

Conflicts:
	drivers/char/random.c
random: fix the tracepoint for get_random_bytes(_arch)

Fix a problem where get_random_bytes_arch() was calling the tracepoint
get_random_bytes().  So add a new tracepoint for
get_random_bytes_arch(), and make get_random_bytes() and
get_random_bytes_arch() call their correct tracepoint.

Also, add a new tracepoint for add_device_randomness()

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>
random: optimize spinlock use in add_device_randomness()

The add_device_randomness() function calls mix_pool_bytes() twice for
the input pool and the non-blocking pool, for a total of four times.
By using _mix_pool_byte() and taking the spinlock in
add_device_randomness(), we can halve the number of times we need
take each pool's spinlock.

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>
random: optimize the entropy_store structure

Use smaller types to slightly shrink the size of the entropy store
structure.

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>

Conflicts:
	drivers/char/random.c
random: cap the rate which the /dev/urandom pool gets reseeded

In order to avoid draining the input pool of its entropy at too high
of a rate, enforce a minimum time interval between reseedings of the
urandom pool.  This is set to 60 seconds by default.

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>

Conflicts:
	drivers/char/random.c
random: speed up the fast_mix function by a factor of four

By mixing the entropy in chunks of 32-bit words instead of byte by
byte, we can speed up the fast_mix function significantly.  Since it
is called on every single interrupt, on systems with a very heavy
interrupt load, this can make a noticeable difference.

Also fix a compilation warning in add_interrupt_randomness() and avoid
xor'ing cycles and jiffies together just in case we have an
architecture which tries to define random_get_entropy() by returning
jiffies.

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>
Reported-by: Jörn Engel <joern@logfs.org>
random: adjust the generator polynomials in the mixing function slightly

Our mixing functions were analyzed by Lacharme, Roeck, Strubel, and
Videau in their paper, "The Linux Pseudorandom Number Generator
Revisited" (see: http://eprint.iacr.org/2012/251.pdf).

They suggested a slight change to improve our mixing functions
slightly.  I also adjusted the comments to better explain what is
going on, and to document why the polynomials were changed.

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>
random: drop trickle mode

The add_timer_randomness() used to drop into trickle mode when entropy
pool was estimated to be 87.5% full.  This was important when
add_timer_randomness() was used to sample interrupts.  It's not used
for this any more --- add_interrupt_randomness() now uses fast_mix()
instead.  By elimitating trickle mode, it allows us to fully utilize
entropy provided by add_input_randomness() and add_disk_randomness()
even when the input pool is above the old trickle threshold of 87.5%.

This helps to answer the criticism in [1] in their hypothetical
scenario where our entropy estimator was inaccurate, even though the
measurements in [2] seem to indicate that our entropy estimator given
real-life entropy collection is actually pretty good, albeit on the
conservative side (which was as it was designed).

[1] http://eprint.iacr.org/2013/338.pdf
[2] http://eprint.iacr.org/2012/251.pdf

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>

Conflicts:
	drivers/char/random.c
random: push extra entropy to the output pools

As the input pool gets filled, start transfering entropy to the output
pools until they get filled.  This allows us to use the output pools
to store more system entropy.  Waste not, want not....

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>

Conflicts:
	drivers/char/random.c