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Bootstrappable Identity-Based Fully Homomorphic Encryption

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Cryptology and Network Security (CANS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8813))

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Abstract

It has been an open problem for a number of years to construct an identity-based fully homomorphic encryption (IBFHE) scheme (first mentioned by Naccache at CHES/CRYPTO 2010). At CRYPTO 2013, Gentry, Sahai and Waters largely settled the problem by presenting leveled IBFHE constructions based on the Learning With Errors problem. However their constructions are not bootstrappable, and as a result, are not “pure” IBFHE schemes. The major challenge with bootstrapping in the identity-based setting is that it must be possible to non-interactively derive from the public parameters an “encryption” of the secret key for an arbitrary identity. All presently-known leveled IBFHE schemes only allow bootstrapping if such an “encryption” of the secret key is supplied out-of-band. In this work, we present a “pure” IBFHE scheme from indistinguishability obfuscation, and extend the result to the attribute-based setting. Our attribute-based scheme is the first to support homomorphic evaluation on ciphertexts with different attributes. Finally, we characterize presently-known leveled IBFHE schemes with a view to developing a “compiler” from a leveled IBFHE scheme to a bootstrappable IBFHE scheme, and sufficient conditions are identified.

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Author information

Authors and Affiliations

  1. School of Computer Science and Statistics, Trinity College Dublin, Ireland

    Michael Clear & Ciarán McGoldrick

Authors
  1. Michael Clear
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  2. Ciarán McGoldrick
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Editor information

Editors and Affiliations

  1. Department of Informatics, Athens University of Economics & Business, 76, Patission Str., 10434, Athens, Greece

    Dimitris Gritzalis

  2. Department of Informatics and Telecommunications, Panepistimiopolis, National and Kapodistrian University of Athens, 15784, Athens, Greece

    Aggelos Kiayias

  3. FORTH-ICS, Vassilika Vouton, P.O. Box 1385, 711 10, Heraklion, Crete, Greece

    Ioannis Askoxylakis

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Clear, M., McGoldrick, C. (2014). Bootstrappable Identity-Based Fully Homomorphic Encryption. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds) Cryptology and Network Security. CANS 2014. Lecture Notes in Computer Science, vol 8813. Springer, Cham. https://doi.org/10.1007/978-3-319-12280-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-12280-9_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12279-3

  • Online ISBN: 978-3-319-12280-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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