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Multi-Client Inner-Product Functional Encryption in the Random-Oracle Model

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Security and Cryptography for Networks (SCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12238))

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Abstract

Multi-client functional encryption (MCFE) is an extension of functional encryption (FE) in which the decryption procedure involves ciphertexts from multiple parties. It is particularly useful in the context of data outsourcing and cloud computing where the data may come from different sources and where some data centers or servers may need to perform different types of computation on this data. In order to protect the privacy of the encrypted data, the server, in possession of a functional decryption key, should only be able to compute the final result in the clear, but no other information regarding the encrypted data. In this paper, we consider MCFE schemes supporting encryption labels, which allow the encryptor to limit the amount of possible mix-and-match that can take place during the decryption. This is achieved by only allowing the decryption of ciphertexts that were generated with respect to the same label. This flexible form of FE was already investigated by Chotard et al. at Asiacrypt 2018 and Abdalla et al. at Asiacrypt 2019. The former provided a general construction based on different standard assumptions, but its ciphertext size grows quadratically with the number of clients. The latter gave a MCFE based on Decisional Diffie-Hellman (DDH) assumption which requires a small inner-product space. In this work, we overcome the deficiency of these works by presenting three constructions with linear-sized ciphertexts based on the Matrix-DDH (MDDH), Decisional Composite Residuosity (DCR) and Learning with Errors (LWE) assumption in the random-oracle model. We also implement our constructions to evaluate their concrete efficiency.

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Notes

  1. 1.

    Note that we have \(\mathbf {Z}_i\cdot \mathcal {H}(\ell )=\textit{\textbf{s}}_i\cdot \textit{\textbf{a}}_\ell +\textit{\textbf{t}}_i\cdot (\mathbf {S}\textit{\textbf{a}}_\ell +\textit{\textbf{e}}_\ell )\).

  2. 2.

    Which is a generalization of the DDH assumption including many other assumptions such as k-LIN and 2-SCasc [14], as special cases.

  3. 3.

    Note that these security notions are respectively called without repetition and with repetition in [11, 12] . Here we are following the terminologies of [1].

  4. 4.

    In their construction, they apply the compiler, for going from \(one \) to \(pos ^+\), which gives \(pos ^+\) directly.

  5. 5.

    All the functions inside the same set \(\mathcal {F}_\rho \) have the same domain and the same range.

  6. 6.

    I.e., \(\big \lfloor a\big \rceil \) is \(\big \lfloor a\big \rfloor \) if \(a\le \big \lfloor a\big \rfloor +1/2\) and it is \((\big \lfloor a\big \rfloor +1)\) if \(a>\big \lfloor a\big \rfloor +1/2\).

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Acknowledgments

This work was supported in part by the European Union’s Horizon 2020 Research and Innovation Programme FENTEC (Grant Agreement no. 780108), by the European Union’s Seventh Framework Programme (FP7/2007–2013 Grant Agreement no. 339563 – CryptoCloud), and by the French FUI project ANBLIC.

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Authors and Affiliations

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

    Michel Abdalla, Florian Bourse, Hugo Marival, David Pointcheval & Azam Soleimanian

  2. INRIA, Paris, France

    Michel Abdalla, Florian Bourse, Hugo Marival, David Pointcheval & Azam Soleimanian

  3. University of Edinburgh, Edinburgh, UK

    Hendrik Waldner

Authors
  1. Michel Abdalla
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  2. Florian Bourse
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  3. Hugo Marival
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  4. David Pointcheval
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  5. Azam Soleimanian
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  6. Hendrik Waldner
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Corresponding authors

Correspondence to Michel Abdalla , Florian Bourse , Hugo Marival , David Pointcheval , Azam Soleimanian or Hendrik Waldner .

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Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

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

    Vladimir Kolesnikov

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Abdalla, M., Bourse, F., Marival, H., Pointcheval, D., Soleimanian, A., Waldner, H. (2020). Multi-Client Inner-Product Functional Encryption in the Random-Oracle Model. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_26

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  • DOI: https://doi.org/10.1007/978-3-030-57990-6_26

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