Cryptology ePrint Archive: Report 2020/1422

Non-interactive classical verification of quantum computation

Gorjan Alagic and Andrew M. Childs and Alex B. Grilo and Shih-Han Hung

Abstract: In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. We show that this same task can in fact be performed non-interactively (with setup) and in zero-knowledge.

Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP.

We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.

Category / Keywords: foundations / quantum prover interactive proofs, interactive verification, delegated computation, quantum cryptography

Original Publication (in the same form): IACR-TCC-2020

Date: received 13 Nov 2020

Contact author: galagic at gmail com, amchilds@umd edu, abgrilo@gmail com, shung@umd edu

Available format(s): PDF | BibTeX Citation

Version: 20201115:074251 (All versions of this report)

Short URL: ia.cr/2020/1422


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