Strong external difference families in abelian and non-abelian groups
Abstract
Strong external difference families (SEDFs) have applications to cryptography and are rich combinatorial structures in their own right. We extend the definition of SEDF from abelian groups to all finite groups, and introduce the concept of equivalence. We prove new recursive constructions for SEDFs and generalized SEDFs (GSEDFs) in cyclic groups, and present the first family of non-abelian SEDFs. We prove there exist at least two non-equivalent (k2 + 1,2,k,1)-SEDFs for every k > 2, and begin the task of enumerating SEDFs, via a computational approach which yields complete results for all groups up to order 24.
Citation
Huczynska , S , Jefferson , C & Nepšinská , S 2021 , ' Strong external difference families in abelian and non-abelian groups ' , Cryptography and Communications , vol. 13 , no. 2 , pp. 331–341 . https://doi.org/10.1007/s12095-021-00473-3
Publication
Cryptography and Communications
Status
Peer reviewed
ISSN
1936-2447Type
Journal article
Rights
Copyright © The Author(s) 2021. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Description
The second author is supported by a Royal Society University Research Fellowship.Collections
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