Zero-Knowledge Proofs for Mix-nets of Secret Shares and a Version of ElGamal with Modular Homomorphism.

Abstract

Mix-nets can be used to shuffle vectors of shared secrets. This operation can be an important building block for solving combinatorial problems where constraints depend on secrets of different participants. A main contribution of this paper is to show how participants in the mix-net can provide Zero-Knowledge proofs to convince each other that they do not tamper with the shuffled secrets, and that inverse permutations are correctly applied at unshu#ing. The approach is related to the proof of knowing an isomorphism between large graphs. We also make a detailed review and comparison with rationales and analysis of Chaum's and Merritt's mix-nets. Another