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Date: Wed, 12 Feb 2014 21:42:13 +0400
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Interleaved attack on random access KDFs (Re: [PHC] Interleaved attack on cache-timeing-resistant KDFs)

On Tue, Feb 11, 2014 at 05:13:20PM -0500, Bill Cox wrote:
> Instead of having
> several MiB of expensive on-chip cache for every guessing core, an
> attacker simply interleaves the memory for many guesses in parallel.

While predictable access pattern makes this sort of interleaving
especially attractive, it is also possible - and might be practical -
with random access, like scrypt's or bcrypt's.  This is like turning
the table: instead of random access to the KDF's lookup table (in
external memory), we get semi-sequential/interleaved access there, but
we pay for it by having random access to other parts of the state
(hopefully in faster local memory) of the many instances of the KDF
being computed in parallel.  We need to have so many parallel instances
that we get many to advance in their computation per each memory lookup,
even though most may be stalled waiting for data (since it's not their
turn yet).  With small values of N (in scrypt terms), this may be
practical.  We need on the order of N^2 parallel instances per device
(where a "device" is something with its local cache and/or local memory,
e.g. one CU in AMD GPU, rather than an entire GPU).  With bcrypt's
256-element S-boxes, this appears impractical e.g. on current GPUs (not
enough local memory to have enough parallel instances to make this
practical), even though it's sufficient to satisfy any of the 4 S-box
lookups for the instance to proceed a bit.  Also, it'd take some
non-trivial algorithm to efficiently and quickly identify which
instances can proceed to run on each turn.  (I am not sure that an
efficiently enough algorithm even exists, except for small N.)  If you
start with N=2 and then proceed to consider slightly higher values, it
is easy to see that for small N this is practical, but it is unclear at
what N it becomes impractical.  It could differ between pre-existing
chips (256 already impractical?) vs. ASICs made for this specific attack
(256 still practical?)

Alexander

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