random: use linear min-entropy accumulation crediting
commit c570449094844527577c5c914140222cb1893e3f upstream.
30e37ec516ae ("random: account for entropy loss due to overwrites")
assumed that adding new entropy to the LFSR pool probabilistically
cancelled out old entropy there, so entropy was credited asymptotically,
approximating Shannon entropy of independent sources (rather than a
stronger min-entropy notion) using 1/8th fractional bits and replacing
a constant 2-2/√𝑒 term (~0.786938) with 3/4 (0.75) to slightly
underestimate it. This wasn't superb, but it was perhaps better than
nothing, so that's what was done. Which entropy specifically was being
cancelled out and how much precisely each time is hard to tell, though
as I showed with the attack code in my previous commit, a motivated
adversary with sufficient information can actually cancel out
everything.
Since we're no longer using an LFSR for entropy accumulation, this
probabilistic cancellation is no longer relevant. Rather, we're now
using a computational hash function as the accumulator and we've
switched to working in the random oracle model, from which we can now
revisit the question of min-entropy accumulation, which is done in
detail in <https://eprint.iacr.org/2019/198>.
Consider a long input bit string that is built by concatenating various
smaller independent input bit strings. Each one of these inputs has a
designated min-entropy, which is what we're passing to
credit_entropy_bits(h). When we pass the concatenation of these to a
random oracle, it means that an adversary trying to receive back the
same reply as us would need to become certain about each part of the
concatenated bit string we passed in, which means becoming certain about
all of those h values. That means we can estimate the accumulation by
simply adding up the h values in calls to credit_entropy_bits(h);
there's no probabilistic cancellation at play like there was said to be
for the LFSR. Incidentally, this is also what other entropy accumulators
based on computational hash functions do as well.
So this commit replaces credit_entropy_bits(h) with essentially `total =
min(POOL_BITS, total + h)`, done with a cmpxchg loop as before.
What if we're wrong and the above is nonsense? It's not, but let's
assume we don't want the actual _behavior_ of the code to change much.
Currently that behavior is not extracting from the input pool until it
has 128 bits of entropy in it. With the old algorithm, we'd hit that
magic 128 number after roughly 256 calls to credit_entropy_bits(1). So,
we can retain more or less the old behavior by waiting to extract from
the input pool until it hits 256 bits of entropy using the new code. For
people concerned about this change, it means that there's not that much
practical behavioral change. And for folks actually trying to model
the behavior rigorously, it means that we have an even higher margin
against attacks.
Cc: Theodore Ts'o <tytso@mit.edu>
Cc: Dominik Brodowski <linux@dominikbrodowski.net>
Cc: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
Reviewed-by: Eric Biggers <ebiggers@google.com>
Reviewed-by: Jean-Philippe Aumasson <jeanphilippe.aumasson@gmail.com>
Signed-off-by: Jason A. Donenfeld <Jason@zx2c4.com>
Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
1 file changed