Fully Homomorphic Encryption over the Integers with Shorter Public Keys

  • Jean-Sébastien Coron
  • Avradip Mandal
  • David Naccache
  • Mehdi Tibouchi
Conference paper

DOI: 10.1007/978-3-642-22792-9_28

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6841)
Cite this paper as:
Coron JS., Mandal A., Naccache D., Tibouchi M. (2011) Fully Homomorphic Encryption over the Integers with Shorter Public Keys. In: Rogaway P. (eds) Advances in Cryptology – CRYPTO 2011. CRYPTO 2011. Lecture Notes in Computer Science, vol 6841. Springer, Berlin, Heidelberg

Abstract

At Eurocrypt 2010 van Dijk et al. described a fully homomorphic encryption scheme over the integers. The main appeal of this scheme (compared to Gentry’s) is its conceptual simplicity. This simplicity comes at the expense of a public key size in \({\cal \tilde O}(\lambda^{10})\) which is too large for any practical system. In this paper we reduce the public key size to \({\cal \tilde O}(\lambda^{7})\) by encrypting with a quadratic form in the public key elements, instead of a linear form. We prove that the scheme remains semantically secure, based on a stronger variant of the approximate-GCD problem, already considered by van Dijk et al.

We also describe the first implementation of the resulting fully homomorphic scheme. Borrowing some optimizations from the recent Gentry-Halevi implementation of Gentry’s scheme, we obtain roughly the same level of efficiency. This shows that fully homomorphic encryption can be implemented using simple arithmetic operations.

Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Jean-Sébastien Coron
    • 1
  • Avradip Mandal
    • 1
  • David Naccache
    • 2
  • Mehdi Tibouchi
    • 1
    • 2
  1. 1.Université du LuxembourgLuxembourg
  2. 2.École normale supérieureFrance

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