Date: Sat, 11 Jul 2015 15:02:16 -0700
From: Bill Cox <waywardgeek@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Cc: John Tromp <john.tromp@...il.com>
Subject: Bandwidth hardened algorithms?

Is this a good term to use to describe password hashing and PoW algorithms
with ASIC defense based on the expense of I/O ports with high data
bandwidth?

Here are the differences I see between bandwidth-hard algorithms vs
memory-hard algorithms:

- Memory hard algorithms compute a serial chain of data values that must be
computed sequentially
- Bandwidth hard algorithms allow an attacker to compute hash values in
parallel
- Memory hard algorithms require significant memory per parallel worker
- Bandwidth hard algorithms allow the data to be shared between parallel
workers, but it must be transmitted between them
- Memory-hard algorithms defend against ASIC attacks through the cost of
memory, the cost of bandwidth, or both
- Bandwidth hardened algorithms limit ASIC attacks through communication
bandwidth
- Memory-hard algorithms tend to have long verification times for PoW
- Bandwidth-hard algorithms tend to have short verification times for PoW

In most of my proposed ASIC attacks against memory-hard algorithms, memory
bandwidth limited the overall speed of the attack.  The cost of the
external memory was rarely significant.  For example, if bandwidth is not a
concern, I can buy a 1TiB hard drive for under $100.  If I need 350 GiB/s,
it will cost several hundred dollars, regardless of the amount of memory
I'm buying.  It seems to me that bandwidth hardening defends more reliably
than memory cost.  While bandwidth hardened algorithms have disadvantages
(like those listed above), the fast verification makes them suitable in
some cases for PoW.

I know of three bandwidth-hardened algorithms: Momentum, Cuckoo Cycle, and
what I was calling "CPU Hash", which ideally is something like Yescrypt
running with a very small amount of RAM, and a reasonable amount of ROM, or
an EARWORM with expanded state size.

SFAICT, all three algorithms provide reasonable ASIC defense.  The benefit
for each is that verification is very fast.  There is also Argon2's
proposed Merkel hash tree built on top of the memory filled by Argon2.
Like Cuckoo Cycle, this allows for log(n) speed verification.  However, the
Merkel hash tree building dominates the runtime, reducing the benefit of
running Argon2 as a pre-process rather than just filling memory in parallel
with hash data.  An advantage of a CPU-hash-like algorithm is simplicity
and I believe a simple proof of security, but then you have to have the ROM
available everywhere to do verification.

An important key for fast-verification PoW bandwidth-hardened algorithms
seems to be high speed computation that fills available memory bandwidth,
with no significant short-cut available to an attacker.  These slower
memory-filling implementations I've seen so far give an ASIC attacker too
much gain.

Bandwidth hardening only works if you use a lot of bandwidth.

Bill

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