Faster Fully Homomorphic Encryption

Damien Stehle; Ron Steinfeld

Paper 2010/299

Faster Fully Homomorphic Encryption

Damien Stehle 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].

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Full version of the corresponding Asiacrypt'10 article
Keywords: fully homomorphic encryption ideal lattices SSSP
Contact author(s): damien stehle @ gmail com
History: 2010-09-09: revised; 2010-05-25: received; See all versions
Short URL: https://ia.cr/2010/299
License: CC BY

BibTeX

@misc{cryptoeprint:2010/299,
      author = {Damien Stehle and Ron Steinfeld},
      title = {Faster Fully Homomorphic Encryption},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/299},
      year = {2010},
      url = {https://eprint.iacr.org/2010/299}
}