Hi Toni, > On 16 Feb 2017, at 00:05, Tony Arcieri <basc...@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 > > 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.
Interesting idea, thanks for sharing! > 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 Thanks for the advertisement. :) And yes I am at EPFL. > > If anyone knows of papers about this particular problem, I'd be very > interested in reading them. To provide some context: We’ve been using NIZK DLEQ proofs for our decentralized randomness beacon project [1] (to be presented at IEEE S&P’17 in May), which in particular uses public verifiable secret sharing (PVSS) [2] as one core building block. In my investigations around that project, I found three papers that are relevant for NIZK DLEQ proofs (mostly by the usual suspects): - Wallet Databases with Observers - David Chaum and Torben Pryds Pedersen [3] - How To Prove Yourself: Practical Solutions to Identification and Signature Problems - Amos Fiat and Adi Shamir [4] - Unique Ring Signatures: A Practical Construction - Matthew Franklin and Haibin Zhang [5] In particular, [5] gives a summary of NIZK DLEQ proofs in Section 3 (also referring to Chaum’s paper) that I used as a basis for the above code. Hope this helps. All the best, Philipp [1] https://eprint.iacr.org/2016/1067 [2] https://www.win.tue.nl/~berry/papers/crypto99.pdf [3] http://www.cs.elte.hu/~rfid/chaum_pedersen.pdf [4] http://www.math.uni-frankfurt.de/~dmst/teaching/SS2012/Vorlesung/Fiat.Shamir.pdf [5] http://fc13.ifca.ai/proc/5-1.pdf _______________________________________________ Curves mailing list Curves@moderncrypto.org https://moderncrypto.org/mailman/listinfo/curves