International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Faster Fully Homomorphic Encryption

Damien Stehlé
Ron Steinfeld
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Abstract: We describe two improvements to Gentry's fully homomorphic scheme based on ideal lattices and its analysis: we provide a refined 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~$\softO(\lambda^{3})$ 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].
  title={Faster Fully Homomorphic Encryption},
  booktitle={IACR Eprint archive},
  keywords={fully homomorphic encryption, ideal lattices, SSSP},
  note={ 14749 received 19 May 2010},
  author={Damien Stehlé and Ron Steinfeld},