Cryptology ePrint Archive: Report 2021/334

Post-Quantum Succinct Arguments: Breaking the Quantum Rewinding Barrier

Alessandro Chiesa and Fermi Ma and Nicholas Spooner and Mark Zhandry

Abstract: We prove that Kilian's four-message succinct argument system is post-quantum secure in the standard model when instantiated with any probabilistically checkable proof and any collapsing hash function (which in turn exist based on the post-quantum hardness of Learning with Errors). This yields the first post-quantum succinct argument system from any falsifiable assumption.

At the heart of our proof is a new quantum rewinding procedure that enables a reduction to repeatedly query a quantum adversary for accepting transcripts as many times as desired. Prior techniques were limited to a constant number of accepting transcripts.

Category / Keywords: foundations / succinct arguments; post-quantum cryptography; quantum rewinding

Date: received 14 Mar 2021, last revised 3 Jun 2021

Contact author: alexch at berkeley edu, nspooner at bu edu, fermima at alum mit edu, mzhandry at gmail com

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Version: 20210603:205700 (All versions of this report)

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