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Revocable Cryptography from Learning with Errors

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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

Quantum cryptography leverages unique properties of quantum information in order to construct cryptographic primitives that are oftentimes impossible classically. In this work, we build on the no-cloning principle of quantum mechanics and design cryptographic schemes with key revocation capabilities. We consider schemes where secret keys are represented as quantum states with the guarantee that, once the secret key is successfully revoked from a user, they no longer have the ability to perform the same functionality as before.

We define and construct several fundamental cryptographic primitives with key-revocation capabilities, namely pseudorandom functions, secret-key and public-key encryption, and even fully homomorphic encryption, assuming the quantum sub-exponential hardness of the learning with errors problem. Central to all our constructions is our method of making the Dual-Regev encryption (Gentry, Peikert and Vaikuntanathan, STOC 2008) scheme revocable.

Full version at https://eprint.iacr.org/2023/325.

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Notes

  1. 1.

    The attack would indeed have gone undetected but for the Snowden revelations.

  2. 2.

    Both of our works were posted online around the same time.

  3. 3.

    The stronger notion was updated in our paper subsequent to posting of our and their work.

  4. 4.

    Their construction achieves the stronger definition where the revocation only needs to succeed with inverse polynomial probability.

  5. 5.

    In the full version of the paper, this is formalized as the procedure \(\textsf{GenGauss}\).

  6. 6.

    Note that the state is not normalized for convenience.

  7. 7.

    For approriate choices of parameters, decryption via rounding succeeds at outputting \(\mu \) with overwhelming probability and hence we can invoke the “almost as good as new” lemma [2] to recover the original state \(\mathinner {|{\psi _{\textbf{y}}}\rangle }\).

  8. 8.

    In the full version of the paper, this is formalized as the procedure QSampGauss.

  9. 9.

    Technically, \(\mathcal D\) can distinguish between \((\textbf{u},\textbf{u}^\intercal \textbf{x}_0 + e')\) and \((\textbf{u},r)\) for a Gaussian error \(e'\). However, by defining a distinguisher \(\tilde{\mathcal D}\) that first shifts \(\textbf{u}\) by a Gaussian vector \(e'\) and then runs \(\mathcal D\), we obtain the desired distinguisher.

  10. 10.

    We remark that, there do exist post-quantum-insecure iO schemes based on well-founded assumptions [42].

  11. 11.

    Acording to the terminology of [11], this refers to finite term secure software leasing.

  12. 12.

    This notion is incomparable with another related notion called unclonable encryption [7, 9, 23], which informally guarantees that it should be infeasible to clone quantum ciphertexts without losing information about the encrypted message.

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Acknowledgements

We thank Fatih Kaleoglu and Ryo Nishimaki for several insightful discussions.

This work was done (in part) while the authors were visiting the Simons Institute for the Theory of Computing. P.A. is supported by a research gift from Cisco. A.P. is partially supported by AFOSR YIP (award number FA9550-16-1-0495), the Institute for Quantum Information and Matter (an NSF Physics Frontiers Center; NSF Grant PHY-1733907) and by a grant from the Simons Foundation (828076, TV). V.V. is supported by DARPA under Agreement No. HR00112020023, NSF CNS-2154149 and a Thornton Family Faculty Research Innovation Fellowship.

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Authors and Affiliations

  1. UC Santa Barbara, Santa Barbara, USA

    Prabhanjan Ananth

  2. California Institute of Technology, Pasadena, USA

    Alexander Poremba

  3. Massachusetts Institute of Technology, Cambridge, USA

    Vinod Vaikuntanathan

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  1. Prabhanjan Ananth
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Correspondence to Alexander Poremba .

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    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Ananth, P., Poremba, A., Vaikuntanathan, V. (2023). Revocable Cryptography from Learning with Errors. 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_4

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