A signature scheme is malleable if, on input a message m and a signature σ, it is possible to efficiently compute a signature σ ′ on a related message m ′ = T (m), for a transformation T that is allowable with respect to this signature scheme. Previous work considered various useful flavors of allowable transformations, such as quoting and sanitizing messages. In this paper, we explore a connection between malleable signatures and anonymous credentials, and give the following contributions: • We define and construct malleable signatures for a broad category of allowable transformation classes, with security properties that are stronger than those that have been achieved previously. Our construction of malleable signatures is generically based on malleable zero-knowledge proofs, and we show how to instantiate it under the Decision Linear assumption. • We construct delegatable anonymous credentials from signatures that are malleable with respect to an appropriate class of transformations; we also show that our construction of malleable signatures works for this class of transformations. The resulting concrete instantiation is the first to achieve security under a standard assumption (Decision Linear) while also scaling linearly with the number of delegations. 1

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.

Abstract. We critically survey game-based security definitions for the privacy of voting schemes. In addition to known limitations, we unveil several previously unnoticed shortcomings. Surprisingly, the conclusion of our study is that none of the existing definitions is satisfactory: they either provide only weak guarantees, or can be applied only to a limited class of schemes, or both. Based on our findings, we propose a new game-based definition of privacy which we call BPRIV. We also identify a new property which we call strong consistency, needed to express that tallying does not leak sensitive information. We validate our security notions by showing that BPRIV, strong consistency (and an additional simple property called strong correctness) for a voting scheme imply its security in a simulation-based sense. This result also yields a proof technique for proving entropy-based notions of privacy which offer the strongest security guarantees but are hard to prove directly: first prove your scheme BPRIV, strongly consistent (and correct),then study the entropy-based privacy of the result function of the election, which is a much easier task.

Abstract—We critically survey game-based security definitions for the privacy of voting schemes. In addition to known lim-itations, we unveil several previously unnoticed shortcomings. Surprisingly, the conclusion of our study is that none of the existing definitions is satisfactory: they either provide only weak guarantees, or can be applied only to a limited class of schemes, or both. Based on our findings, we propose a new game-based definition of privacy which we call BPRIV. We also identify a new property which we call strong consistency, needed to express that tallying does not leak sensitive information. We validate our security notions by showing that BPRIV, strong consistency (and an additional simple property called strong correctness) for a voting scheme imply its security in a simulation-based sense. This result also yields a proof technique for proving entropy-based notions of privacy which offer the strongest security guarantees but are hard to prove directly: first prove your scheme BPRIV, strongly consistent (and correct), then study the entropy-based privacy of the result function of the election, which is a much easier task. I.