Efficient Zero-Knowledge Arguments in Discrete Logarithm Setting: Sublogarithmic Proof or Sublinear Verifier

Sungwook Kim, Hyeonbum Lee, Jae Hong Seo

Abstract: We propose three interactive zero-knowledge arguments for arithmetic circuit of size N in the common random string model, which can be converted to be non-interactive by Fiat-Shamir heuristics in the random oracle model. First argument features \(O(\sqrt{\log N})\) communication and round complexities and O(N) computational complexity for the verifier. Second argument features \(O(\log N)\) communication and \(O(\sqrt{N})\) computational complexity for the verifier. Third argument features \(O(\log N)\) communication and \(O(\sqrt{N}\log N)\) computational complexity for the verifier. Contrary to first and second arguments, the third argument is free of reliance on pairing-friendly elliptic curves. The soundness of three arguments is proven under the standard discrete logarithm and/or the double pairing assumption, which is at least as reliable as the decisional Diffie-Hellman assumption.