phc-discussions - Re: [PHC] Scrypt can have highest time*average memory cost

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Message-ID: <20140329173641.GA2530@openwall.com>
Date: Sat, 29 Mar 2014 21:36:42 +0400
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Scrypt can have highest time*average memory cost

On Sat, Mar 29, 2014 at 01:01:36AM +0400, Solar Designer wrote:
> However, what if we normalize for defender's time per hash computed?
> When we do that, it turns out that scrypt reaches its highest normalized
> AT cost at 2*N (just the way it's defined)

BTW, this holds true even when we consider the case where scrypt's TMTO
is fully exploited in an attack.  The AT cost of SMix's second loop is
reduced by a factor of 2, but it's still optimal to stop at 2*N time (so
at N iterations for SMix's second loop):

scrypt assuming TMTO is fully exploited
t       AT      AT/t    ATnorm
...
1.90    0.45    0.237   0.997
2.00    0.50    0.250   1.000
2.10    0.55    0.262   0.998

In absolute terms, this is lower AT cost than yescrypt's native at
4/3*N (and more than twice lower than yescrypt's at 2*N), assuming that
yescrypt is 100% effective at preventing any TMTO exploits from reducing
AT cost.  (I think it is nearly that effective.)

Alexander