Faster Fully Homomorphic Encryption

Damien Stehlé and 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].

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