Theory of Cryptography

Volume 7785 of the series Lecture Notes in Computer Science pp 100-119

Succinct Malleable NIZKs and an Application to Compact Shuffles

  • Melissa ChaseAffiliated withLancaster UniversityMicrosoft Research Redmond
  • , Markulf KohlweissAffiliated withLancaster UniversityMicrosoft Research Cambridge
  • , Anna LysyanskayaAffiliated withLancaster UniversityBrown University
  • , Sarah MeiklejohnAffiliated withCarnegie Mellon UniversityUC San Diego

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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 problems remained: (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.

In this paper, we address these issues by providing a generic construction of controlled-malleable proofs using succinct non-interactive arguments of knowledge, or SNARGs for short. Our construction can support very general classes of transformations, as we no longer rely on the transformations that Groth-Sahai proofs can support.