Paper 2010/299

Faster Fully Homomorphic Encryption

Damien Stehle and Ron Steinfeld


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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Publication info
Published elsewhere. Full version of the corresponding Asiacrypt'10 article
fully homomorphic encryptionideal latticesSSSP
Contact author(s)
damien stehle @ gmail com
2010-09-09: revised
2010-05-25: received
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      author = {Damien Stehle and Ron Steinfeld},
      title = {Faster Fully Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2010/299},
      year = {2010},
      note = {\url{}},
      url = {}
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