random: mix in architectural randomness earlier in extract_buf()

Previously if CPU chip had a built-in random number generator (i.e.,
RDRAND on newer x86 chips), we mixed it in at the very end of
extract_buf() using an XOR operation.

We now mix it in right after the calculate a hash across the entire
pool.  This has the advantage that any contribution of entropy from
the CPU's HWRNG will get mixed back into the pool.  In addition, it
means that if the HWRNG has any defects (either accidentally or
maliciously introduced), this will be mitigated via the non-linear
transform of the SHA-1 hash function before we hand out generated
output.

Signed-off-by: "Theodore Ts'o" <tytso@mit.edu>
random: statically compute poolbitshift, poolbytes, poolbits

Use a macro to statically compute poolbitshift (will be used in a
subsequent patch), poolbytes, and poolbits.  On virtually all
architectures the cost of a memory load with an offset is the same as
the one of a memory load.

It is still possible for this to generate worse code since the C
compiler doesn't know the fixed relationship between these fields, but
that is somewhat unlikely.

Signed-off-by: H. Peter Anvin <hpa@linux.intel.com>
Signed-off-by: Theodore Ts'o <tytso@mit.edu>
random: allow fractional bits to be tracked

Allow fractional bits of entropy to be tracked by scaling the entropy
counter (fixed point).  This will be used in a subsequent patch that
accounts for entropy lost due to overwrites.

[ Modified by tytso to fix up a few missing places where the
  entropy_count wasn't properly converted from fractional bits to
  bits. ]

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

Conflicts:

	drivers/char/random.c

also sync with mainline kernel

Signed-off-by: Paul Reioux <reioux@gmail.com>
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>