Proofs of Restricted Shuffles

A proof of a shuffle is a zero-knowledge proof that one list of ciphertexts is a permutation and re-encryption of another list of ciphertexts. We call a shuffle restricted if the permutation is chosen from a public subset of all permutations. In this paper, we introduce a general technique for constructing proofs of shuffles which restrict the permutation to a group that is characterized by a public polynomial. This generalizes previous work by Reiter and Wang [22], and de Hoogh et al. [7]. Our approach also gives a new efficient proof of an unrestricted shuffle that we think is conceptually simpler and allow a simpler analysis than all previous proofs of shuffles.