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Date: Wed, 4 Nov 2015 08:24:09 -0800
From: Bill Cox <waywardgeek@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Simple Argon2 ASIC analysis for 4MiB hashes

Some good news: The multiplication chains in Argon2 heavily dominate the
runtime for the attacker.
Result: An ASIC attacker with 1ns multipliers runs about 27X faster per
core, each core using 4MiB of on-chip RAM, compared to a Haswell CPU.
Comparison: The best PHC algorithm for ASIC defense limits the attacker to
about 5.4X speedup.

The 8-way parallelism makes the on-chip SRAM design simpler and faster, as
well as the fact that we really only need one low-latency read port.  A
single high latency write port is fine.  This is a dramatic simplification
of Intel's L3 cache architecture, which has a latency of 36 cycles in
Haswell.  It is even simpler than the L2 cache, which has 12 cycle
latency.  Instead of a single 4MiB cache, the 8-way parallelism let's an
attacker build 8 512KiB caches, which I think would easily run as fast as
Intel's L2 cache, or about 12 cycle latency.  With these assumptions, the
multiplication chains in BlaMka heavily dominate runtime.
The time to hash a block is ~= 12 cycles RAM latency + multiplication chain
time = 12/3.5GHz + 32 mults = 35.4ns.  The time for the ASIC to hash 4MiB
is 0.15ms, compared to the current Argon2 code at about 4ms.  This leads to
about a 27X speedup for the attacker.

While TwoCats does the same number of sequential multiplies when hashing
4MiB, it runs in 0.7ms.  Assuming the attacker has only multiplication
chain delay, he will run 5.4X faster when attacking Argon2 than when
attacking TwoCats.

Bill

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