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Multi-Client Functional Encryption with Fine-Grained Access Control

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Advances in Cryptology – ASIACRYPT 2022 (ASIACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13791))

Abstract

Multi-Client Functional Encryption (\(\textsf {MCFE}\)) and Multi-Input Functional Encryption (\(\textsf {MIFE}\)) are very interesting extensions of Functional Encryption for practical purpose. They allow to compute joint function over data from multiple parties. Both primitives are aimed at applications in multi-user settings where decryption can be correctly output for users with appropriate functional decryption keys only. While the definitions for a single user or multiple users were quite general and can be realized for general classes of functions as expressive as Turing machines or all circuits, efficient schemes have been proposed so far for concrete classes of functions: either only for access control, i.e. the identity function under some conditions, or linear/quadratic functions under no condition.

In this paper, we target classes of functions that explicitly combine some evaluation functions independent of the decrypting user under the condition of some access control. More precisely, we introduce a framework for \(\textsf {MCFE}\) with fine-grained access control and propose constructions for both single-client and multi-client settings, for inner-product evaluation and access control via Linear Secret Sharing Schemes (LSSS), with selective and adaptive security. The only known work that combines functional encryption in multi-user setting with access control was proposed by Abdalla et al. (Asiacrypt ’20), which relies on a generic transformation from the single-client schemes to obtain \(\textsf {MIFE} \) schemes that suffer a quadratic factor of n (where n denotes the number of clients) in the ciphertext size. We follow a different path, via \(\textsf {MCFE} \): we present a duplicate-and-compress technique to transform the single-client scheme and obtain a \(\textsf {MCFE}\) with fine-grained access control scheme with only a linear factor of n in the ciphertext size. Our final scheme thus outperforms the Abdalla et al.’s scheme by a factor n, as one can obtain \(\textsf {MIFE}\) from \(\textsf {MCFE}\) by making all the labels in \(\textsf {MCFE}\) a fixed public constant. The concrete constructions are secure under the \(\textsf{SXDH}\) assumption, in the random oracle model for the \(\textsf {MCFE}\) scheme, but in the standard model for the \(\textsf {MIFE}\) improvement.

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Notes

  1. 1.

    See [1, 12] for discussions about this relaxation. The general reason is that some functionality might contain \(\bot \) in its range and if \(F_\lambda (x) = \bot \) we do not impose \(\textsf{Dec}(\textsf{sk}_{F_\lambda ,\mathsf {ac{-}k}},\textsf{Enc}(\textsf{pk}, x, \mathsf {ac{-}ct})) = F_\lambda (x)\), neither do we disallow it..

  2. 2.

    If all clients must use the same set of attributes , we can treat as a virtual attribute in \(\textsf{S}\), while enforcing the same for all i. This implies that all must be the same. However, this approach requires a consensus among all n clients on \(\textsf{S}\), which general might be more complicated than agreeing on \(\textsf{tag}\).

  3. 3.

    Since our single-client scheme is public-key, we can obtain multi-challenge security using a standard hybrid argument.

  4. 4.

    For instance, the adversary might corrupt \(i^*\), query a left-or-right challenge \((\textbf{x}_0,\textbf{x}_1)\) where \(\varDelta \textbf{x}[i^*] {:}{=}\textbf{x}_0[i^*] - \textbf{x}_1[i^*]\ne 0\) and \(\varDelta \textbf{x}[i] = 0\) for \(i\ne i^*\), then decrypt the challenge ciphertext with a satisfied key for \(\textbf{y}^{\scriptscriptstyle (\ell )}\) whose \(i^*\)-th entry is non-zero.

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Acknowledgements

This work was supported in part by the European Union Horizon 2020 ERC Programme (Grant Agreement no. 966570 – CryptAnalytics), the Beyond5G project and the French ANR Project ANR-19-CE39-0011 PRESTO.

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Authors and Affiliations

  1. DIENS, École normale supérieure, CNRS, Inria, PSL University, Paris, France

    Ky Nguyen & David Pointcheval

  2. LTCI, Telecom Paris, Institut Polytechnique de Paris, Palaiseau, France

    Duong Hieu Phan

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  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Nguyen, K., Phan, D.H., Pointcheval, D. (2022). Multi-Client Functional Encryption with Fine-Grained Access Control. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_4

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