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Multi-Client Inner Product Encryption: Function-Hiding Instantiations Without Random Oracles

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Public-Key Cryptography – PKC 2023 (PKC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13940))

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Abstract

In a Multi-Client Functional Encryption (MCFE) scheme, n clients each obtain a secret encryption key from a trusted authority. During each time step t, each client i can encrypt its data using its secret key. The authority can use its master secret key to compute a functional key given a function f, and the functional key can be applied to a collection of n clients’ ciphertexts encrypted to the same time step, resulting in the outcome of f on the clients’ data. In this paper, we focus on MCFE for inner-product computations.

If an MCFE scheme hides not only the clients’ data, but also the function f, we say it is function hiding. Although MCFE for inner-product computation has been extensively studied, how to achieve function privacy is still poorly understood. The very recent work of Agrawal et al. showed how to construct a function-hiding MCFE scheme for inner-product assuming standard bilinear group assumptions; however, they assume the existence of a random oracle and prove only a relaxed, selective security notion. An intriguing open question is whether we can achieve function-hiding MCFE for inner-product without random oracles.

In this work, we are the first to show a function-hiding MCFE scheme for inner products, relying on standard bilinear group assumptions. Further, we prove adaptive security without the use of a random oracle. Our scheme also achieves succinct ciphertexts, that is, each coordinate in the plaintext vector encrypts to only O(1) group elements.

Our main technical contribution is a new upgrade from single-input functional encryption for inner-products to a multi-client one. Our upgrade preserves function privacy, that is, if the original single-input scheme is function-hiding, so is the resulting multi-client construction. Further, this new upgrade allows us to obtain a conceptually simple construction.

N. Vanjani—Author ordering is randomized.

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Notes

  1. 1.

    Throughout this paper, the term “inner-product encryption” always means “inner-product functional encryption”. This terminology is standard in this space.

  2. 2.

    In Appendix E of the online full version, we show that a variant of the strawman scheme can indeed be proven secure in a different selective model, i.e., the adversary must submit all encryption queries ahead of \(\textbf{KGen} \) queries. However, we do not know any easy way to build from this selective scheme and get adaptive security eventually.

  3. 3.

    For convenience, we may imagine that the labels t have been renamed to be the integers \(\{1, 2, \ldots , Q_\textrm{enc}\}\).

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    Elaine Shi & Nikhil Vanjani

Authors
  1. Elaine Shi
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  2. Nikhil Vanjani
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Correspondence to Nikhil Vanjani .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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© 2023 International Association for Cryptologic Research

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Shi, E., Vanjani, N. (2023). Multi-Client Inner Product Encryption: Function-Hiding Instantiations Without Random Oracles. In: Boldyreva, A., Kolesnikov, V. (eds) Public-Key Cryptography – PKC 2023. PKC 2023. Lecture Notes in Computer Science, vol 13940. Springer, Cham. https://doi.org/10.1007/978-3-031-31368-4_22

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  • DOI: https://doi.org/10.1007/978-3-031-31368-4_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-31367-7

  • Online ISBN: 978-3-031-31368-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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