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Date: Tue, 28 Jul 2015 17:17:41 -0700
From: Bill Cox <waywardgeek@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Re: [PHC] Argon Indexing Function

Here's the code I used to compute the distance-cubed value in TwoCats.  It
works fine:

        uint64_t v = i;
        uint64_t v2 = v*v >> 32;
        uint64_t v3 = v*v2 >> 32;
        uint32_t distance = ((1llu << 22)-1)*v3 >> 32;

I verified that it generates a very smooth histogram for memory hash sizes
up to 64 GiB.

The important thing here is to use a full 32-bit random number, and to use
64-bit arithmetic.  A 64-GiB Argon2 hash will have 2^26 blocks.  You index
these with a 32-bit number, so that gives you 6 fractional bits.

I've attached code you can run to verify the histogram.  The Argon2 team is
welcome to copy/modify it.

Bill

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