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Collusion Resistant Copy-Protection for Watermarkable Functionalities

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13747))

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Abstract

Copy-protection is the task of encoding a program into a quantum state to prevent illegal duplications. A line of recent works studied copy-protection schemes under “\(1\rightarrow 2\) attacks”: the adversary receiving one program copy can not produce two valid copies. However, under most circumstances, vendors need to sell more than one copy of a program and still ensure that no duplicates can be generated. In this work, we initiate the study of collusion resistant copy-protection in the plain model. Our results are twofold:

  • The feasibility of copy-protecting all watermarkable functionalities is an open question raised by Aaronson et al. (CRYPTO’ 21). In the literature, watermarking decryption, digital signature schemes and PRFs have been extensively studied. For the first time, we show that digital signature schemes can be copy-protected. Together with the previous work on copy-protection of decryption and PRFs by Coladangelo et al. (CRYPTO’ 21), it suggests that many watermarkable functionalities can be copy-protected, partially answering the above open question by Aaronson et al.

  • We make all the above schemes (copy-protection of decryption, digital signatures and PRFs) k bounded collusion resistant for any polynomial k, giving the first bounded collusion resistant copy-protection for various functionalities in the plain model.

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Notes

  1. 1.

    The general functionality copy protection schemes in [2, 4] and the schemes in [7, 13] all satisfy this format. The copy-protection schemes for point/compute-and-compare functions in [2, 6, 11, 14] are not necessarily of such a format.

  2. 2.

    The formal security definitions for SSL in [4, 7, 11, 14, 21] vary slightly from one to another. We will discuss them in Sect. 1.2.

  3. 3.

    All constructions discussed in this section are not proved under collusion resistant security unless otherwise specified.

  4. 4.

    For simplicity, we only use the inefficient estimation procedure. The same argument in the technical overview holds using an efficient and approximated version. Similarly for \(\textsf{TI}\).

  5. 5.

    In the actual proof, two non-communicating parties will extract two vectors, one in the primal coset and the other in the dual coset of a coset state. This will violate the strong computational monogamy-of-entanglement property of coset states.

  6. 6.

    The probability estimation \(\textsf{PI}_j\) will preserve the success probability of the state but nothing else. Applying \(\textsf{PI}_j\) will likely change \(\sigma _{j-1}\).

  7. 7.

    The choice of 0.1 is arbitrary here. Indeed, they are polynomially related. For the sake of simplicity, we assume they are linearly related.

  8. 8.

    The approach for simultaneous extraction when showing \(1\rightarrow 2\) anti-piracy in [4] bears a high-level similarity with [13]. We have discussed [13] in the overview since we focus on unclonable decryption.

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Authors and Affiliations

  1. University of Texas at Austin, Austin, USA

    Jiahui Liu

  2. Simons Institute for the Theory of Computing, Berkeley, USA

    Qipeng Liu

  3. Boston University, Boston, USA

    Luowen Qian

  4. Princeton University and NTT Research, Princeton, USA

    Mark Zhandry

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  1. Jiahui Liu
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Correspondence to Qipeng Liu .

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Editors and Affiliations

  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Liu, J., Liu, Q., Qian, L., Zhandry, M. (2022). Collusion Resistant Copy-Protection for Watermarkable Functionalities. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13747. Springer, Cham. https://doi.org/10.1007/978-3-031-22318-1_11

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  • DOI: https://doi.org/10.1007/978-3-031-22318-1_11

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