Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability

TL;DR

This paper introduces a quantum game-playing proof framework that extends classical techniques to quantum settings, enabling the proof of quantum indifferentiability of cryptographic constructions like the sponge.

Contribution

It generalizes two recent proof techniques—quantum lazy sampling with compressed oracles and the one-way-to-hiding lemma—to quantum game-playing proofs, facilitating quantum security analyses.

Findings

Developed a quantum framework for game-playing proofs using compressed quantum oracles.

Proved quantum indifferentiability of the sponge construction under certain assumptions.

Extended classical proof techniques to the quantum setting for cryptographic security.

Abstract

Game-playing proofs constitute a powerful framework for non-quantum cryptographic security arguments, most notably applied in the context of indifferentiability. An essential ingredient in such proofs is lazy sampling of random primitives. We develop a quantum game-playing proof framework by generalizing two recently developed proof techniques. First, we describe how Zhandry's compressed quantum oracles~(Crypto'19) can be used to do quantum lazy sampling of a class of non-uniform function distributions. Second, we observe how Unruh's one-way-to-hiding lemma~(Eurocrypt'14) can also be applied to compressed oracles, providing a quantum counterpart to the fundamental lemma of game-playing. Subsequently, we use our game-playing framework to prove quantum indifferentiability of the sponge construction, assuming a random internal function.