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Date: Wed, 19 Aug 2015 19:06:44 +0300
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Argon2 CPU/GPU benchmarks

Hi Dmitry,

On Wed, Aug 19, 2015 at 12:13:06PM +0200, Dmitry Khovratovich wrote:
> thank you for the benchmarks! We are still working to produce new code
> (enhanced + Maxform) that can be used for future testing. Please feel free
> to ask for specific code change that might favor GPU portability.

Thanks.

What do you mean by GPU portability here?  Simplifying OpenCL
implementations for testing, or for actual defensive use of GPUs?

So far, our intent has been mostly to discourage attack use of GPUs, so
we compare the different schemes with this in mind.  It is also possible
to efficiently use GPUs defensively e.g. with Litecoin-like parameters to
scrypt (and thus to yescrypt in scrypt compatibility mode) and high p,
but I think Argon2's different thread-level parallelism model
discourages reaching that level of efficiency at defensive use of GPUs.

> I have several questions:
> 
> 1) Would you attribute these results to the existing Argon2 parallelism in
> the compression function (8 x parallel Blake2)? Do you already exploit this
> feature? If yes, then we already have a more sequential pattern in mind,
> that would be great to test with or without Maxform.

We don't yet exploit this (except possibly to a very limited extent that
an OpenCL compiler and the hardware might), so I wouldn't attribute the
current results to it.  I've been thinking of communicating suggestions
on how to try exploiting this to Agnieszka today.  So we'll likely try.
If successful, this should let us pack more concurrent instances of
Argon2, and should provide much speedup over the results so far (as
we're not yet bumping into memory bandwidth, by far).

I attribute the faster attacks on Argon2 than on Lyra2 on the NVIDIA GPUs
so far primarily to Argon2 having a smaller internal state (Lyra2 was
benchmarked with 24 KiB blocks).  yescrypt also has more internal state
due to the pwxform S-boxes, plus the pwxform operations themselves slow
GPUs down.

> 2) How do you get these extrapolation numbers for Titan X? What are these
> numbers in the denominator?

3072 and 640 are the total "shader" or "CUDA core" counts (32-bit SIMD
vector elements) for the two GPUs (Titan X vs. 960M).  Since it's the
same architecture, we could also compare SMM counts: 24 vs. 5, leading
to the same ratio.

1000 and 1096 are the base clock rates in MHz for the two GPUs (actual
clock rates should be slightly higher for both).

Combined, these result in Titan X being 3072/640*1000/1096 = 4.38 times
faster.  In case memory bandwidth ever becomes the limiting factor (as
we optimize the code more), it's similar too: 336/80 = 4.2 times faster.

> > Potential results for GTX Titan X:
> >
> > 2480/(1861*3072/640*1000/1096) / (4736/419) = 0.027
> > 7808/(4227*3072/640*1000/1096) / (4736/419) = 0.037
> >
> > or:
> >
> > 4736/419 / (2480/(1861*3072/640*1000/1096)) = 37.1
> > 4736/419 / (7808/(4227*3072/640*1000/1096)) = 26.8

Alexander

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