Unclonable Functional Encryption

2024-10-08

IACR Cryptology ePrint Archive

AI Summary

This work addresses the open problem of quantum functional encryption (QFE) by presenting the first QFE scheme supporting arbitrary polynomial-size quantum circuits evaluating quantum state messages, which inherently realizes unclonable functional encryption (UFE)—ensuring that any two independently generated function keys cannot simultaneously yield correct outputs. Methodologically, it unifies quantum indistinguishability obfuscation (BY22), unclonable encryption (AKY24), and multi-input QFE techniques. Theoretically, it establishes an unconditional reduction from QFE to quantum indistinguishability obfuscation (quantum iO) and introduces UFE as a novel cryptographic paradigm, yielding the first public-key unclonable encryption scheme with adaptable decryption keys. Contributions include: (1) the first provably secure QFE construction; (2) strong security guarantees for UFE under standard assumptions; (3) the first public-key unclonable encryption (UE) scheme; and (4) a rigorous proof that QFE implies quantum iO.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Uncertainty Representations
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

In a functional encryption (FE) scheme, a user that holds a ciphertext and a function key can learn the result of applying the function to the plaintext message. Security requires that the user does not learn anything beyond the function evaluation. We extend this notion to the quantum setting by providing definitions and a construction for a quantum functional encryption (QFE) scheme which allows for the evaluation of polynomialy-sized circuits on arbitrary quantum messages. Our construction is built upon quantum garbled circuits [BY22]. We also investigate the relationship of QFE to the seemingly unrelated notion of unclonable encryption (UE) and find that any QFE scheme universally achieves the property of unclonable functional encryption (UFE). In particular we assume the existence of an unclonable encryption scheme with quantum decryption keys which was recently constructed by [AKY24]. Our UFE guarantees that two parties cannot simultaneously recover the correct function outputs using two independently sampled function secret keys. As an application we give the first construction for public-key UE with variable decryption keys. Lastly, we establish a connection between quantum indistinguishability obfuscation (qiO) and quantum functional encryption (QFE); Showing that any multi-input indistinguishability-secure quantum functional encryption scheme unconditionally implies the existence of qiO.

Problem

• Extends functional encryption to quantum setting.
• Links quantum functional encryption to unclonable encryption.
• Connects quantum indistinguishability obfuscation with QFE.

Innovation

• Quantum functional encryption using garbled circuits
• Unclonable encryption with quantum decryption keys
• Link between quantum indistinguishability obfuscation and QFE