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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