The Breakdown of Classical Minicrypt Equivalences in the Quantum-Computation Classical-Communication Model

Abstract:Classically, it is well-known that several fundamental cryptographic primitives, including one-way functions, pseudorandom number generators, commitments, and signatures, characterize the same cryptographic world, which is known as "Minicrypt". In this paper, we investigate to what extent this picture persists in the quantum-computation classical-communication (QCCC) setting, where parties may perform quantum local computation, but communicate through only classical messages. We demonstrate that the classical Minicrypt landscape breaks down in the QCCC model by oracle separations. We construct two oracle worlds where efficiently verifiable one-way puzzles (EV-OWPuzz) exist. By a known equivalence, QCCC one-time signatures also exist in both worlds. In the first, one-way functions do not exist, even if we allow quantum pseudodeterministic evaluation. In the second, QCCC bit commitments do not exist. Thus, the classical Minicrypt reductions from signatures to one-way functions and bit commitments have no fully black-box counterparts in the QCCC setting. Our proofs develop techniques for analyzing the random phase states, including a concentration theorem and an LOCC decoupling theorem, which may be of independent interest.

arXiv:2609.33098 [quant-ph]

(or arXiv:2609.33098v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.33098 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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