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One-Out-of-Many Unclonable Cryptography: Definitions, Constructions, 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

The no-cloning principle of quantum mechanics enables us to achieve amazing unclonable cryptographic primitives, which is impossible in classical cryptography. However, the security definitions for unclonable cryptography are tricky. Achieving desirable security notions for unclonability is a challenging task. In particular, there is no indistinguishable-secure unclonable encryption and quantum copy-protection for single-bit output point functions in the standard model. To tackle this problem, we introduce and study relaxed but meaningful security notions for unclonable cryptography in this work. We call the new security notion one-out-of-many unclonable security.

We obtain the following results.

  • We show that one-time strong anti-piracy secure secret key single-decryptor encryption (SDE) implies one-out-of-many indistinguishable-secure unclonable encryption.

  • We construct a one-time strong anti-piracy secure secret key SDE scheme in the standard model from the LWE assumption. This scheme can encrypt multi-bit messages.

  • We construct one-out-of-many copy-protection for single-bit output point functions from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption.

  • We construct one-out-of-many unclonable predicate encryption (PE) from one-out-of-many indistinguishable-secure unclonable encryption and the LWE assumption.

Thus, we obtain one-out-of-many indistinguishable-secure unclonable encryption, one-out-of-many copy-protection for single-bit output point functions, and one-out-of-many unclonable PE in the standard model from the LWE assumption. In addition, our one-time SDE scheme is the first multi-bit SDE scheme that does not rely on any oracle heuristics and strong assumptions such as indistinguishability obfuscation and witness encryption.

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Notes

  1. 1.

    Some lines of works [13, 22] studied quantum copy-protection for cryptographic functionalities that are not captured by programs. Quantum copy-protections for cryptographic functionalities have different names, such as unclonable decryption or single decryptor encryption. In this work, unless stated otherwise, we use the term quantum copy-protection to indicate quantum copy-protection for point functions. For the previous works on quantum copy-protection for cryptographic functionalities, see Sect. 1.5.

  2. 2.

    For example, indistinguishability-based unclonability for unclonable encryption implies (one-time) IND-CPA security, but one-wayness-based unclonability does not.

  3. 3.

    One might think that copy protection for multi-bit output point functions implies that for single-bit output point functions. However, this is not the case. This is because the security of copy protection for multi-bit output point functions usually relies on the high min-entropy of the multi-bit output string, and it is broken if the output string does not have enough entropy as in the case of single-bit output. Realizing copy protection for single-bit output point function is challenging in the sense that we have to achieve the security without relying on the entropy of the output string.

  4. 4.

    We focus on ciphertext-policy ABE in this work.

  5. 5.

    We omit the security parameter for simplicity in this overview. The same is applied to other cryptographic primitives.

  6. 6.

    Ananth and Kaleoglu [4] also proposed a similar construction.

  7. 7.

    The notion of unclonable encryption by Gottesman is slightly different from the one in this paper. His definition focuses on tamper detection.

  8. 8.

    Selectively secure secret key SDE in the setting of honestly generated keys. See [17] for the detail.

  9. 9.

    For the detail on the rational security flavor of one-out-of-many unclonability, see Remark 3.

  10. 10.

    They call “CPA-style anti-piracy security”.

  11. 11.

    Ananth et al. [7] show the relationship between one-wayness-based security with the same ciphertext and one with the different ciphertexts.

  12. 12.

    Suppose \(\mathcal {A}_0\) forwards the given quantum state to \(\mathcal {A}_1\) and nothing to \((\mathcal {A}_2,\ldots ,\mathcal {A}_n)\). If \(\alpha =1\) is chosen, the adversaries win with probability 1 because the additional information, together with the original quantum object, can be used to compute the challenge bit \(\textsf{coin}\) correctly. If one of \((\mathcal {A}_2,\ldots ,\mathcal {A}_n)\) is chosen, the adversaries win with probability \(\frac{1}{2}\) by random guess. Hence, the advantage is \(\frac{1}{n}\cdot 1+\frac{n-1}{n}\cdot \frac{1}{2}=\frac{1}{2}+\frac{1}{2n}\), which we consider as the trivial advantage.

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Authors and Affiliations

  1. NTT Social Informatics Laboratories, Tokyo, Japan

    Fuyuki Kitagawa & Ryo Nishimaki

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  1. Fuyuki Kitagawa
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Correspondence to Fuyuki Kitagawa .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Kitagawa, F., Nishimaki, R. (2023). One-Out-of-Many Unclonable Cryptography: Definitions, Constructions, 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_10

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