dc.contributor.author | Beierle, Christof | |
dc.contributor.author | Carlet, Claude Michael | |
dc.date.accessioned | 2023-03-20T13:14:55Z | |
dc.date.available | 2023-03-20T13:14:55Z | |
dc.date.created | 2022-11-17T14:39:42Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 0925-1022 | |
dc.identifier.uri | https://hdl.handle.net/11250/3059285 | |
dc.description.abstract | In the independent works by Kalgin and Idrisova and by Beierle, Leander and Perrin, it was observed that the Gold APN functions over \(\mathbb {F}_{2^5}\) give rise to a quadratic APN function in dimension 6 having maximum possible linearity of \(2^5\) (that is, minimum possible nonlinearity \(2^4\)). In this article, we show that the case of \(n \le 5\) is quite special in the sense that Gold APN functions in dimension \(n>5\) cannot be extended to quadratic APN functions in dimension \(n+1\) having maximum possible linearity. In the second part of this work, we show that this is also the case for APN functions of the form \(x \mapsto x^3 + \mu (x)\) with \(\mu \) being a quadratic Boolean function. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Gold functions and switched cube functions are not 0-extendable in dimension n > 5 | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2022 The Author(s) | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | 10.1007/s10623-022-01111-6 | |
dc.identifier.cristin | 2075712 | |
dc.source.journal | Designs, Codes and Cryptography | en_US |
dc.source.pagenumber | 433-449 | en_US |
dc.identifier.citation | Designs, Codes and Cryptography. 2023, 91, 433-449. | en_US |
dc.source.volume | 91 | en_US |