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Cryptography and Communications

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30-05-2019

Image sets with regularity of differences

Authors: Patrick G. Cesarz, Robert S. Coulter

Published in: Cryptography and Communications | Issue 6/2019

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Abstract

In the last few decades we’ve seen several results connecting the image sets of some special functions to differences sets and partial difference sets. Examples here include planar functions (skew-Hadamard difference sets), and (more classically) monomials (cyclotomic DS). It can be observed that there is a commonality (in the main) among the behaviour of these functions, in that there tends to be a certain regularity in the number of times each image occurs. In this paper, we instigate a new approach to constructing sets with regularity of differences based on the above observation. Specifically, we show how functions over finite fields exhibiting a regularity of images can yield image sets that exhibit some sort of difference regularity.

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Title: Image sets with regularity of differences
Authors: Patrick G. Cesarz
Robert S. Coulter
Publication date: 30-05-2019
Publisher: Springer US
Published in: Cryptography and Communications / Issue 6/2019
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-019-00358-6

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