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

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(root logN) communication and round complexities and O(N) computational complexity for the verifier. Second argument features O(logN) communication and O(root N) computational complexity for the verifier. Third argument features O(logN) communication and O(root N logN) 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.