Strong external difference families in abelian and non-abelian groups

Sophie Huczynska; Christopher Jefferson; Silvia Nepšinská

doi:10.1007/s12095-021-00473-3

Strong external difference families in abelian and non-abelian groups

Sophie Huczynska, Christopher Jefferson, Silvia Nepšinská

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	331–341
Number of pages	11
Journal	Cryptography and Communications
Volume	13
Issue number	2
Early online date	8 Feb 2021
DOIs	https://doi.org/10.1007/s12095-021-00473-3
Publication status	Published - Mar 2021

Keywords

Strong external difference family
R-optimal AMD code

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10.1007/s12095-021-00473-3Licence: CC BY

Huczynska_2021_CC_Strongexternal_CC
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/.
Final published version, 277 KBLicence: CC BY

RS Research Fellowship Renewal: RS Research Fellowship Renewal
Jefferson, C. A. (PI)
The Royal Society
1/10/18 → 31/03/22
Project: Fellowship

Cite this

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keywords = "Strong external difference family, R-optimal AMD code",

author = "Sophie Huczynska and Christopher Jefferson and Silvia Nep{\v s}insk{\'a}",

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AU - Huczynska, Sophie

AU - Jefferson, Christopher

AU - Nepšinská, Silvia

N1 - The second author is supported by a Royal Society University Research Fellowship.

PY - 2021/3

Y1 - 2021/3

N2 - 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.

AB - 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.

KW - Strong external difference family

KW - R-optimal AMD code

U2 - 10.1007/s12095-021-00473-3

DO - 10.1007/s12095-021-00473-3

M3 - Article

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VL - 13

SP - 331

EP - 341

JO - Cryptography and Communications

JF - Cryptography and Communications

IS - 2

ER -

Strong external difference families in abelian and non-abelian groups

Abstract

Keywords

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Projects

RS Research Fellowship Renewal: RS Research Fellowship Renewal

Cite this