Quantum Relational Hoare Logic with Expectations

We present a variant of the quantum relational Hoare logic from (Unruh, POPL 2019) that allows us to use "expectations" in pre- and postconditions. That is, when reasoning about pairs of programs, our logic allows us to quantitatively reason about how much certain pre-/postconditions are satisfied that refer to the relationship between the programs inputs/outputs

Post-Quantum Verification of Fujisaki-Okamoto

We present a computer-verified formalization of the post-quantum security proof of the Fujisaki-Okamoto transform (as analyzed by Hövelmanns, Kiltz, Schäge, and Unruh, PKC 2020). The formalization is done in quantum relational Hoare logic and checked in the qrhl-tool (Unruh, POPL 2019)

Local Reasoning about Probabilistic Behaviour for Classical-Quantum Programs

Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the verification task greatly. We propose a new quantum Hoare logic for local reasoning about probabilistic behaviour by introducing distribution formulas to specify probabilistic properties. We show that the proof rules in the logic are sound with respect to a denotational semantics. To demonstrate the effectiveness of the logic, we formally verify the correctness of non-trivial quantum algorithms including the HHL and Shor's algorithms.Comment: 27 pages. arXiv admin note: text overlap with arXiv:2107.0080

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