### Somewhat Practical Fully Homomorphic Encryption

Junfeng Fan and Frederik Vercauteren

##### Abstract

In this paper we port Brakerski's fully homomorphic scheme based on the Learning With Errors (LWE) problem to the ring-LWE setting. We introduce two optimised versions of relinearisation that not only result in a smaller relinearisation key, but also faster computations. We provide a detailed, but simple analysis of the various homomorphic operations, such as multiplication, relinearisation and bootstrapping, and derive tight worst case bounds on the noise caused by these operations. The analysis of the bootstrapping step is greatly simplified by using a modulus switching trick. Finally, we derive concrete parameters for which the scheme provides a given level of security and becomes fully homomorphic.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Fully homomorphic encryption
Contact author(s)
frederik vercauteren @ gmail com
History
Short URL
https://ia.cr/2012/144

CC BY

BibTeX

@misc{cryptoeprint:2012/144,
author = {Junfeng Fan and Frederik Vercauteren},
title = {Somewhat Practical Fully Homomorphic Encryption},
howpublished = {Cryptology ePrint Archive, Paper 2012/144},
year = {2012},
note = {\url{https://eprint.iacr.org/2012/144}},
url = {https://eprint.iacr.org/2012/144}
}

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