Verification of a Paillier Based Shuffle Using Representations of the Symmetric Group

Abstract

Abstract. We use an idea of linear representations of the symmetric group to reduce the number of communication rounds in the verification protocol, proposed in Crypto 2005 by Peng et al., of a shuffling. We assume Paillier encryption scheme with which we can apply some known zero-knowledge proofs following the same line of approaches of Peng et al. Incidence matrices of 1-subsets and 2-subsets of a finite set is intensively used for the implementation, and the idea of λ-designs is employed for the improvement of the computational complexity.