Name
Title | ||
|---|---|---|
Vectorial Bent Functions Weakly/Strongly Outside The Completed Maiorana-Mcfarland Class |
Abstract | ||
|---|---|---|
Two new classes of bent functions derived from the Maiorana-McFarland (M) class, so-called C and D, were introduced by Carlet (1994) two decades ago. The difficulty of satisfying their defining conditions was emphasized in Mandal et al. (2016). In a recent work Zhang et al. (2017) a set of efficient sufficient conditions for specifying bent functions in C and D which are outside the completed M class, denoted by M-#, was given. A natural follow up question is whether there is a possibility of extending this approach to the vectorial case. We introduce the property of vectorial bent functions that we call weakly or strongly outside M-#, referring respectively to the case whether some or all nonzero linear combinations (called components) of its coordinate functions are in class C (or D) but provably outside M-#. For the first time, quite different to a straightforward vectorial extension of the Maiorana-McFarland class and the class of Dillon PS ap , we show the existence of several classes of vectorial bent functions whose component functions come from different classes of bent functions, mainly from M and D, and in many cases being weakly outside M-#. We also address a difficult problem of specifying vectorial bent functions whose all components are in class C but provably outside M-#, thus being strongly outside M-#. Even though we could only specify a class of such functions whose dimension of bent vector space is only two, thus F : F-2(n) -> F-2(2), this is the very first evidence of their existence. (C) 2021 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.dam.2021.02.003 | DISCRETE APPLIED MATHEMATICS |
Keywords | DocType | Volume |
Bent functions, C and D class, Completed Maiorana-McFarland class, Class membership, Weakly and strongly outside M | Journal | 294 |
ISSN | Citations | PageRank |
0166-218X | 2 | 0.37 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Enes Pasalic | 1 | 362 | 42.34 |
| Fengrong Zhang | 2 | 10 | 3.61 |
| S. Kudin | 3 | 2 | 0.71 |
| Yongzhuang Wei | 4 | 69 | 16.94 |