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Date: Sat, 4 Jan 2014 14:13:07 -0500
From: Bill Cox <waywardgeek@...il.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Re: Reworked KDF available on github for feedback: NOELKDF

Being able to generate V[i] where V is memory in short time would defeat
the memory-hardness property.

Alexander had a good concern in this area.  We can quickly determine the
"random" previous page addresses because we only need to compute the first
value of each page, which is used as the random address.  If we can't
determine these addresses quickly, then clearly we can't compute V[i]
quickly, since we wont even know what previous values it depends on.

The relevant line in the code which generates each V[i] is:

 *toPage++ = *prevPage + ((*fromPage * *(prevPage + 1)) ^ *(fromPage - 1));

Given the non-linear nature of this hash, an attacker is going to have to
compute the entire operator tree all the way back to the original page of
sha256 data.  Not a single value can be left out.  By the time we get 64MB
into the hashing, this computation depends on all 16KB of the sha256 output
in the first page, and any single bit change will drastically restructure
the operator tree, and the intermediate values.  Passing the Dieharder
tests is empirical evidence that the intermediate values don't seem to
develop any obvious long-term bias, which is really all that would worry me
in an algorithm like this.

I'm beginning to feel pretty good about it's security.

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