Post-Quantum Succinct Arguments: Breaking the Quantum Rewinding Barrier

TL;DR

This paper establishes the first post-quantum secure succinct argument system based on collapsing hash functions and introduces a novel quantum rewinding technique that enhances security proofs against quantum adversaries.

Contribution

It proves the post-quantum security of Kilian's four-message argument system in the standard model using collapsing hash functions and develops a new quantum rewinding method for security reductions.

Findings

First post-quantum succinct argument system from falsifiable assumptions

Introduces a quantum rewinding procedure for multiple transcript queries

Achieves security based on Learning with Errors hardness

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.