[curves] Non-interactive zero knowledge proofs of discrete log equivalence

[Oleg Andreev]

Correction:

DLEQ proves that two curve points P and Q share the _same_ discrete log with respect to two different bases:

P = x*G
Q = x*J


> On 15 Feb 2017, at 15:48, Tony Arcieri <bascule at gmail.com> wrote:
> 
> Hello all,
> 
> We have just published a blog post on how we have attempted to harden a system we're developing (a "blockchain"-based money-moving system) against certain types of post-quantum attacks, and also provide a contingency plan for post-quantum attacks:
> 
> https://blog.chain.com/preparing-for-a-quantum-future-45535b316314#.jqhdrrmhi <https://blog.chain.com/preparing-for-a-quantum-future-45535b316314#.jqhdrrmhi>
> 
> Personally I'm not too concerned about these sorts of attacks happening any time soon, but having a contingency plan that doesn't hinge on still shaky-seeming post-quantum algorithms seems like a good idea to me. If you have any feedback on this post, feel free to ping me off-list or start specific threads about anything we've claimed here that may be bogus.
> 
> One of the many things discussed in this post is non-interactive zero knowledge proofs of discrete log equivalence ("DLEQ"): proving that two curve points are ultimately different scalar multiples of the same curve point without revealing the common base point or the discrete logs themselves.
> 
> I was particularly curious if there were any papers about this idea. I had come across similar work (h/t Philipp Jovanovic) in this general subject area (I believe by EPFL?) but I have not specifically found any papers on this topic:
> 
> https://github.com/dedis/crypto/blob/master/proof/dleq.go#L104 <https://github.com/dedis/crypto/blob/master/proof/dleq.go#L104>
> 
> If anyone knows of papers about this particular problem, I'd be very interested in reading them.
> 
> -- 
> Tony Arcieri

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