Cryptomania v.s. Minicrypt in a Quantum World
Longcheng Li, Qian Li, Xingjian Li, Qipeng Liu
TL;DR
The paper resolves a fundamental question about the limits of constructing public-key cryptography from one-way functions in the quantum setting. By working in the quantum random oracle model and employing an approximate quantum Markov-chain framework plus a win-win low-degree polynomial reprogramming technique, the authors prove that perfect-complete quantum PKE with classical keys and classical ciphertext cannot be secure from quantum OWFs in a black-box manner, removing prior conjectures and key-generation restrictions. They further extend the impossibility to quantum ciphertext and to quantum public keys under certain determinism conditions, demonstrating the tightness of existing QPKE constructions and clarifying the boundary between Minicrypt and Cryptomania in the quantum regime. The results have significant implications for the feasibility of extracting nontrivial quantum cryptographic primitives from OWFs and provide a rigorous foundation for future work on non-perfect or multi-round quantum cryptographic separations.
Abstract
We prove that it is impossible to construct perfect-complete quantum public-key encryption (QPKE) with classical keys from quantumly secure one-way functions (OWFs) in a black-box manner, resolving a long-standing open question in quantum cryptography. Specifically, in the quantum random oracle model (QROM), no perfect-complete QPKE scheme with classical keys, and classical/quantum ciphertext can be secure. This improves the previous works which require either unproven conjectures or imposed restrictions on key generation algorithms. This impossibility even extends to QPKE with quantum public key if the public key can be uniquely determined by the secret key, and thus is tight to all existing QPKE constructions.