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Date: Fri, 14 Feb 2014 13:52:04 -0500
From: Bill Cox <>
Subject: Re: [PHC] multiply-hardening (Re: NoelKDF ready for submission)

On Fri, Feb 14, 2014 at 10:21 AM, Solar Designer <> wrote:
> Maybe try precomputing the random address one iteration in advance.
> In bcrypt, there are 4 S-box lookups, which means that computation (on
> results of first 2 lookups) doesn't have to start (or be stalled) until
> all 4 lookups are issued.  So you have a little bit of room for
> parallelism too, without necessarily becoming worse than bcrypt.
> Alexander

I wrote a file called fasthash.c which incorporates a lot of these
ideas.  I do 4 scalar multiplication hashes in a loop with SSE
instructions that do a simple XOR/ADD hashing of 8 32-bit lanes (256
bits), reading from "from" and "prev" and writing to "to".  On my Ivy
Bridge processor using SSE4.1, this is a decent match, where the
memory bottleneck is just kicking in while the multiplication hardness
is still taking most of the loop time.  I randomized "prev" reads as
you suggested, and most of the caching issues go away, though there is
about a 20% speed penalty when hashing 256 bits at a time before
switching the prev address.  I made the randomization length tuneable,
so it is possible to make most of the 20% penalty go away.  I also do
a SHA256 hash on the 8 lanes every 64 blocks - if I do it more often,
the SHA256 begins to hurt runtime.

On my machine, the inner loop before any of these upgrades did 13GB/s
bandwidth on one thread (factoring out the memory allocation
overhead), matching the best I've been able to do combining multiple
threads and SSE in the past.  The loop time was about 64% longer than
a single multiply instruction, so it's a bit worse than before, but I
think this is a fair trade-off.

After the upgrades, I take some hit for the SHA256 and some for the
tunable random read lengths.  It does about 10.25GB/s when using no
randomization in the prev reads, which isn't too bad.  It's doing 2GB,
doing 1 read and 1 write, in .39 seconds.

I tried making the multiply chain tunable relative to the SSE hashing.
 Putting a loop around the scalar multiplication loop slowed it down,
so we make this tunable in the same loop, I'd probably instantiate
multiple versions of the loop with different numbers of multiplies and
select which one to run.

With memory allocation overhead, it runs in .47 seconds, which is
8.5GB/s, and about 50% multiplication time hardened, which isn't too
bad, though the old one was about 2/3rds compute hardened, and hashed
2GB in 0.72 seconds, or 5.5GB/s.  With 256 bit random reads it takes
closer to .6s.


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