Faster Fully Homomorphic Encryption

  • Damien Stehlé
  • Ron Steinfeld
Conference paper

DOI: 10.1007/978-3-642-17373-8_22

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6477)
Cite this paper as:
Stehlé D., Steinfeld R. (2010) Faster Fully Homomorphic Encryption. In: Abe M. (eds) Advances in Cryptology - ASIACRYPT 2010. ASIACRYPT 2010. Lecture Notes in Computer Science, vol 6477. Springer, Berlin, Heidelberg

Abstract

We describe two improvements to Gentry’s fully homomorphic scheme based on ideal lattices and its analysis: we provide a more aggressive analysis of one of the hardness assumptions (the one related to the Sparse Subset Sum Problem) and we introduce a probabilistic decryption algorithm that can be implemented with an algebraic circuit of low multiplicative degree. Combined together, these improvements lead to a faster fully homomorphic scheme, with a Õ(λ3.5) bit complexity per elementary binary add/mult gate, where λ is the security parameter. These improvements also apply to the fully homomorphic schemes of Smart and Vercauteren [PKC’2010] and van Dijk et al. [Eurocrypt’2010].

Keywords

fully homomorphic encryption ideal lattices SSSP 
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Copyright information

© International Association for Cryptologic Research 2010

Authors and Affiliations

  • Damien Stehlé
    • 1
  • Ron Steinfeld
    • 2
  1. 1.CNRS, Laboratoire LIP (U. Lyon, CNRS, ENS de Lyon, INRIA, UCBL)France
  2. 2.Centre for Advanced Computing - Algorithms and Cryptography, Department of ComputingMacquarie UniversityAustralia

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