Cryptomania v.s. Minicrypt in a Quantum World

2025-04-08

AI Summary

This work resolves a long-standing open problem in quantum cryptography: whether perfectly complete quantum public-key encryption (QPKE) with classical keys can be constructed, in a black-box manner, solely from quantum-secure one-way functions (OWFs) in the quantum random oracle model (QROM). The authors provide a negative answer, delivering the first rigorous impossibility proof—requiring no unproven assumptions and imposing no restrictions on key-generation mechanisms. Their result is tight and universal, subsuming all known QPKE paradigms. The proof integrates black-box reductions, quantum complexity-theoretic analysis, and security arguments under perfect completeness. It establishes a fundamental separation between Cryptomania and Minicrypt in the quantum setting: perfectly complete QPKE with classical keys is provably not black-box realizable from quantum-secure OWFs. This reveals an intrinsic limitation of quantum public-key cryptography—namely, that certain cryptographic primitives essential for quantum-secure public-key infrastructure cannot be instantiated from minimal quantum-hardness assumptions via black-box techniques.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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.

Problem

• Impossible perfect-complete QPKE from OWFs
• No secure QPKE in QROM model
• Impossibility extends to quantum public keys

Innovation

• Black-box quantum public-key encryption impossibility
• Quantum random oracle model analysis
• Tight bounds on QPKE constructions