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International Conference on Cryptology in Africa

AFRICACRYPT 2012: Progress in Cryptology - AFRICACRYPT 2012 pp 234–251Cite as

Shift-Type Homomorphic Encryption and Its Application to Fully Homomorphic Encryption

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7374))

Abstract

This work addresses the characterization of homomorphic encryption schemes both in terms of security and design. In particular, we are interested in currently existing fully homomorphic encryption (FHE) schemes and their common structures and security. Our main contributions can be summarized as follows:

  • We define a certain type of homomorphic encryption that we call shift-type and identify it as the basic underlying structure of all existing homomorphic encryption schemes. It generalizes the already known notion of shift-type group homomorphic encryption.

  • We give an IND-CPA characterization of all shift-type homomorphic encryption schemes in terms of an abstract subset membership problem.

  • We show that this characterization carries over to all leveled FHE schemes that arise by applying Gentry’s bootstrapping technique to shift-type homomorphic encryption schemes. Since this is the common structure of all existing schemes, our result actually characterizes the IND-CPA security of all existing bootstrapping-based leveled FHE.

  • We prove that the IND-CPA security of FHE schemes that offer a certain type of circuit privacy (for FHE schemes with a binary plaintext space we require circuit privacy for a single AND-gate and, in fact, all existing binary-plaintext FHE schemes offer this) and are based on Gentry’s bootstrapping technique is equivalent to the circular security of the underlying bootstrappable scheme.

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Author information

Authors and Affiliations

  1. Theoretical Computer Science and IT Security Group, Universität Mannheim, Germany

    Frederik Armknecht

  2. Security Engineering Group, Technische Universität Darmstadt and CASED, Germany

    Stefan Katzenbeisser & Andreas Peter

Authors
  1. Frederik Armknecht
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  2. Stefan Katzenbeisser
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  3. Andreas Peter
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Editors and Affiliations

  1. Ecole Polytechnice Fédérale de Lausanne, IC - LASEC, Bâtiment INF 238, Station 14, 1015, Lausanne, Switzerland

    Aikaterini Mitrokotsa  & Serge Vaudenay  & 

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Armknecht, F., Katzenbeisser, S., Peter, A. (2012). Shift-Type Homomorphic Encryption and Its Application to Fully Homomorphic Encryption. In: Mitrokotsa, A., Vaudenay, S. (eds) Progress in Cryptology - AFRICACRYPT 2012. AFRICACRYPT 2012. Lecture Notes in Computer Science, vol 7374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31410-0_15

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  • DOI: https://doi.org/10.1007/978-3-642-31410-0_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31409-4

  • Online ISBN: 978-3-642-31410-0

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