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Hidden Cosets and Applications to Unclonable Cryptography

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12825))

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Abstract

In 2012, Aaronson and Christiano introduced the idea of hidden subspace states to build public-key quantum money [STOC ’12]. Since then, this idea has been applied to realize several other cryptographic primitives which enjoy some form of unclonability.

In this work, we propose a generalization of hidden subspace states to hidden coset states. We study different unclonable properties of coset states and several applications:

  • We show that, assuming indistinguishability obfuscation (\(\mathsf{iO}\)), hidden coset states possess a certain direct product hardness property, which immediately implies a tokenized signature scheme in the plain model. Previously, a tokenized signature scheme was known only relative to an oracle, from a work of Ben-David and Sattath [QCrypt ’17].

  • Combining a tokenized signature scheme with extractable witness encryption, we give a construction of an unclonable decryption scheme in the plain model. The latter primitive was recently proposed by Georgiou and Zhandry [ePrint ’20], who gave a construction relative to a classical oracle.

  • We conjecture that coset states satisfy a certain natural (information-theoretic) monogamy-of-entanglement property. Assuming this conjecture is true, we remove the requirement for extractable witness encryption in our unclonable decryption construction, by relying instead on compute-and-compare obfuscation for the class of unpredictable distributions. As potential evidence in support of the monogamy conjecture, we prove a weaker version of this monogamy property, which we believe will still be of independent interest.

  • Finally, we give the first construction of a copy-protection scheme for pseudorandom functions (PRFs) in the plain model. Our scheme is secure either assuming \(\mathsf{iO}\), \(\mathsf{OWF}\) and extractable witness encryption, or assuming \(\mathsf{iO}, \mathsf{OWF}\), compute-and-compare obfuscation for the class of unpredictable distributions, and the conjectured monogamy property mentioned above.

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Notes

  1. 1.

    Again, we point out that we could not draw this conclusion if only a single party were able to do the following two things, each with non-negligible probability: produce a vector in \(A+s_i\) and produce a vector in \(A^{\perp }+s_i'\). This is because in a quantum world, being able to perform two tasks with good probability, does not imply being able to perform both tasks simultaneously. So it is crucial that both parties are able to separately recover the vectors.

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Acknowledgements

A.C. is supported by the Simons Institute for the Theory of Computing, through a Quantum Postdoctoral Fellowship. J. L., Q. L. and M. Z. are supported by the NSF. J. L. is also supported by Scott Aaronson’s Simons Investigator award. The authors are grateful for the support of the Simons Institute, where this collaboration was initiated.

Author information

Authors and Affiliations

  1. University of California, Berkeley, USA

    Andrea Coladangelo

  2. The University of Texas at Austin, Austin, USA

    Jiahui Liu

  3. Princeton University, Princeton, USA

    Qipeng Liu

  4. Princeton University and NTT Research, Princeton, USA

    Mark Zhandry

Authors
  1. Andrea Coladangelo
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  2. Jiahui Liu
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  3. Qipeng Liu
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  4. Mark Zhandry
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Editor information

Editors and Affiliations

  1. Columbia University, New York City, NY, USA

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Coladangelo, A., Liu, J., Liu, Q., Zhandry, M. (2021). Hidden Cosets and Applications to Unclonable Cryptography. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12825. Springer, Cham. https://doi.org/10.1007/978-3-030-84242-0_20

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  • DOI: https://doi.org/10.1007/978-3-030-84242-0_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-84241-3

  • Online ISBN: 978-3-030-84242-0

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