March 25, 2020. Youssef El Housni

Title:  Optimized and secure pairing-friendly elliptic curves suitable for one layer proof composition

Abstract:  A zero-knowledge proof is a method by which one can prove knowledge of general non-deterministic polynomial (NP) statements. SNARKs are in addition non-interactive, short and cheap to verify. This property makes them suitable for recursive proof composition, that is proofs attesting to the validity of other proofs. Recursive proof composi- tion has been empirically demonstrated for pairing-based SNARKs via tailored constructions of expensive elliptic curves. We thus construct on top of the curve BLS12-377 a new pairing-friendly elliptic curve which is STNFS-secure and optimized for one layer composition. We show that it is at least five times faster to verify a composed SNARK proof on this curve compared to the previous state-of-the-art. We propose to name the new curve BW6-761.

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