> On 21 Mar 2018, at 09:39, Xenophon Tsekas <tsekasxenophon [ at ] gmail [ dot ] com> wrote: > > Hello, > > Regarding the Zeus platform's mixnet, I have some questions about the common reference string (CRS) used to enable NIZK. Is the goal to provide a standard way to generate / extract the CRS at the time of the election? Could it be any random string or does it need to meet certain requirements? It cannot be any random string. It must be generated with a given algorithm. The algorithm must be executed by a trusted third party, who provides the CRS to the election operators—the election operators should know all the information about how the CRS has been generated (in more technical terms, it must not know the trapdoor). Alternatively, the CRS can be generated via a Multi-Party Computation scheme, but this beyond the scope of GSoC, and AFAIK still an open problem. > Finally, could you provide some pointers on where to look regarding pairing-based ECC and NIZK proofs? (I have experience in cryptography but unfortunately not in those fields.) I searched for Dan Boneh's crypto lectures on YouTube but they appear to have been removed. Here is some basic stuff: Galbraith et al., Pairings for cryptographers: http://www.sciencedirect.com/science/article/pii/S0166218X08000449 Alfred Menezes, An Introduction to Pairing-Based Cryptography: https://www.math.uwaterloo.ca/~ajmeneze/publications/pairings.pdf Vitalik Buterin, Exploring Elliptic Curve Pairings: https://medium.com/@VitalikButerin/exploring-elliptic-curve-pairings-c73c1864e627 Perhaps the best introduction to NIZK proofs are in the zCash blog: https://z.cash/technology/zksnarks.html πλ
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