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Date: Mon, 20 Jan 2014 17:04:06 +0100
From: Christian Forler <christian.forler@...-weimar.de>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Native server relief support for password hashing in browsers

On 20.01.2014 14:38, Bill Cox wrote:
[...]
> Thanks for the link!  I don't know why I had not seen it before.  I
> just ran catena-blake2b-opt-test on my development machine, and I got
> this:
> 
> runtime: 0.296 seconds
> garlic: 18
> lambda: 3
> memory: 64*2^18 = 16MB
> memory access: 5 reads, 4 writes: 9*16MB = 144MB
> bandwidth: 487 MB/s
> 
> I could have some of these numbers wrong... blake2 runs a bit faster
> than SHA512, so I only benchmarked blake2b.


> For comparison, the default build of scrypt on the same machine
> (running 64-bit arch linux) fills 500MB in 1.8 seconds, doing 1 read
> and 1 write.  If fills 5X more memory in the same time, though it's
> memory bandwidth is only 16% higher.

OK. Lets check if we want to compute both algorithms without without L3
cache misses. Let Assume that we have 2 MB of L3 cache, and that the
absence of cache mises improve the runtime by the factor of 10. Then we have

Runtime scrypt : 2^8/10 * 0.3 seconds = 7.68 seconds, and
Runtime Catena:  ((2^3)^3)/10 * 0.3 seconds = 15.36 seconds.

Observation: On low memory devices, scrypt runs faster then Catena.



>>> The Catena paper blew me away and I stole some of their ideas
>>> wholesale. However, it seems like an academic solution at this stage.
>>> It has nothing to support modern memory architectures, no useful
>>> parallelism, and no high performance hashing. Of course, all of that
>>> can be added, but until I see a real-world solution, it remains
>>> theoretical work in my mind.
>>
>> Catena uses Blake2b which has parallelism in it. SHA512 was added
>> because there was a PHP implementation that used SHA512. SHA512 is
>> built into PHP and will be faster than Blake2b written in PHP.

> The implicit parallelism in Blake2b and other hashing algorithms is a
> bad thing for memory-hard KDFs, IMO.  Any parallelism that our CPUs
> can't take advantage of is an advantage to the attacker. 

Blake2b was designed to use the parallelism that is internally available
in common CPUs. Almost all "modern" CPUs support SIMD instructions.

"Most modern processors are superscalar, that is, able to run several
instructions per cycle through pipelining, out-of-order execution, and
other related techniques. BLAKE2 has a natural instruction parallelism
of 4 instructions within the G function; processors that are able to
handle more instruction-level parallelism can do so in BLAKE2bp, by
interleaving independent compression function calls.
...
Limits in both semiconductor manufacturing processes, as well as
instruction-level parallelism have driven CPU manufacturers towards yet
another kind of coarse-grained parallelism, where multiple independent
CPUs are placed inside the same die, and enable the programmer to get
thread-level parallelism. While sequential BLAKE2 does not take
advantage of this..." -- https://blake2.net/blake2_lncs.pdf


> - Even blake2b is too slow for this competition, though I seem to
> remain in the minority in feeling this way.  What's wrong with r[i] =
> r[i-1]*(prevRow[reverse(i)] | 1) + 12345?

Why do you think that your almost-linear equation is a good hash function?


Best regards,
Christian






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