phc-discussions - Re: [PHC] Argon2

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Date: Tue, 31 Mar 2015 12:11:28 +0200
From: Dmitry Khovratovich <khovratovich@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Re: [PHC] Argon2

Hi Alexander,

On Tue, Mar 31, 2015 at 1:18 AM, Solar Designer <solar@...nwall.com> wrote:
>
> Note that your yescrypt benchmark also invokes 8 rounds of Salsa20 per
> 1024-byte block.  That's equivalent to 1/2 a round of Salsa20 per 64-byte
> sub-block, so you're actually comparing 2 rounds of pwxform + 0.5 rounds
> of Salsa20 vs. 2 rounds of Blake2b in Argon2.  I am lucky yescrypt is on
> par with Argon2 in this test, despite of doing maybe 1.25x more computation
> per byte (and containing a lot less parallelism, see below).  (And even
> more than that if we consider hardware rather than software.)

I think there is some confusion about the total computational
complexity of both schemes. To produce a 1 KB-block,
Argon2d applies the Blake2b round 16 times in total. 1 Blake2b round
is equivalent to 2 rounds of Salsa20, extended to 64-bit words.

As I understand the yescrypt pseudocode, r=8 yields 1 KB blocks.
BlockMIX then applies pwxform r1=16 times, and Salsa20/8 one time.

The latency of the compression function/block of Argon2d is 2 Blake2b
rounds. Since the compression function has full diffusion (every input
bit of 1 KB-block affects every output bit), any output byte has also
latency of 2 Blake2b rounds.

In yescrypt, the SIMD lanes are mixed only in the Salsa20 call, which
means that the block latency is not 16 pwxform calls+ 8 Salsa rounds,
but far smaller, only the equivalent of 4 pwxform+8 Salsa rounds. This
is for the block; all the subblocks but the last one do not need
Salsa, so their individual latencies are only 4 pwxform.

Thus indeed, yescrypt block function has higher latency, though not
that much higher compared to Argon2d (2-3x for most of the blocks).
However, the yescrypt's BlockMIX is not memory-hard, as most of it can
be computed using only 16 bytes of RAM (not including the storage) by
computing it lanewise. This property might be mitigated by subblock
shuffling, but I have not analyzed it.

Do I understand yescrypt right?

>
>>
>
> That's cool, but that's 8192-bit parallelism, right?

I would like to comment on this as well, but I do not quite understand
how you measure the parallelism. Maybe the compression function
picture in Argon2 specification helps.

Thanks for other thanks:) and to Bill too,

Dmitry