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Malleability in Modern Cryptography

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In recent years, malleable cryptographic primitives have advanced from being seen as a weakness allowing for attacks, to being considered a potentially useful feature. Malleable primitives are cryptographic objects that allow for meaningful computations, as most notably in the example of fully homomorphic encryption. Malleability is, however, a notion that is difficult to capture both in the hand-written and the formal security analysis of protocols.

In my work, I look at malleability from both angles. On one hand, it is a source of worrying attacks that have, e.g., to be mitigated in a verified implementation of the transport layer security (TLS) standard used for securing the Internet. On the other hand, malleability is a feature that helps to build efficient protocols, such as delegatable anonymous credentials and fast and resource friendly proofs of computations for smart metering. We are building a zero-knowledge compiler for a high-level relational language (ZQL), that systematically optimizes and verifies the use of such cryptographic evidence.

We recently discovered that malleability is also applicable to verifiable shuffles, an important building block for universally verifiable, multi-authority election schemes. We construct a publicly verifiable shuffle that for the first time uses one compact proof to prove the correctness of an entire multi-step shuffle. In our work, we examine notions of malleability for non-interactive zero-knowledge (NIZK) proofs. We start by defining a malleable proof system, and then consider ways to meaningfully ‘control’ the malleability of the proof system. In our shuffle application controlled-malleable proofs allow each mixing authority to take as input a set of encrypted votes and a controlled-malleable NIZK proof that these are a shuffle of the original encrypted votes submitted by the voters; it then permutes and re-randomizes these votes and updates the proof by exploiting its controlled malleability.

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