Sebastian Zur

The compressed oracle technique, introduced in the context of quantum cryptanalysis, is the latest method for proving quantum query lower bounds, and has had an impressive number of applications since its introduction, due in part to the ease of importing classical lower bound intuition into the quantum setting via this method. Previously, the main quantum query lower bound methods were the polynomial method, the adversary method, and the multiplicative adversary method, and their relative powers were well understood. In this work, we situate the compressed oracle technique within this established landscape, by showing that it is a special case of the multiplicative adversary method. To accomplish this, we introduce a simplified restriction of the multiplicative adversary method, the MLADV method, that remains powerful enough to capture the polynomial method and exhibit a strong direct product theorem, but is much simpler to reason about. We show that the compressed oracle technique is also captured by the MLADV method. This might make the MLADV method a promising direction in the current quest to extend the compressed oracle technique to non-product distributions.

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~\cite{zhandry2018record} can be used to do quantum lazy sampling from non-uniform function distributions. Second, we observe how Unruh’s one-way-to-hiding lemma~\cite{unruh2015revocable} 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.