Date: Sat, 4 Apr 2015 00:01:22 +0300
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] yescrypt throughput vs. PWXrounds

On Fri, Apr 03, 2015 at 09:09:14PM +0200, Dmitry Khovratovich wrote:
> Could you also clarify how you measure "GPU-unfriendliness"?

I was referring specifically to bcrypt-like GPU-unfriendliness.

I run an optimized defensive implementation of bcrypt on a machine,
using as many threads as the hardware supports (e.g. 8 on FX-8120) to
compute independent bcrypt hashes.  I take note of the cumulative hashes
per second rate, like this:

user@...l:~/crypt_blowfish-1.2-hack$ ./crypt_test_threads 
497.4 c/s real, 497.4 c/s virtual
0: 384.0 c/s real
1: 383.6 c/s real
2: 384.0 c/s real
3: 383.6 c/s real
4: 384.4 c/s real
5: 383.8 c/s real
6: 383.8 c/s real
7: 383.8 c/s real

(The "-hack" has runtime self-test removed.)  That's 384*8 = 3072 c/s.
This is for bcrypt cost 5, as traditionally used for benchmarking.

I tune yescrypt for roughly the same throughput on the same machine.
As I've posted, with the current pwxform default settings it achieves
2772 c/s at 2 MB.  This is 10% lower, but is still close enough.
I normally keep t_cost at 0, adjusting only m_cost.  I use the "userom"
program included in the current yescrypt submission for this test (this
program can work without a ROM too).  The memory allocation overhead is
bypassed, because an authentication server can similarly have it out of
the loop (yescrypt provides such APIs).

Then I count the number of S-box lookups performed by bcrypt and by
yescrypt in these tests.

bcrypt at cost 5 performs this many S-box lookups:

((512+9)*(1+32*2)+64*3)*16*4 = 2179648

and they are 32-bit to 4 KB S-boxes, with 4x parallelism.

yescrypt performs this many S-box lookups:

2*1024*1024 * 4/3 / 64 * 6 * 4 * 2 = 2097152

and they are 128-bit to 8 KB S-boxes, with 8x parallelism.

For GPU local memory attacks, the doubled size of the S-boxes
compensates for the doubled parallelism, whereas the frequency of
lookups is roughly the same.  For GPU global memory attacks, it's just
the frequency of lookups, which is roughly the same.

Overall, by these metrics yescrypt at its current default settings
achieves 2772/3072 * 2097152/2179648 = 87% of bcrypt's GPU resistance.

This is close enough, and maybe yescrypt's use of 128-bit S-box lookups,
vs. bcrypt's 32-bit, will make attacking it slower than bcrypt, in fact
up to 128/32*0.87 = ~3.5 times slower on GPUs with no spare width in the
ports used for gather loads from local memory (but they'd probably
achieve a smaller slowdown by using global memory, as e.g. on HD 7970
bcrypt using global memory ran only ~2x slower than with local memory).
As you have seen I am not counting on the lookups width difference in my
calculations above, in part because it is not relevant to possible GPU
global memory attacks.

Alexander

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