Minimizing the Number of Bootstrappings in Fully Homomorphic Encryption View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2016

AUTHORS

Marie Paindavoine , Bastien Vialla

ABSTRACT

There has been great progress regarding efficient implementations of fully homomorphic encryption schemes since the first construction by Gentry. However, evaluating complex circuits is still undermined by the necessary resort to the bootstrapping procedure. Minimizing the number of times such procedure is called is a simple yet very efficient way to critically improve performances of homomorphic evaluations. To tackle this problem, a first solution has been proposed in 2013 by Lepoint and Paillier, using boolean satisfiability. But their method cannot handle the versatility of fully homomorphic encryption schemes. In this paper, we go one step forward providing two main contributions. First, we prove that the problem of minimizing bootstrapping is NP-complete with a reduction from a graph problem. Second, we propose a flexible technique that permits to determine both such minimal number of bootstrappings and where to place them in the circuit. Our method is mainly based on linear programming. Our result can advantageously be applied to existing constructions. As an example, we show that for the Smart-Tillich AES circuit, published on the Internet in 2012, we find about 70 % less bootstrappings than naive methods. More... »

PAGES

25-43

References to SciGraph publications

  • 2005. Evaluating 2-DNF Formulas on Ciphertexts in THEORY OF CRYPTOGRAPHY
  • 2015-04-14. FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second in ADVANCES IN CRYPTOLOGY -- EUROCRYPT 2015
  • 2012. Homomorphic Evaluation of the AES Circuit in ADVANCES IN CRYPTOLOGY – CRYPTO 2012
  • 2011. Fully Homomorphic Encryption over the Integers with Shorter Public Keys in ADVANCES IN CRYPTOLOGY – CRYPTO 2011
  • 1999-04-15. Public-Key Cryptosystems Based on Composite Degree Residuosity Classes in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’99
  • 2010. Fully Homomorphic Encryption over the Integers in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2010
  • 2013. Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based in ADVANCES IN CRYPTOLOGY – CRYPTO 2013
  • 2000-11-24. A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms in ADVANCES IN CRYPTOLOGY
  • 2012. Fully Homomorphic Encryption with Polylog Overhead in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2012
  • 2013. On the Minimal Number of Bootstrappings in Homomorphic Circuits in FINANCIAL CRYPTOGRAPHY AND DATA SECURITY
  • Book

    TITLE

    Selected Areas in Cryptography – SAC 2015

    ISBN

    978-3-319-31300-9
    978-3-319-31301-6

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-31301-6_2

    DOI

    http://dx.doi.org/10.1007/978-3-319-31301-6_2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1036619867


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