The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dans cette lettre, nous présentons une construction de fonctions courbées qui généralise un travail de Zhang et al. en 2016. Sur cette base, nous obtenons une fonction cubique courbée en 10 variables et prouvons qu'elle n'a pas de dérivée affine et n'appartient pas à la classe complète de Maiorana-McFarland, qui est opposée à toutes les fonctions courbées cubiques à 6/8 variables. car ils sont à l'intérieur de la classe Maiorana-McFarland terminée. C'est la première fois qu'une preuve théorique est donnée pour montrer que les fonctions cubiques courbées à 10 variables peuvent être en dehors de la classe complète de Maiorana-McFarland. Avant cela, seul un exemple sporadique présentant de telles propriétés était connu par recherche informatique. Nous montrons également que notre fonction est EA-ineéquivalente à cette fonction sporadique.
Yanjun LI
Anhui University of Finance and Economics
Haibin KAN
Fudan University
Jie PENG
Shanghai Normal University
Chik How TAN
National University of Singapore
Baixiang LIU
Fudan University
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Yanjun LI, Haibin KAN, Jie PENG, Chik How TAN, Baixiang LIU, "A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 9, pp. 1353-1356, September 2021, doi: 10.1587/transfun.2021EAL2003.
Abstract: In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2003/_p
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@ARTICLE{e104-a_9_1353,
author={Yanjun LI, Haibin KAN, Jie PENG, Chik How TAN, Baixiang LIU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class},
year={2021},
volume={E104-A},
number={9},
pages={1353-1356},
abstract={In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.},
keywords={},
doi={10.1587/transfun.2021EAL2003},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - A New 10-Variable Cubic Bent Function Outside the Completed Maiorana-McFarland Class
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1353
EP - 1356
AU - Yanjun LI
AU - Haibin KAN
AU - Jie PENG
AU - Chik How TAN
AU - Baixiang LIU
PY - 2021
DO - 10.1587/transfun.2021EAL2003
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2021
AB - In this letter, we present a construction of bent functions which generalizes a work of Zhang et al. in 2016. Based on that, we obtain a cubic bent function in 10 variables and prove that, it has no affine derivative and does not belong to the completed Maiorana-McFarland class, which is opposite to all 6/8-variable cubic bent functions as they are inside the completed Maiorana-McFarland class. This is the first time a theoretical proof is given to show that the cubic bent functions in 10 variables can be outside the completed Maiorana-McFarland class. Before that, only a sporadic example with such properties was known by computer search. We also show that our function is EA-inequivalent to that sporadic one.
ER -