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Semi-quantum Copy-Protection and More

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14372))

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Abstract

Properties of quantum mechanics have enabled the emergence of quantum cryptographic protocols achieving important goals which are proven to be impossible classically. Unfortunately, this usually comes at the cost of needing quantum power from every party in the protocol, while arguably a more realistic scenario would be a network of classical clients, classically interacting with a quantum server.

In this paper, we focus on copy-protection, which is a quantum primitive that allows a program to be evaluated, but not copied, and has shown interest especially due to its links to other unclonable cryptographic primitives. Our main contribution is to show how to dequantize quantum copy-protection schemes constructed from hidden coset states, by giving a construction for classically-instructed remote state preparation for coset states, which preserves hardness properties of hidden coset states. We then apply this dequantizer to obtain semi-quantum cryptographic protocols for copy-protection and tokenized signatures with strong unforgeability. In the process, we present the first secure copy-protection scheme for point functions in the plain model and a new direct product hardness property of coset states which immediately implies a strongly unforgeable tokenized signature scheme.

Work done while at CRED and DIENS.

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Notes

  1. 1.

    This is called hybrid quantum cryptography in [3].

  2. 2.

    The only known exception is the construction of copy-protection of single-bit point functions in the quantum random oracle model based on BB84 states [6]. In this work, we focus only on constructions in the plain model.

  3. 3.

    These coset states actually satisfy a strong monogamy-of-entanglement property, which we elaborate later in Sect. 2.

  4. 4.

    We emphasize that we use the same challenge distribution as in [16]. While being non-trivial, this is not the natural challenge distribution for point functions. Please see the full version [13] for the details.

  5. 5.

    A hybrid QFHE scheme is one where every encryption of a quantum state \(\left| {\psi } \right\rangle \) consists of a quantum one-time pad encryption of \(\left| {\psi } \right\rangle \) with Pauli keys \((x, z) \in \{0,1\}^{*}\), and \(\textsf{ct}_{x, z}\) which is a classical FHE encryption of the Pauli keys.

  6. 6.

    We refer the reader to [23, Section 4] for further details on ENTCF families.

  7. 7.

    We omit the details of this decoding procedure, and refer the reader to Sect. 4.2. We note that with the trapdoor \(t\), this procedure can be implemented efficiently by the verifier.

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Acknowledgements

This work was supported in part by the French ANR projects CryptiQ (ANR-18-CE39-0015) and SecNISQ (ANR-21-CE47-0014). QHV was supported in part by the French ANR project TCS-NISQ (ANR-22-CE47-0004), and by the PEPR integrated project EPiQ ANR-22-PETQ-0007 part of Plan France 2030. The authors would like to thank Thomas Vidick, Christian Majenz, Alexandru Gheorghiu, as well as the anonymous reviewers for their helpful discussion and feedback.

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Authors and Affiliations

  1. DIENS, École normale supérieure, PSL University, CNRS, INRIA, Paris, France

    Céline Chevalier & Paul Hermouet

  2. CRED, Université Panthéon-Assas Paris II, Paris, France

    Céline Chevalier & Paul Hermouet

  3. LIP6, Sorbonne Université, Paris, France

    Paul Hermouet & Quoc-Huy Vu

Authors
  1. Céline Chevalier
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  2. Paul Hermouet
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  3. Quoc-Huy Vu
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Correspondence to Céline Chevalier .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Chevalier, C., Hermouet, P., Vu, QH. (2023). Semi-quantum Copy-Protection and More. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14372. Springer, Cham. https://doi.org/10.1007/978-3-031-48624-1_6

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