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Unclonable Functional Encryption

Arthur Mehta, Anne Müller

TL;DR

This work formalizes Quantum Functional Encryption (QFE) and its multi-input variant, establishing SIM- and IND-security notions applicable to adaptive, non-adaptive, and multi-message regimes. It provides a QFE construction for polynomial-sized circuits using quantum garbled circuits and randomized encodings, and shows how to extend QFE to Unclonable QFE (Unclonable-QFE) by leveraging unclonable encryption with quantum decryption keys, yielding a universal, unclonable FE scheme. The paper further connects QMIFE to quantum indistinguishability obfuscation (qiO), showing that single-query QMIFE implies qiO, and demonstrates that SIM-security can imply VBBO-style obfuscation in the quantum setting. Collectively, these results advance secure delegated quantum computation, quantum money-type applications, and foundational links between quantum FE, UE, and qiO, while outlining open questions for succinct QFE, multi-key security, and broader obfuscation frameworks.

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.

Unclonable Functional Encryption

TL;DR

This work formalizes Quantum Functional Encryption (QFE) and its multi-input variant, establishing SIM- and IND-security notions applicable to adaptive, non-adaptive, and multi-message regimes. It provides a QFE construction for polynomial-sized circuits using quantum garbled circuits and randomized encodings, and shows how to extend QFE to Unclonable QFE (Unclonable-QFE) by leveraging unclonable encryption with quantum decryption keys, yielding a universal, unclonable FE scheme. The paper further connects QMIFE to quantum indistinguishability obfuscation (qiO), showing that single-query QMIFE implies qiO, and demonstrates that SIM-security can imply VBBO-style obfuscation in the quantum setting. Collectively, these results advance secure delegated quantum computation, quantum money-type applications, and foundational links between quantum FE, UE, and qiO, while outlining open questions for succinct QFE, multi-key security, and broader obfuscation frameworks.

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.
Paper Structure (23 sections, 5 theorems, 4 equations)

This paper contains 23 sections, 5 theorems, 4 equations.

Table of Contents

  1. Introduction
  2. Summary of Results.
  3. Quantum Functional Encryption
  4. QFE.$(\mathsf{Setup}, \mathsf{KeyGen}, \mathsf{Enc}, \mathsf{Dec})$
  5. Correctness.
  6. Simulation Security.
  7. Indistinguishability Security.
  8. Multi-message Security.
  9. Multi-query/Collusion Security
  10. QFE for Poly-sized Circuits
  11. Randomized Encodings
  12. Outline of QFE Construction
  13. Unclonable QFE
  14. Unclonable Encryption
  15. Vairable-key UE
  16. ...and 8 more sections

Key Result

theorem thmcountertheorem

Given a QGC scheme with perfect correctness and a public key encryption scheme there exists a single-query adaptive SIM-secure QFE scheme for the class of polynomial-sized circuits.

Theorems & Definitions (5)

  • theorem thmcountertheorem: Informal
  • theorem thmcountertheorem: Informal
  • corollary thmcountercorollary: Informal
  • theorem thmcountertheorem: Informal
  • theorem thmcountertheorem: Informal