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

Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability