Vectorial bent functions in odd characteristic and their components

被引:0
|
作者
Ayça Çeşmelioğlu
Wilfried Meidl
Alexander Pott
机构
[1] İstanbul Bilgi University,Johann Radon Institute for Computational and Applied Mathematics
[2] Austrian Academy of Sciences,undefined
[3] Otto von Guericke University,undefined
[4] Faculty of Mathematics,undefined
来源
Cryptography and Communications | 2020年 / 12卷
关键词
Vectorial bent functions; 94B25; 11T71;
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中图分类号
学科分类号
摘要
Bent functions in odd characteristic can be either (weakly) regular or non-weakly regular. Furthermore one can distinguish between dual-bent functions, which are bent functions for which the dual is bent as well, and non-dual bent functions. Whereas a weakly regular bent function always has a bent dual, a non-weakly regular bent function can be either dual-bent or non-dual-bent. The classical constructions (like quadratic bent functions, Maiorana-McFarland or partial spread) yield weakly regular bent functions, but meanwhile one knows constructions of infinite classes of non-weakly regular bent functions of both types, dual-bent and non-dual-bent. In this article we focus on vectorial bent functions in odd characteristic. We first show that most p-ary bent monomials and binomials are actually vectorial constructions. In the second part we give a positive answer to the question if non-weakly regular bent functions can be components of a vectorial bent function. We present the first construction of vectorial bent functions of which the components are non-weakly regular but dual-bent, and the first construction of vectorial bent functions with non-dual-bent components.
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页码:899 / 912
页数:13
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