Four decades of research on bent functions
C Carlet, S Mesnager - Designs, codes and cryptography, 2016 - Springer
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, and we describe the main results obtained on these functions during these …
Design of highly nonlinear substitution boxes based on I-Ching operators
This paper is to design substitution boxes (S-Boxes) using innovative I-Ching operators
(ICOs) that have evolved from ancient Chinese I-Ching philosophy. These three operators …
(ICOs) that have evolved from ancient Chinese I-Ching philosophy. These three operators …
A survey on the applications of Niho exponents
The Niho exponent was introduced by Yoji Niho, who investigated the cross-correlation
function between an m-sequence and its decimation sequence in 1972. Since then, Niho …
function between an m-sequence and its decimation sequence in 1972. Since then, Niho …
Highly nonlinear balanced S-boxes with good differential properties
Substitution boxes (S-boxes) play a central role in the modern design of iterative block
ciphers. While in substitution-permutation networks the S-boxes are bijective, thus ensuring …
ciphers. While in substitution-permutation networks the S-boxes are bijective, thus ensuring …
[HTML][HTML] Constructions of (vectorial) bent functions outside the completed Maiorana–McFarland class
A Bapić, E Pasalic - Discrete Applied Mathematics, 2022 - Elsevier
Two new classes of bent functions derived from the Maiorana–McFarland (M) class, so-
called C and D, were introduced by Carlet (1993) almost three decades ago. In Zhang …
called C and D, were introduced by Carlet (1993) almost three decades ago. In Zhang …
On the maximum number of bent components of vectorial functions
In this paper, we show that the maximum number of bent component functions of a vectorial
function F: GF (2) n→ GF (2) n is 2 n-2 n/2. We also show that it is very easy to construct such …
function F: GF (2) n→ GF (2) n is 2 n-2 n/2. We also show that it is very easy to construct such …
On constructions and properties of (n, m)-functions with maximal number of bent components
L Zheng, J Peng, H Kan, Y Li, J Luo - Designs, Codes and Cryptography, 2020 - Springer
For any positive integers n= 2k n= 2 k and m such that m ≥ k, m≥ k, in this paper we show
that the maximal number of bent components of any (n, m)-function is equal to 2^ m-2^ mk, 2 …
that the maximal number of bent components of any (n, m)-function is equal to 2^ m-2^ mk, 2 …
Linear codes from perfect nonlinear functions over finite fields
In this paper, a class of p-ary 3-weight linear codes and a class of binary 2-weight linear
codes are proposed respectively by virtue of the properties of the perfect nonlinear functions …
codes are proposed respectively by virtue of the properties of the perfect nonlinear functions …
Classification of bent monomials, constructions of bent multinomials and upper bounds on the nonlinearity of vectorial functions
Y Xu, C Carlet, S Mesnager… - IEEE Transactions on …, 2017 - ieeexplore.ieee.org
This paper is composed of two main parts related to the nonlinearity of vectorial functions.
The first part is devoted to maximally nonlinear (n, m) functions (the so-called bent vectorial …
The first part is devoted to maximally nonlinear (n, m) functions (the so-called bent vectorial …