"Proofs for Inner Pairing Products and Applications"
Psi Vesely (UCSD)
Monday, November 1st 2021, 2-3pm
Abstract:
Cryptographic arguments of knowledge (AoK) enable a prover to efficiently convince a verifier they know a witness y such that C(x,y) = 1, where the predicate C is an arithmetic circuit and x and y are each partial assignments of input wires. We say an AoK is succinct if both the communication size and verifier computation time are polylogarithmic in the size of C. GIPA (generalized inner product argument) is an AoK for languages considering inner products G1^n x G2^n -> G3 for groups of prime order p. We show how succinctness can be achieved via a setup algorithm run by a trusted party when the inner product map is a bilinear pairing. Previous work shows this implies succinct AoKs for all of NP. The preprint is available at https://eprint.iacr.org/2019/1177.pdf.