Cryptology ePrint Archive: Report 2016/250

Fixed Point Arithmetic in SHE Scheme

A. Costache and N.P. Smart and 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.

Category / Keywords: implementation /

Original Publication (in the same form): SAC 2016

Date: received 7 Mar 2016, last revised 25 Sep 2016

Contact author: anamaria costache at bristol ac uk,nigel@cs bris ac uk,sv venkatesh@bristol ac uk,Adrian Waller@uk thalesgroup com

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Version: 20160925:165122 (All versions of this report)

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