In this survey, we revisit the Rothaus paper and the chapter of Dillon's thesis dedicated to
bent functions, and we describe the main results obtained on these functions during these …

Bent Functions: Results and Applications to Cryptography offers a unique survey of the
objects of discrete mathematics known as Boolean bent functions. As these maximal …

We introduce a new class of bent functions on (GF (2)) n (n even). We prove that this class is
not included in one of the known classes of bent functions, and that, when n equals 6, it …

One of the classes of bent Boolean functions introduced by John Dillon in his thesis is family
H. While this class corresponds to a nice original construction of bent functions in bivariate …

Bent functions are maximally nonlinear Boolean functions with an even number of variables.
They were introduced by Rothaus in 1976. For their own sake as interesting combinatorial …

Boolean functions are important objects in discrete mathematics. They play a role in
mathematics and almost all the domains of computer science. In this book, we are mainly …

For any Boolean function f on GF (2) m, we define a sequence of ranks ri (f), 1⩽ i⩽ m, which
are invariant under the action of the general linear group GL (m, 2). If f is a cubic bent …

Bent functions have maximal minimum distance to the set of affine functions. In other words,
they achieve the maximal minimum distance to all the coordinate functions of affine …

In this paper, we investigate the properties of generalized bent functions defined on Z _2^ n
with values in Z _q, where q≥ 2 is any positive integer. We characterize the class of …

Almost bent functions oppose an optimum resistance to linear and differential cryptanalysis.
We present basic properties of almost bent functions; particularly we give an upper bound …