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Bent functions in the partial spread class generated by linear recurring sequences

Gadouleau, Maximilien; Mariot, Luca; Picek, Stjepan

Bent functions in the partial spread class generated by linear recurring sequences Thumbnail


Authors

Luca Mariot

Stjepan Picek



Abstract

We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if their feedback polynomials are relatively prime. Then, we characterize the appropriate parameters for a family of pairwise coprime polynomials to generate a partial spread required for the support of a bent function, showing that such families exist if and only if the degrees of the underlying polynomials are either 1 or 2. We then count the resulting sets of polynomials and prove that, for degree 1, our LRS construction coincides with the Desarguesian partial spread. Finally, we perform a computer search of all PS− and PS+ bent functions of n=8 variables generated by our construction and compute their 2-ranks. The results show that many of these functions defined by polynomials of degree d=2 are not EA-equivalent to any Maiorana–McFarland or Desarguesian partial spread function.

Citation

Gadouleau, M., Mariot, L., & Picek, S. (2023). Bent functions in the partial spread class generated by linear recurring sequences. Designs, Codes and Cryptography, 91(1), 63-82. https://doi.org/10.1007/s10623-022-01097-1

Journal Article Type Article
Acceptance Date Jul 28, 2022
Online Publication Date Aug 13, 2022
Publication Date 2023-01
Deposit Date Sep 13, 2022
Publicly Available Date Mar 15, 2023
Journal Designs, Codes and Cryptography
Print ISSN 0925-1022
Electronic ISSN 1573-7586
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 91
Issue 1
Pages 63-82
DOI https://doi.org/10.1007/s10623-022-01097-1

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
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/.







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