Constructions of Quadratic and Cubic Rotation Symmetric Bent Functions

被引：42
|
作者：
Gao, Guangpu [1 ]
Zhang, Xiyong [1 ]
Liu, Wenfen [1 ]
Carlet, Claude [2 ,3 ,4 ]
机构：
[1] Zhengzhou Informat Sci & Technol Inst, Dept Appl Math, Zhengzhou 450002, Peoples R China
[2] Univ Paris 08, LAGA, F-93526 St Denis, France
[3] Univ Paris 13, LAGA, F-93526 St Denis, France
[4] CNRS, F-93526 St Denis, France
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2012年 / 58卷 / 07期
关键词：
Bent function; cubic function; Maiorana-McFarland class of bent function; quadratic function; rotation symmetric (RotS) Boolean function; BOOLEAN FUNCTIONS;
D O I：
10.1109/TIT.2012.2193377
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we consider constructions of rotation symmetric bent functions, which are of the forms: f(c)(x) = Sigma(m-1)(i=1) c(i)(Sigma(n-1)(j=0) x(j)x(i+j)) + c(m) (Sigma(m-1)(j=0) x(j)x(m+j)) and, f(t)(x) = Sigma(n-1)(i=0) (x(i)x(t)+(i)x(m+i) + x(i)x(t+i)) + Sigma(m-1)(i=0) x(i)x(m+i) where, n = 2m, c(i) is an element of {0, 1} (the subscript u of x(u) in the previous expressions is taken as u modulo n). For each case, a necessary and sufficient condition is obtained. To the best of our knowledge, this class of cubic rotation symmetric bent functions is the first example of an infinite class of nonquadratic rotation symmetric bent functions.
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收藏
页码：4908 / 4913
页数：6
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