On the Impossibility of Simulation Security for Quantum Functional Encryption

2026-01-24

AI Summary

This work investigates whether functional encryption in the quantum setting can achieve simulation-based security, thereby circumventing known impossibility results from the classical regime. By extending classical impossibility arguments to the quantum domain and leveraging tools such as pseudorandom quantum states, public-key encryption foundations, and information-theoretic techniques, the paper conducts security reductions and impossibility analyses under various adversarial models—including adversaries with unbounded challenge messages or access to multiple functional keys. It establishes, for the first time, that simulation-secure functional encryption remains impossible even in the quantum setting. Furthermore, the authors introduce a novel property of pseudorandom quantum states—namely, incompressibility—and use it to derive a stronger and independent impossibility result, thereby delineating fundamental limits in the theoretical foundations of quantum cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Functional encryption is a powerful cryptographic primitive that enables fine-grained access to encrypted data and underlies numerous applications. Although the ideal security notion for FE (simulation security) has been shown to be impossible in the classical setting, those impossibility results rely on inherently classical arguments. This leaves open the question of whether simulation-secure functional encryption can be achieved in the quantum regime. In this work, we rule out this possibility by showing that the classical impossibility results largely extend to the quantum world. In particular, when the adversary can issue an unbounded number of challenge messages, we prove an unconditional impossibility, matching the classical barrier. In the case where the adversary may obtain many functional keys, classical arguments only yield impossibility under the assumption of pseudorandom functions; we strengthen this by proving impossibility under the potentially weaker assumption of pseudorandom quantum states. In the same setting, we also establish an alternative impossibility based on public-key encryption. Since public-key encryption is not known to imply pseudorandom quantum states, this provides independent evidence of the barrier. As part of our proofs, we show a novel incompressibility property for pseudorandom states, which may be of independent interest.

Problem

• quantum functional encryption
• simulation security
• impossibility
• pseudorandom quantum states
• public-key encryption

Innovation

• quantum functional encryption
• simulation security
• pseudorandom quantum states
• impossibility result
• incompressibility