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Efficient Integer Encoding for Homomorphic Encryption via Ring Isomorphisms

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Book cover Progress in Cryptology - LATINCRYPT 2014 (LATINCRYPT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8895))

Abstract

Homomorphic encryption allows computation on encrypted data at the cost of a significant loss in efficiency. In this paper we propose a powerful integer encoding for homomorphic encryption. The proposed encoding offers more efficient and convenient homomorphic computations on integers compared to previously used methods. This is possible by making the message space of the encryption scheme isomorphic to an integer quotient ring. The encoding can be used across various lattice-based homomorphic encryption schemes such as NTRU and various ring-LWE based schemes. We analyse the efficiency of our proposed encoding, which shows a significant gain compared to a naive integer encoding for a ring-LWE based scheme.

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Notes

  1. 1.

    We use the notation \([a_{i,j}]\) to represent a matrix of input values.

  2. 2.

    We set \(p'=3\) for \(p=x-2\) because for \(a\in R\) it holds that \(\left\| [(x-2)*a]_R\right\| _\infty \le 3\cdot \left\| a\right\| _\infty \).

  3. 3.

    Benchmarks were written in C++ using NTL, a library for doing number theory, and run on a machine with an Intel Core i5-2557M CPU and 4GB of RAM.

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Author information

Authors and Affiliations

  1. Technische Universität Darmstadt, Darmstadt, Germany

    Matthias Geihs

  2. Universidad Nacional de Colombia Sede Medellín, Medellín, Colombia

    Daniel Cabarcas

Authors
  1. Matthias Geihs
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  2. Daniel Cabarcas
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Correspondence to Matthias Geihs .

Editor information

Editors and Affiliations

  1. University of Campinas, Campinas, Brazil

    Diego F. Aranha

  2. University of Waterloo, Waterloo, Ontario, Canada

    Alfred Menezes

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Geihs, M., Cabarcas, D. (2015). Efficient Integer Encoding for Homomorphic Encryption via Ring Isomorphisms. In: Aranha, D., Menezes, A. (eds) Progress in Cryptology - LATINCRYPT 2014. LATINCRYPT 2014. Lecture Notes in Computer Science(), vol 8895. Springer, Cham. https://doi.org/10.1007/978-3-319-16295-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-16295-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16294-2

  • Online ISBN: 978-3-319-16295-9

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