Date: Thu, 28 Aug 2014 12:07:24 -0400
From: Bill Cox <waywardgeek@...hershed.org>
To: discussions@...sword-hashing.net
Subject: Memory performance and ASIC attacks

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TwoCats and Yescrypt are the most ASIC attack resistant algorithms in
the competition for hash sizes of 32MiB and up.  Lyra2 is a close
second, off by about 2X in my tests, only because Lyra2 does not have
a multi-threading option.

Here's why...

On my machine, doing 16-byte unpredictable memory accesses to external
DDR3 memory take 7.5X longer per byte.  Any PHC entry with no plan to
mitigate this 7.5X penalty will run quite a bit slower than Script!
This alone, IMO, limits candidates suitable for replacing Scrypt to
Lyra2, TwoCats, and Yescrypt.  A factor of 7.5X is important!

Any PHC entry doing unpredictable memory accesses that maxes out
external memory bandwidth will have decent ASIC defense.  This can be
done with large or small block sizes.  For example, Yarn, in my
theoretical optimized version, maxes out memory bandwidth to external
RAM when doing 1GiB hashes, and my ASIC attack gains only a 16X
advantage, because my ASIC attack 16 banks of RAM.  Memory bandwidth
hardening cannot defend against this any better.

However, my ASIC will still guess memory-bandwidth limited 1 seccond
Yarn hashes 3.25 times faster than Yescrypt or TwoCats memory limited
1 second hashes.  This assumes my 1GiB GDDR5 memory banks have the
same latency as DDR3, but twice the total bandwidth (assuming the same
bandwidth, we'd get back to a 7.5X difference).  Also, if the ASIC
uses lower-latency RAM, it gains a lot on Yarn, but almost nothing on
Yescrypt or TwoCats.

Lyra2 does have adjustable memory block sizes, which enables it to use
about half of my memory bandwidth with one thread.  It's pretty good
for ASIC defense!  With a threading "tweak", Lyra2 would be equal to
both Yescrypt and Twocats at providing the best possible DRAM
bandwidth-limited ASIC defense.


Here's two sets of cache tests.  The first does pseudo random reads,
writes, and read-then-write to different memory sizes.  The 16KiB
tests my L1 speed, the 128KiB tests my L2 speed, the 4MiB tests my L3
speed, and the 1GiB tests my DRAM speed.  The first run is for 16-byte
memory accesses, and the second is for 4096 byte memory accesses.

cachetest> ./cachetest16
Access times for random read then write of 16 byte blocks
For random writes to 16384 memory: 1.30032ns per block, or 0.0812698ns
per byte
For random reads from 16384 memory: 0.953253ns per block, or
0.0595783ns per byte
For readom read-then-write from 16384 memory: 1.63673ns per block, or
0.102296ns per byte

For random writes to 131072 memory: 1.49561ns per block, or
0.0934755ns per byte
For random reads from 131072 memory: 1.17821ns per block, or
0.0736378ns per byte
For readom read-then-write from 131072 memory: 2.19711ns per block, or
0.137319ns per byte

For random writes to 4194304 memory: 2.2032ns per block, or 0.1377ns
per byte
For random reads from 4194304 memory: 1.50234ns per block, or
0.0938961ns per byte
For readom read-then-write from 4194304 memory: 2.93296ns per block,
or 0.18331ns per byte

For random writes to 1073741824 memory: 9.88037ns per block, or
0.617523ns per byte
For random reads from 1073741824 memory: 9.377ns per block, or
0.586063ns per byte
For readom read-then-write from 1073741824 memory: 15.6555ns per
block, or 0.978472ns per byte


Here's draw data with using 4096 byte blocks

cachetest> ./cachetest4096
Access times for random read then write of 4096 byte blocks
For random writes to 16384 memory: 262.686ns per block, or 0.0641324ns
per byte
For random reads from 16384 memory: 205.491ns per block, or
0.0501686ns per byte
For readom read-then-write from 16384 memory: 365.972ns per block, or
0.0893486ns per byte

For random writes to 131072 memory: 261.884ns per block, or
0.0639364ns per byte
For random reads from 131072 memory: 210.799ns per block, or
0.0514647ns per byte
For readom read-then-write from 131072 memory: 369.852ns per block, or
0.0902959ns per byte

For random writes to 4194304 memory: 262.403ns per block, or
0.0640631ns per byte
For random reads from 4194304 memory: 217.096ns per block, or
0.053002ns per byte
For readom read-then-write from 4194304 memory: 373.642ns per block,
or 0.0912211ns per byte

For random writes to 1073741824 memory: 476.278ns per block, or
0.116279ns per byte
For random reads from 1073741824 memory: 331.367ns per block, or
0.0809001ns per byte
For readom read-then-write from 1073741824 memory: 544.697ns per
block, or 0.132983ns per byte
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