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Date: Fri, 4 Sep 2015 16:51:31 -0700
From: Bill Cox <waywardgeek@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Re: [PHC] Low Argon2 performance in L3 cache

On Fri, Sep 4, 2015 at 4:34 AM, Dmitry Khovratovich <khovratovich@...il.com>
wrote:

> I think you're mistaken in squaring the difference factor: area is the
> same but the time differs, so cost is only 3.5x (or how much?).
>

It goes as the square for external DRAM bandwidth limited ASIC attacks.
For an on-chip RAM 4MiB ASIC attacks, it depends on the
computation-hardness * hashing speed.  TwoCats has about a 2X better
compute-time hardness for L3 caching than Argon2ds, and about a 3.5X better
memory hashing speed.  I did more accurate benchmarks below, but the actual
memory * time difference was very close to 9.1X.

I assume MAXFORM will be used in the final Argon2d, and that speed
improvements will get it to the point that it can hash 4MiB in 2.5ms.  I
assume this below.  This is decent speed, though I happen to be comparing
to an algorithm that is about 3X faster, and need to argue that Argon2 is
better.

For on-chip hashing, Argon2d without any multiplies would not be latency or
bandwidth bound, but computation bound.  The attacker can run Bake2b maybe
16X faster, and Argon2's free 8x parallelism increases that to 128X faster
for the attacker.  This is worse than Scrypt, but this was the case for
Argon2d v.1.1.  You guys have upgraded the algorithm, improving it's
defense a lot.  The Blake2 version with multiplications will leave the ASIC
attacker with a maybe a 4X speed improvement in computation speed, but the
free 8X from parallelism increases that to maybe 32X benefit to the
attacker.  That's not terrible, but with MAXFORM, I estimate the attacker
will be limited to about 4X faster.  TwoCats limits the attacker to about
2.6X faster, assuming the same speed multipliers on the ASIC and CPU.

Here's some more benchmark numbers I ran.  I'm using Argon2, not Argon2ds
but I think this will be pretty close once Argon2ds is tuned up a bit:

Argon2d memory for 1.2ms hash: 2200 KiB
Serial multiplies: 2200*96 = 211,200
ASIC attacker speed using 1ns multipliers: 0.211ms
area-time product: 0.465 s-KiB

TwoCats memory for 1.2ms hash: 8192 KiB
Serial multiplies: 526336
ASIC attacker speed using 1ns multipliers: 0.526ms
area-time product: 4.31 s-KiB

It looks like TwoCats will have about 9X improved time-area defense, when
we take into account the multiplication chains.

Bill

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