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Abstract

The MPC-in-the-head technique (Ishai et al., STOC 2007) is a celebrated method to build zero-knowledge protocols with desirable theoretical properties and high practical efficiency. This technique has generated a large body of research and has influenced the design of real-world post-quantum cryptographic signatures. In this work, we present a generalization of the MPC-in-the-head paradigm to the quantum setting, where the MPC is running a quantum computation. As an application of our framework, we propose a new approach to build zeroknowledge protocols where security holds even against a verifier that can obtain a superposition of transcripts. In this work we revisit this problem, and present two new three-round protocols in the common reference string model: (i) A zero-knowledge argument for NP, whose security reduces to the standard learning with errors (LWE) problem. (ii) A zero-knowledge argument for QMA from the same assumption.