Proofs of Knowledge with Several Challenge Values.

Abstract

Abstract. In this paper we consider the problem of increasing the number of possible challenge values from 2 to s in various zero-knowledge cut and choose protocols. First we discuss doing this for graph isomorphism protocol. Then we show how increasing this number improves efficiency of protocols for double discrete logarithm and e-th root of discrete logarithm which are potentially very useful tools for constructing complex cryptographic protocols. The practical improvement given by our paper is 2-4 times in terms of both time complexity and transcript size. 1