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On Constructing Homomorphic Encryption Schemes from Coding Theory

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Cryptography and Coding (IMACC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7089))

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Abstract

We introduce a generic construction principle for homomorphic encryption schemes based on coding theory These possess several non-standard positive features. First, they are not restricted to linear homomorphism but allow for evaluating multivariate polynomials up to a fixed (but arbitrary) degree μ on encrypted field elements. Second, they can be instantiated with various error correcting codes, even for codes with poor correcting capabilities. Third, depending on the deployed code, one can achieve very efficient schemes.

As a concrete example, we present an instantiation based on Reed-Muller codes where for μ = 2 and μ = 3 and security levels between 80 and 128 bits, all operations take less than a second (after some pre-computation). However, our analysis reveals also limitations on this approach. For structural reasons, such schemes cannot be public-key, allow for a limited number of fresh encryptions only, and cannot be combined with the bootstrapping technique. We argue why such schemes are nonetheless useful in certain application scenarios and discuss possible directions on how to overcome these issues.

The work described in this paper has been supported by the Commission of the European Communities through the ICT program under contract ICT-2007-216676 (ECRYPT-II). L. Perret is also supported by the french ANR under the CAC project (ANR-09-JCJCJ-0064-01) and the EXACTA project (ANR-09-BLAN-0371-01).

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Author information

Authors and Affiliations

  1. Universität Mannheim, Germany

    Frederik Armknecht

  2. LIX - INRIA Saclay-Ile de, France

    Daniel Augot

  3. UPMC, University Paris 06/INRIA, France

    Ludovic Perret

  4. Technische Universität Darmstadt, Germany & Fraunhofer SIT, Germany

    Ahmad-Reza Sadeghi

Authors
  1. Frederik Armknecht
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  2. Daniel Augot
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  3. Ludovic Perret
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  4. Ahmad-Reza Sadeghi
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Editors and Affiliations

  1. Hewlett-Packard Laboratories, UK

    Liqun Chen

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Armknecht, F., Augot, D., Perret, L., Sadeghi, AR. (2011). On Constructing Homomorphic Encryption Schemes from Coding Theory. In: Chen, L. (eds) Cryptography and Coding. IMACC 2011. Lecture Notes in Computer Science, vol 7089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25516-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-25516-8_3

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