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Optimal Security Notion for Decentralized Multi-Client Functional Encryption

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Applied Cryptography and Network Security (ACNS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13906))

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Abstract

Research on (Decentralized) Multi-Client Functional Encryption (or (D)MCFE) is very active, with interesting constructions, especially for the class of inner products. However, the security notions have been evolving over the time. While the target of the adversary in distinguishing ciphertexts is clear, legitimate scenarios that do not consist of trivial attacks on the functionality are less obvious. In this paper, we wonder whether only trivial attacks are excluded from previous security games. And, unfortunately, this was not the case.

We then propose a stronger security notion, with a large definition of admissible attacks, and prove it is optimal: any extension of the set of admissible attacks is actually a trivial attack on the functionality, and not against the specific scheme. In addition, we show that all the previous constructions are insecure w.r.t. this new security notion. Eventually, we propose new DMCFE schemes for the class of inner products that provide the new features and achieve this stronger security notion.

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Notes

  1. 1.

    The work of [7] constructs function-hiding dynamic decentralized FE, which directly yields a DMCFE with a stronger property of function secrecy. Even though their proposed security model captures separated corruption of \(\textsf{ek}_i\) and \(\textsf{sk}_i\), implying they are different, their dynamic decentralized FE construction uses the same key for both and so does the resulting DMCFE, i.e. \(\textsf{sk}_i = \textsf{ek}_i\) for every i.

  2. 2.

    We use the metrics employed in the context of the \(\textsf{LWE}\)-based \(\textsf {(D)MCFE}\) in [24].

  3. 3.

    The admissibility for \(\textsf {MCFE}\) is the particular condition when \(\mathcal {H}_\textsf{skey}= [m]\) and thus \(\textbf{y}_\textsf{skey}=\textbf{y}\), meaning the only deducible function is F itself.

  4. 4.

    There are further involved technicalities to ensure that \(\textsf{ek}_i\) is constructed consistently, e.g. see the transition \(\textsf{G}_7\rightarrow \textsf{G}_8\) in the proof of Theorem 16.

  5. 5.

    In addition, we can allow dynamic corruption on one type but static corruption on the other type of keys, such as \(\mathsf {dmc\!\!\!\,\,\text {-}stat\text {-}sk\text {-}ind\!\!\!\,\,\text {-}cpa}\) to indicate partially static IND-security with adaptive challenges, dynamic corruption of \(\textsf{ekey}\), and static corruption of \(\textsf{skey}\).

  6. 6.

    Similarly, we can allow dynamic corruption on one type but static corruption on the other type of keys, such as \(\mathsf {dmc\!\!\!\,\,\text {-}stat\text {-}sk\text {-}ind\!\!\!\,\,\text {-}cpa}+\) to indicate partially static IND-security with adaptive challenges, dynamic corruption of \(\textsf{ekey}\), and static corruption of \(\textsf{skey}\).

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Acknowledgment

This work was supported in part by the France 2030 ANR Project ANR-22-PECY-003 SecureCompute, the French ANR Project ANR-19-CE39-0011 PRESTO and the Beyond5G Project as part of the plan “France Relance”.

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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. Ky Nguyen
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Correspondence to Ky Nguyen .

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  1. NTT Social Informatics Laboratories, Tokyo, Japan

    Mehdi Tibouchi

  2. Indiana University at Bloomington, Bloomington, IN, USA

    XiaoFeng Wang

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Nguyen, K., Phan, D.H., Pointcheval, D. (2023). Optimal Security Notion for Decentralized Multi-Client Functional Encryption. In: Tibouchi, M., Wang, X. (eds) Applied Cryptography and Network Security. ACNS 2023. Lecture Notes in Computer Science, vol 13906. Springer, Cham. https://doi.org/10.1007/978-3-031-33491-7_13

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  • DOI: https://doi.org/10.1007/978-3-031-33491-7_13

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