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Mergeable Functional Encryption

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Provable Security (ProvSec 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10592))

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Abstract

In this paper we put forward a new generalization of Functional Encryption (FE) that we call Mergeable FE (mFE). In a mFE system, given a ciphertext \(c_1\) encrypting \(m_1\) and a ciphertext \(c_2\) encrypting \(m_2\), it is possible to produce in an oblivious way a ciphertext encrypting the merged string \(m_1||m_2\) under the security constraint that the new ciphertext does not leak more information about the original ciphertexts. For instance, let us suppose to have a token for a program (for inputs of variable length) \(P_x\) that, on input a string D representing a list of elements, checks if a given element x is in D, and suppose that \(c_1\) (resp. \(c_2\)) encrypts a list \(D_1\) (resp. \(D_2\)). Then the token evaluated on \(c_1\) (resp. \(c_2\)) reveals if x is in list \(D_1\) (resp. \(D_2\)) but the same token evaluated on c, the ciphertext resulting from the merge of \(c_1\) and \(c_2\), should only reveal if x is in \(D_1\) or x is in \(D_2\) but not in which of the two lists it is in.

This primitive is in some sense FE with the “best possible” homomorphic properties and, besides being interesting in itself, it offers wide applications. For instance, it has as special case multi-inputs FE (and thus indistinguishability obfuscation), but enables applications not possible with the latter.

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Notes

  1. 1.

    This holds for the public-key setting where the adversary is given the public-key that allows to encrypt messages corresponding to any dimension.

  2. 2.

    Notice that the order is important, so the operation \((x_1,x_2)\) is different from \((x_2,x_1)\).

  3. 3.

    Formally, the procedure should also take as input the bound \(m(\lambda )\) on the size of the messages (since it is used to generate the commitment) but for simplicity we omit such details.

  4. 4.

    Formally we should define it as a family of languages indexed by the security parameter but henceforth for simplicity we omit this detail.

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Author information

Authors and Affiliations

  1. University of Luxembourg, Luxembourg City, Luxembourg

    Vincenzo Iovino

  2. University of Warsaw, Warsaw, Poland

    Karol Żebrowski

Authors
  1. Vincenzo Iovino
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  2. Karol Żebrowski
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Correspondence to Vincenzo Iovino .

Editor information

Editors and Affiliations

  1. NTT Laboratories, Tokyo, Japan

    Tatsuaki Okamoto

  2. Shaanxi Normal University, Xi’an, China

    Yong Yu

  3. Hong Kong Polytechnic University, Hong Kong, China

    Man Ho Au

  4. University of Wollongong, Wollongong, New South Wales, Australia

    Yannan Li

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Iovino, V., Żebrowski, K. (2017). Mergeable Functional Encryption. In: Okamoto, T., Yu, Y., Au, M., Li, Y. (eds) Provable Security. ProvSec 2017. Lecture Notes in Computer Science(), vol 10592. Springer, Cham. https://doi.org/10.1007/978-3-319-68637-0_26

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  • DOI: https://doi.org/10.1007/978-3-319-68637-0_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68636-3

  • Online ISBN: 978-3-319-68637-0

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