Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability

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

Quantum Indifferentiability of SHA-3

In this paper we prove quantum indifferentiability of the sponge construction instantiated with random (invertible) permutations. With this result we bring the post-quantum security of the standardized SHA-3 hash function to the level matching its security against classical adversaries. To achieve our result, we generalize the compressed-oracle technique of Zhandry (Crypto\u2719) by defining and proving correctness of a compressed permutation oracle. We believe our technique will find applications in many more cryptographic constructions

Tight Quantum Indifferentiability of a Rate-1/3 Compression Function

We prove classical and quantum indifferentiability of a rate-1/3 compression function introduced by Shrimpton and Stam (ICALP \u2708). This construction was one of the first constructions based on three random functions that achieved optimal collision-resistance. We also prove that our result is tight, we define a classical and a quantum attackers that match the indifferentiability security level. Our tight indifferentiability results provide a negative result on the optimality of security of the construction by Shrimpton and Stam, security level of the strong indifferentiability notion is below that of collision-resistance. To arrive at these results, we generalize the results of Czajkowski, Majenz, Schaffner, and Zur (arXiv \u2719). Our generalization allows to analyze quantum security of constructions based on multiple independent random functions, something not possible before

Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability

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