Cryptology ePrint Archive: Report 2019/428

Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability

Jan Czajkowski and Christian Majenz and Christian Schaffner and Sebastian Zur

Abstract: Game-playing proofs constitute a powerful framework for classical 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 [Zha18] can be used to do quantum lazy sampling from non-uniform function distributions. Second, we observe how Unruh's one-way-to-hiding lemma [Unr14] 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 or a random permutation. Our results upgrade post-quantum security of SHA-3 to the same level that is proven against classical adversaries.

Category / Keywords: foundations / game-playing proofs, QROM, indifferentiability, sponge construction

Date: received 25 Apr 2019

Contact author: j czajkowski at uva nl, c majenz@uva nl, c schaffner@uva nl, zursebastian@gmail com

Available format(s): PDF | BibTeX Citation

Version: 20190428:025621 (All versions of this report)

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