Hyper-bent functions as a subclass of bent functions attract much interest and it is elusive to completely characterize hyper-bent functions. Most of known hyper-bent functions are Boolean functions with Dillon exponents and they are often characterized by special values of Kloosterman sums. In this paper, we present a method for characterizing hyper-bent functions with Dillon exponents. A clas...

In this paper, we introduce a class of cubic rotation symmetric (RotS) functions and prove that it can yield bent and semi-bent functions. To the best of our knowledge, this is the second primary construction of an infinite class of nonquadratic RotS bent functions which could be found and the first class of nonquadratic RotS semi-bent functions. We also study a class of idempotents (giving Rot...

We introduce the notion of k-bent function, here k is integer, 1 6 k 6 m/2, and m is an even number of variables. The parameter k makes the property of “bentness” more strong as k grows up. 1-Bent functions and bent functions coincide. The constructions of k-bent functions for any k are given. We study the cryptanalysis (of a block cipher) based on special quadratic approximations and prove tha...

Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied firstly by Dillon and next by many researchers for four decades. Since the complete classification of bent functions seems elusive, many researchers turn to design constructions of bent functions. In this note, we show that linear involutions (which are an important class of ...

The maximum length sequences, also called m-sequences, have received a lot of attention since the late sixties. In terms of LFSR synthesis they are usually generated by certain power polynomials over finite field and in addition characterized by a low cross correlation and high nonlinearity. We say that such sequence is generated by a semi-bent function. Some new families of such function, repr...

The paper is dealing with two important subclasses of plateaued functions: bent and semi-bent functions. In the first part of the paper, we construct mainly bent and semi-bent functions in the Maiorana-McFarland class using Boolean functions having linear structures (linear translators) systematically. Although most of these results are rather direct applications of some recent results, using l...

In this paper, we obtain the cross-correlation spectrum of generalized bent Boolean functions in a subclass of MaioranaMcFarland class (GMMF). An affine transformation which preserve the cross-correlation spectrum of two generalized Boolean functions, in absolute value is also presented. A construction of generalized bent Boolean functions in (n+ 2) variables from four generalized Boolean funct...

Boolean functions form basic building blocks in various cryptographic algorithms. They are used for instance as filters in stream ciphers. Maximally non-linear (necessarily non-balanced) Boolean functions with an even number of variables are called bent functions. Bent functions can be modified to get balanced highly non-linear Boolean functions. Recently the first author has demonstrated how b...

Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh spectrum of two class of 2-plateaued functions obtained in this paper is completely determined. Additionally, we construct the first class of p-ary bent functions ...