The quantum random oracle model (QROM) has become the standard model in which to prove the post-quantum security of random-oracle-based constructions. Unfortunately, none of the known proof techniques allow the reduction to record information about the adversary’s queries, a crucial feature of many classical ROM proofs, including all proofs of indifferentiability for hash function domain extension. In this work, we give a new QROM proof technique that overcomes this “recording barrier”. We do so by giving a new “compressed oracle” which allows for efficient on-the-fly simulation of random oracles, roughly analogous to the usual classical simulation. We then use this new technique to give the first proof of quantum indifferentiability for the Merkle-Damgård domain extender for hash functions. We also give a proof of security for the Fujisaki-Okamoto transformation; previous proofs required modifying the scheme to include an additional hash term. Given the threat posed by quantum computers and the push toward quantum-resistant cryptosystems, our work represents an important tool for efficient post-quantum cryptosystems.
CITATION STYLE
Zhandry, M. (2019). How to Record Quantum Queries, and Applications to Quantum Indifferentiability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11693 LNCS, pp. 239–268). Springer Verlag. https://doi.org/10.1007/978-3-030-26951-7_9
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