## Maximally Nonlinear Functions and Bent Functions

Published in Designs, Codes and Cryptography

We give a construction of bent functions in 2n variables, here n is odd, by using maximally nonlinear functions on GF(2n).

Published in Designs, Codes and Cryptography

We give a construction of bent functions in 2n variables, here n is odd, by using maximally nonlinear functions on GF(2n).

We introduce the notion of a bent function on a finite nonabelian group which is a natural generalization of the well-known notion of bentness on a finite abelian group due to Logachev, Salnikov and Yashchenko. Using the theory of linear representations and noncommutative harmonic analysis of finite groups we obtain several properties of such funct...

Bent or perfect nonlinear Boolean functions represent the best resistance against the so-called linear and differential cryptanalysis. But this kind of cryptographic relevant functions only exists when the number of input bits m is an even integer and is larger than the double of the number of output bits n. Unfortunately the non-existence cases, t...

Published in Frontiers of Electrical and Electronic Engineering in China

Bent functions in trace forms play an important role in the constructions of generalized binary Bent sequences. Trace representation of some degree two Bent functions are presented in this paper. A sufficient and necessary condition is derived to determine whether the sum of the combinations of Gold functions, \documentclass[12pt]{minimal} \usepack...

A function from a finite Abelian group G and with values in the unit circle T of the complex field is called bent if its Fourier transform (i.e., the decomposition of f in the basis of characters of G) has a constant magnitude equals to the number of elements of G. In this contribution we define a modulo 2 notion of characters by allowing the chara...

The left-regular multiplication is explicitly embedded in the notion of perfect nonlinearity. But there exist many other group actions. By replacing translations by another group action the new concept of group action-based perfect nonlinearity has been introduced. In this paper we show that this generalized concept of nonlinearity is actually equi...

In this presentation a technique for constructing bent func- tions from plateaued functions is introduced. This generalizes earlier techniques for constructing bent from near-bent functions. Analysing the Fourier spectrum of quadratic functions we then can construct weakly regular as well as non-weakly regular bent functions both in even and odd di...

Published in Cryptography and Communications

Perfect nonlinear functions from a finite group G to another one H are those functions f: G →H such that for all nonzero α ∈ G, the derivative \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6...

Published in Journal of Systems Science and Complexity

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding ...

To identify and specify trace bent functions of the form T r n 1 (P (x)), where P (x) ∈ GF (2 n)[x], has been an important research topic lately. We show that an infinite class of quadratic vectorial bent functions can be specified in the univariate polynomial form as F (x) = T r^n_k (αx^2^i (x + x^k)), where n = 2k, i = 0,n-1, and α \notin GF(2^k)...