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Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers

  • Jean-Sébastien Coron
  • David Naccache
  • Mehdi Tibouchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7237)

Abstract

We describe a compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan’s (DGHV) fully homomorphic scheme over the integers from \({\cal \tilde O}(\lambda^{7})\) to \({\cal \tilde O}(\lambda^5)\). Our variant remains semantically secure, but in the random oracle model. We obtain an implementation of the full scheme with a 10.1 MB public key instead of 802 MB using similar parameters as in [7]. Additionally we show how to extend the quadratic encryption technique of [7] to higher degrees, to obtain a shorter public-key for the basic scheme.

This paper also describes a new modulus switching technique for the DGHV scheme that enables to use the new FHE framework without bootstrapping from Brakerski, Gentry and Vaikuntanathan with the DGHV scheme. Finally we describe an improved attack against the Approximate GCD Problem on which the DGHV scheme is based, with complexity \({\cal \tilde O}(2^\rho)\) instead of \({\cal \tilde O}(2^{3\rho/2})\).

Keywords

Full Version Homomorphic Encryption Random Oracle Model Cryptology ePrint Archive Homomorphic Encryption Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Jean-Sébastien Coron
    • 1
  • David Naccache
    • 2
  • Mehdi Tibouchi
    • 3
  1. 1.Université du LuxembourgLuxembourg
  2. 2.École normale supérieureFrance
  3. 3.NTT Information Sharing Platform LaboratoriesJapan

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