Fixed-point arithmetic in SHE schemes

Ana Costache, Nigel Smart, Srinivas Vivek, Adrian Waller

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

12 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationSelected Areas in Cryptography - SAC 2016
Subtitle of host publication23rd International Conference, St. John’s, NL, Canada, August 10-12, Revised Selected Papers
Number of pages22
ISBN (Electronic)9783319694535
ISBN (Print)9783319694528
Publication statusE-pub ahead of print - 20 Oct 2017

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
ISSN (Print)0302-9743

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