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Homomorphic Encryption with Access Policies: Characterization and New Constructions

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Progress in Cryptology – AFRICACRYPT 2013 (AFRICACRYPT 2013)

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Abstract

A characterization of predicate encryption (PE) with support for homomorphic operations is presented and we describe the homomorphic properties of some existing PE constructions. Even for the special case of IBE, there are few known group-homomorphic cryptosystems. Our main construction is an XOR-homomorphic IBE scheme based on the quadratic residuosity problem (variant of the Cocks’ scheme), which we show to be strongly homomorphic. We were unable to construct an anonymous variant that preserves this homomorphic property, but we achieved anonymity for a weaker notion of homomorphic encryption, which we call non-universal. A related security notion for this weaker primitive is formalized. Finally, some potential applications and open problems are considered.

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Author information

Authors and Affiliations

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

    Michael Clear, Arthur Hughes & Hitesh Tewari

Authors
  1. Michael Clear
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  2. Arthur Hughes
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  3. Hitesh Tewari
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Editor information

Editors and Affiliations

  1. Concordia Institute for Information Systems Engineering, Concordia University, 1515 St. Catherine Street West, H3G 2W1, Montreal, QC, Canada

    Amr Youssef

  2. Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Basse-Normandie, BP 5186, 14032, Caen, France

    Abderrahmane Nitaj

  3. Department of Information Technology, Cairo University, 5 Dr. Ahmed Zewil Street, 12613, Cairo, Giza, Egypt

    Aboul Ella Hassanien

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Clear, M., Hughes, A., Tewari, H. (2013). Homomorphic Encryption with Access Policies: Characterization and New Constructions. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds) Progress in Cryptology – AFRICACRYPT 2013. AFRICACRYPT 2013. Lecture Notes in Computer Science, vol 7918. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38553-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-38553-7_4

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