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Lecture notes in computer science

Doubly Efficient Cryptography: Commitments, Arguments and RAM MPC

Wei-Kai Lin, Ethan Mook, Daniel Wichs

Published Jan 1, 2024• 1 citation
Publisher
DOI
10.1007/978-3-031-68397-8_8

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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 zero-knowledge protocols where security holds even against a verifier that can obtain a superposition of transcripts. This notion was pioneered by Damgard et al., who built a zero-knowledge protocol for NP (in the common reference string model) secure against superposition attacks, by relying on perfectly hiding and unconditionally binding dual-mode commitments. Unfortunately, no such commitments are known from standard cryptographic assumptions. 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.
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 zero-knowledge protocols where security holds even against a verifier that can obtain a superposition of transcripts. This notion was pioneered by Damgard et al., who built a zero-knowledge protocol for NP (in the common reference string model) secure against superposition attacks, by relying on perfectly hiding and unconditionally binding dual-mode commitments. Unfortunately, no such commitments are known from standard cryptographic assumptions. 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.