Succinct Malleable NIZKs and an Application to Compact Shuffles

Abstract

Depending on the application, malleability in cryptography can be viewed as either a flaw or — especially if sufficiently understood and restricted — a feature. In this vein, Chase, Kohlweiss, Lysyanskaya, and Meiklejohn recently defined malleable zero-knowledge proofs, and showed how to control the set of allowable transformations on proofs. As an application, they construct the first compact verifiable shuffle, in which one such controlled-malleable proof suffices to prove the correctness of an entire multi-step shuffle. Despite these initial steps, a number of natural open problems remain: (1) their construction of controlled-malleable proofs relies on the inherent malleability of Groth-Sahai proofs and is thus not based on generic primitives; (2) the classes of allowable transformations they can support are somewhat restrictive; and (3) their construction of a compactly verifiable shuffle has proof size O(N 2 + L) (where N is the number of votes and L is the number of mix authorities), whereas in theory such a proof could be of size O(N + L). In this paper, we address these open problems by providing a generic construction of controlledmalleable proofs using succinct non-interactive arguments of knowledge, or SNARGs for short. Our construction has the advantage that we can support a very general class of transformations (as we no longer rely on the transformations that Groth-Sahai proofs can support), and that we can use it to obtain a proof of size O(N + L) for the compactly verifiable shuffle.