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Title:
Faster Fully Homomorphic Encryption
Authors: Damien Stehle, Ron Steinfeld
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~\softO(\lambda^{3.5}) bit complexity per elementary binary add/mult gate, where~\lambda 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].
ePrint: https://eprint.iacr.org/2010/299
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