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Date: Tue, 15 Apr 2014 17:25:19 -0400
From: Bill Cox <>
Subject: Re: [PHC] more woes, last woes

On Tue, Apr 15, 2014 at 3:22 PM, Marcos Antonio Simplicio Junior <> wrote:

> Hi.
> I tried to add some strengths to the Lyra2 algorithm. Please feel free to
> edit (or suggest modifications) if you feel it is not clear/fair enough.
> By the way, maybe some "weaknesses  by design" should be explicitly
> mentioned too? I would list that Lyra2 is "only partially resistant against
> cache-timing attacks", for example, in opposition to Catena's listed
> strength.
> BR,
> Marcos.
Hi, Marcos.  I ran my pebbling algorithm on what I think the Lyra2 first
loop does.  If I am not mistaken, it generates a DAG with one edge to the
prior node, and one to a  "reverse" node?  For example, my 16-node graph is:

-   n0                 3 pointers 0
-   n1                 2 pointers 0
-   n2                 2 pointers 0
-   n3      -> n0      1 pointers 0
    n4                 1 pointers 0
    n5      -> n2      1 pointers 0
    n6      -> n1      1 pointers 0
    n7      -> n0      0 pointers 0
    n8                 0 pointers 0
    n9      -> n6      0 pointers 0
    n10     -> n5      0 pointers 0
-   n11     -> n4      0 pointers 0
-   n12     -> n3      0 pointers 0
-   n13     -> n2      0 pointers 0
-   n14     -> n1      0 pointers 0
*   n15     -> n0      0 pointers 0

I don't allow the second edge to be 1-long, which would be in parallel with
the edge to the prior node, which is why some are blank.  Edges in parallel
don't impact pebbling more than just one edge.

If I have the graph right, it does not perform well against my pebbling
algorithm.  At 1024 nodes, using 128 pebbles, the recomputation penalty was
only 1.8X (meaning 80% more total computations than normal).  I can provide
data showing how pebbling proceeds, but basically it fixes pebbles every 16
places, and tries to avoid recomputations in a greedy fashion.

I think I have to recommend a different DAG architecture than what I think
Lyra2 is using.  Did I get the DAG right?


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