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Date: Mon, 01 Sep 2014 07:10:14 -0400
From: Bill Cox <waywardgeek@...hershed.org>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Response to recent comments on Rig

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On 08/31/2014 05:30 PM, Somitra Sanadhya wrote:
> 4. Another comment by Mr Cox is: "the memory swapping algorithm
> that the Catena guys invented fairly recently is there..."
> 
> We would like to know which memory swapping algorithm is being
> referred to in the above statement ? Catena takes two inputs,
> hashes the concatenation of these two, and writes the result in
> some location in the array. On the other hand, Rig does two
> different memory overwrite operations. In the first one, we use
> sequential XOR of the chaining variable with the value of the same
> variable from the previous round at the same location. In the 
> second one, we XOR the chaining variable with the input variable
> indexed by the bit-reversal permutation from the previous round.

I was wrong here, because I had not noticed your bug yet.  Your
suggested fix will not work.  To get it to work, you will need to do
what I though you were doing, and use Catena's trick to use one array
for KeySet instead of two.

Your suggested fix is to replace:

    k[br(j)] = k[br(j)] XOR truncate(ChainingValue)

with

    k[j] = k[br(j)] XOR truncate(ChainingValue)

This will overwrite the value in position j.  Later, for all values of
j where br(j) > j, when you read from k[j] to compute k[br(j)], you
will read the value from the current row, when you meant to read the
value from the previous row.

Catena's trick is to realize that once you read from k[br(j)], you no
longer need to remember the value stored in k[br(j)].  Instead of
writing to k[j], write to k[br(j)], just like your submission does,
which is why I thought you were using this trick.

On the next row, instead of reading from k[br(j)], you need to read
from k[j], because the data is already stored in bit-reversal order.
You will also need to write to k[j], since that is the location no
longer needed.  You will need different code for the even vs odd row
updates, but it saves you from having to have two k arrays.

I recommend you use this trick and simply acknowledge it the code
and/or paper.

I think you have an error in your security proof.

Look at the proof starting on page 16.  In the first line "E1", you
convert the probability that a value is stored from Pr(value at Pj is
stored) to i/m.  You simply assume that the probability of the value
being stored is proportional to the ration of values stored divided by
the total values, independent of any property of Pr.

If Pr were the identity permutation, an attacker simply needs one
memory location, and he can compute the entire row sequentially, with
no recomputations at all.  Clearly there needs to be some mathematical
property of Pr that we can depend on to avoid this.  A pebbling proof
like Catena's is needed here.

Bill
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