Date: Thu, 27 Feb 2014 18:32:09 +0400
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] GPU multiplication speed?

On Thu, Feb 27, 2014 at 09:13:52AM -0500, Bill Cox wrote:
> Given this description, I would guess that Script is sped up on GPUs
> only for small memories, like the 128KiB used in LiteCoin.  Large
> memory hashes, such as 1GiB would be limited by memory space on the
> card, and the fact that instructions take something like 11-ish ns
> each.  If that's the case, GPUs should be very bad at large memory
> sized Script hashing.  Is this right?

As I mentioned before, the threshold where current GPUs are on par with
current CPUs per chip appears to be at around 4 MiB for scrypt, as we
know from YAC mining.  How much slower the GPUs will become when the
per-hash memory cost setting grows further we'll know in a few months
when YAC moves to 8 MiB.  Indeed, you can simulate this right now (just
hack a YAC miner's source code), but a monetary incentive might mean more.

> Also, on a GPU, there's nothing special about multiply (maybe 32 bit
> vs 24 is helpful by).  Any memory hashing algorithm will slow down a
> GPU so long as there are enough sequential operations that depend on
> the previous result.

Right.

There might or might not be a few cycles of extra latency for a
multiply, but compared to the latency incurred with any instruction this
is only a small advantage (for the defender).

> However, SHA-256, Blake2, and other hash
> functions have a lot of parallelism, so a GPU can interleave
> instructions that don't act on results from the prior few
> instructions, reducing the latency impact.

As far as I'm aware, no current code takes advantage of this as it's
incompatible with OpenCL and CUDA programming models, and as GPUs lack
ability to issue more than one instruction per cycle from the same
hardware thread (unlike CPUs).  Also, the parallelism available in those
algorithms is insufficient to make it worthwhile to introduce any kind
of data dependencies across threads.

So e.g. in Litecoin and YAC mining, the parallelism comes purely from
concurrent instances of scrypt.  Their number is doubled via scrypt's
TMTO, though.  ... Oh and yes, this means that the 4 MiB I mentioned
above actually means 2 MiB for a TMTO-unfriendly variation of scrypt.

> If this is correct, wouldn't an effective strategy be to have a long
> chain of sequential operations that depend on the prior result, and to

We have this with bcrypt, yes.

> hash a lot of memory?

Yes, but when it's a lot of memory your latency dependency reduces since
your random memory accesses are not as rapid on the defender's system.

> It wouldn't have to be multiply - anything
> would do, such as a chain of addition, rotation, and XOR.  If I did
> this, causing an 11-ish cycle effective computation time, and hashed 1
> GiB, then a modern Nvidia GPU with 12GiB would only be able to compute
> 12 hashes in parallel due to memory limitations, and his 11-cycle
> latency vs my 1-ish cycles for simple operations should limit his
> advantage to maybe 2x-ish?  If I run 2 threads, than would it be a
> 1x-ish non-advantage?

The advantage from GPUs (comparing currently available CPUs and GPUs)
should become negative at a few MiB or (preferably) less.  For bcrypt,
CPUs and GPUs are on par at bcrypt's 4 KiB. :-)

Alexander

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