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Date: Sat, 16 Jan 2016 18:23:04 -0800
From: Henry Corrigan-Gibbs <henrycg@...nford.edu>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Re: Attack on Argon2i?

Hi Krisztián,

I am one of the authors of the Balloon Hashing paper. Thanks for taking 
a look at it!

You raise a good point here:

On 1/12/16 9:44 AM, Krisztián Pintér wrote:

> so i'm long since against pseudorandom but fix access patterns. first,
> i don't see the benefit of a pseudorandom but fixed over a simple and
> fixed. it is still fixed. second, i see the risk that anything chosen
> randomly might be suboptimal. especially if it depends on a value
> (like salt) out of control. i don't like their approach for the same
> reason.
>
> analogy: s-boxes. it is known, that random s-boxes are suboptimal in
> comparison to carefully crafted ones. this is the expected thing,
> since why would a random object be optimal? it only happens if the
> vast majority of possible objects are optimal, which at least needs a
> proof.

I completely agree that it does not make sense to use a pseudo-random 
memory access pattern unless there is a good reason for doing so.

In our case, the security of the construction relies on the fact that 
the data-dependency graph of the computation (i.e., the access pattern) 
is an "expander graph."

There is a famous theorem, cited as Theorem 6 in our paper, that says 
that a random graph of a certain type is almost always an expander. So, 
if you choose a graph of this type at random, the probability that it is 
_not_ an expander is very very small -- something like 2^{-80} (and you 
can make this probability as small as you like).

In contrast, it is quite difficult to construct expander graphs 
deterministically: the constructions are less efficient and are harder 
to implement.

We are not wedded to using pseudo-random access patterns at all -- it 
would even be possible to instantiate the Balloon functions with 
deterministically constructed expanders. The pseudo-random construction 
is just much simpler to implement.

Henry


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