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Date: Sat, 8 Feb 2014 12:00:30 +0400
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: multiply-hardening (Re: NoelKDF ready for submission)

On Fri, Feb 07, 2014 at 05:32:45PM -0500, Bill Cox wrote:
> On Fri, Feb 7, 2014 at 1:35 PM, Steve Thomas <steve@...tu.com> wrote:
> > value = ROTATE_LEFT(value*(mem[prevAddr + i] | 3) + mem[fromAddr + i], 1);
> 
> It's still a little creepy having that modulo 4 math eliminating the
> multiply.  Gary sent a quick response to my initial NoelKDF hash
> function, where he thought the OR was an AND, and his complaint that
> an attacker could skip the multiply wasn't as far off as I'd thought.
> If anyone can think of a reason to worry about it, I'll put in the
> rotate, or something like it.  I do want to keep the number of
> non-multiply operations to a minimum.

As an option, you might want to reuse the operations and the constant
used in Mersenne twister's initialization:

#define NEXT_STATE(x, i) \
	(x) = 1812433253U * ((x) ^ ((x) >> 30)) + (i);

where "x" is the current state (32-bit) and "i" is the iteration number.

If there's a shortcut to evaluating multiple iterations of this, it
would also be useful in mt_rand() seed crackers, and so far I'm not
aware of any implementing any such shortcut (this, of course, is no
proof that no such shortcut exists - yet it is something).

A drawback is that a multiplier by a (good) constant probably takes
twice less die area in ASIC than an arbitrary 32x32 multiplier does - do
I guess correctly?  I guess you're the best person in here to confirm
this. :-)  Does such specialization of a multiplier reduce its latency?

> I ran 1,000,000 runs of NoelKDF with 1MiB memory and the last 32 bits
> had 113 collisions, right in the middle of the expected range.  That's
> in addtion to the dieharder tests.

It's nice to hear you've adopted this test too.

Alexander

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