Paper 2019/187

Fully homomorphic encryption modulo Fermat numbers

Antoine Joux

Abstract

In this paper, we recast state-of-the-art constructions for fully homomorphic encryption in the simple language of arithmetic modulo large Fermat numbers. The techniques used to construct our scheme are quite standard in the realm of (R)LWE based cryptosystems. However, the use of arithmetic in such a simple ring greatly simplifies exposition of the scheme and makes its implementation much easier. In terms of performance, our test implementation of the proposed scheme is slower than the current speed records but remains within a comparable range. We hope that the detailed study of our simplified scheme by the community can make it competitive and provide new insights into FHE constructions at large.