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2022 | OriginalPaper | Buchkapitel

Collusion Resistant Copy-Protection for Watermarkable Functionalities

verfasst von : Jiahui Liu, Qipeng Liu, Luowen Qian, Mark Zhandry

Erschienen in: Theory of Cryptography

Verlag: Springer Nature Switzerland

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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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Vorheriges Kapitel Candidate Trapdoor Claw-Free Functions from Group Actions with Applications to Quantum Protocols

Nächstes Kapitel On Secret Sharing, Randomness, and Random-less Reductions for Secret Sharing

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.

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.

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

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 \(\textsf{TI}\).

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.

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

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

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.

Aaronson, S.: Limitations of quantum advice and one-way communication. Theory Comput. 1(1), 1–28 (2005). https://doi.org/10.4086/toc.2005.v001a001MathSciNetCrossRefMATH

Aaronson, S.: Quantum copy-protection and quantum money. In: Proceedings of the 24th Annual IEEE Conference on Computational Complexity, CCC 2009, Paris, France, 15–18 July 2009, pp. 229–242. IEEE Computer Society (2009). https://doi.org/10.1109/CCC.2009.42

Aaronson, S., Christiano, P.: Quantum money from hidden subspaces. Theory Comput. 9(9), 349–401 (2013). https://doi.org/10.4086/toc.2013.v009a009MathSciNetCrossRefMATH

Aaronson, S., Liu, J., Liu, Q., Zhandry, M., Zhang, R.: New approaches for quantum copy-protection. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12825, pp. 526–555. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84242-0_19CrossRef

Ananth, P., Kaleoglu, F.: A note on copy-protection from random oracles (2022). https://doi.org/10.48550/ARXIV.2208.12884. https://arxiv.org/abs/2208.12884

Ananth, P., Kaleoglu, F., Li, X., Liu, Q., Zhandry, M.: On the feasibility of unclonable encryption, and more. In: Dodis, Y., Shrimpton, T. (eds.) Advances in Cryptology - CRYPTO 2022. Lecture Notes in Computer Science, vol. 13507. Springer (2022). https://doi.org/10.1007/978-3-031-15979-4_8

Ananth, P., La Placa, R.L.: Secure software leasing. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12697, pp. 501–530. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77886-6_17CrossRef

Barak, B., et al.: On the (Im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_1CrossRef

Ben-David, S., Sattath, O.: Quantum tokens for digital signatures (2016)

10.

Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of International Conference on Computers, Systems & Signal Processing, 9–12 Dec 1984, pp. 175–179. Bangalore, India (1984)

11.

Broadbent, A., Jeffery, S., Lord, S., Podder, S., Sundaram, A.: Secure software leasing without assumptions. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13042, pp. 90–120. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90459-3_4CrossRef

12.

Cohen, A., Holmgren, J., Nishimaki, R., Vaikuntanathan, V., Wichs, D.: Watermarking cryptographic capabilities. SIAM J. Comput. 47(6), 2157–2202 (2018)MathSciNetCrossRefMATH

13.

Coladangelo, A., Liu, J., Liu, Q., Zhandry, M.: Hidden cosets and applications to unclonable cryptography. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12825, pp. 556–584. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84242-0_20CrossRef

14.

Coladangelo, A., Majenz, C., Poremba, A.: Quantum copy-protection of compute-and-compare programs in the quantum random oracle model (2020). https://arxiv.org/abs/2009.13865

15.

Culf, E., Vidick, T.: A monogamy-of-entanglement game for subspace coset states (2021)

16.

Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. SIAM J. Comput. 45(3), 882–929 (2016). https://doi.org/10.1137/14095772XMathSciNetCrossRefMATH

17.

Georgiou, M., Zhandry, M.: Unclonable decryption keys (2020). https://eprint.iacr.org/2020/877

18.

Goyal, R., Kim, S., Manohar, N., Waters, B., Wu, D.J.: Watermarking public-key cryptographic primitives. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 367–398. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_12CrossRef

19.

Kim, S., Wu, D.J.: Watermarking cryptographic functionalities from standard lattice assumptions. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 503–536. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_17CrossRef

20.

Kim, S., Wu, D.J.: Watermarking PRFs from lattices: stronger security via extractable PRFs. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 335–366. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_11CrossRef

21.

Kitagawa, F., Nishimaki, R., Yamakawa, T.: Secure software leasing from standard assumptions. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13042, pp. 31–61. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90459-3_2CrossRef

22.

Kretschmer, W.: Quantum pseudorandomness and classical complexity. In: Hsieh, M. (ed.) 16th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2021, 5–8 July 2021, Virtual Conference. LIPIcs, vol. 197, pp. 1–20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.TQC.2021.2

23.

Marriott, C., Watrous, J.: Quantum arthur-merlin games. computational complexity 14(2), 122–152 (2005). https://doi.org/10.1007/s00037-005-0194-x

24.

Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information: 10th Anniversary Edition. Cambridge University Press (2010). https://doi.org/10.1017/CBO9780511976667

25.

Sahai, A., Waters, B.: How to use indistinguishability obfuscation: Deniable encryption, and more. SIAM J. Comput. 50(3), 857–908 (2021). https://doi.org/10.1137/15M1030108MathSciNetCrossRefMATH

26.

Vidick, T., Zhang, T.: Classical proofs of quantum knowledge. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12697, pp. 630–660. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77886-6_22CrossRef

27.

Wiesner, S.: Conjugate coding. SIGACT News 15(1), 78–88 (1983). https://doi.org/10.1145/1008908.1008920

28.

Yang, R., Au, M.H., Lai, J., Xu, Q., Yu, Z.: Collusion resistant watermarking schemes for cryptographic functionalities. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 371–398. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_14CrossRef

29.

Yang, R., Au, M.H., Yu, Z., Xu, Q.: Collusion resistant watermarkable PRFs from standard assumptions. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12170, pp. 590–620. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56784-2_20CrossRef

30.

Zhandry, M.: Schrödinger’s pirate: how to trace a quantum decoder. In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12552, pp. 61–91. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64381-2_3CrossRef

Titel: Collusion Resistant Copy-Protection for Watermarkable Functionalities
verfasst von: Jiahui Liu
Qipeng Liu
Luowen Qian
Mark Zhandry
Verlag: Springer Nature Switzerland
Buch: Theory of Cryptography
Print ISBN: 978-3-031-22317-4

Electronic ISBN: 978-3-031-22318-1

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-031-22318-1_11

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