Paper 2016/250
Fixed Point Arithmetic in SHE Scheme
A. Costache, N. P. Smart, S. Vivek, and A. Waller
Abstract
The purpose of this paper is to investigate fixed-point arithmetic in ring-based Somewhat Homomorphic Encryption (SHE) schemes. We provide three main contributions: firstly, we investigate the representation of fixed-point numbers. We analyse the two representations from Dowlin et al, representing a fixed-point number as a large integer (encoded as a scaled polynomial) versus a polynomial-based fractional representation. We show that these two are, in fact, isomorphic by presenting an explicit isomorphism between the two that enables us to map the parameters from one representation to another. Secondly, given a computation and a bound on the fixed-point numbers used as inputs and scalars within the computation, we achieve a way of producing lower bounds on the plaintext modulus $p$ and the degree of the ring $d$ needed to support complex homomorphic operations. Finally, as an application of these bounds, we investigate homomorphic image processing.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Published elsewhere. SAC 2016
- Contact author(s)
-
anamaria costache @ bristol ac uk
nigel @ cs bris ac uk
sv venkatesh @ bristol ac uk
Adrian Waller @ uk thalesgroup com - History
- 2016-09-25: revised
- 2016-03-07: received
- See all versions
- Short URL
- https://ia.cr/2016/250
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2016/250,
author = {A. Costache and N. P. Smart and S. Vivek and A. Waller},
title = {Fixed Point Arithmetic in {SHE} Scheme},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/250},
year = {2016},
url = {https://eprint.iacr.org/2016/250}
}
