Nonlinear functions, also called S-Boxes, are building blocks for symmetric cryptography primitives. The robustness of S-Boxes is measured using properties of Boolean functions, such as differential uniformity and non-linearity. In particular, the lower the differential uniformity, the better the resistance to differential attacks. Functions which ...
In this paper we compare various normal form representations of Boolean functions. We extend the study of [4], pertaining to the comparison of the asymptotic efficiency of representations that are produced by normal form systems (NFSs) that are factorizations of the clone Ω of all Boolean functions. We identify some properties, such as associativit...
Published in Moscow University Computational Mathematics and Cybernetics
The following problem is considered: Find Boolean function f of n variables with the property that, given any polynomial p of degree at most s, there exists a set of n-tuples such that p is the only polynomial of degree at most s taking the same values as f at these n-tuples. It is shown that for any fixed s and sufficiently large n, such a functio...
La cryptologie est une des disciplines des mathématiques, elle est composée de deux sous-ensembles: la cryptographie et la cryptanalyse. Tandis que la cryptographie s'intéresse aux algorithmes permettant de modifier une information afin de la rendre inintelligible sans la connaissance d'un secret, la seconde s'intéresse aux méthodes mathématiques p...
Published in Cybernetics and Systems Analysis
This article considers the synthesis of a neural-like Hamming network with a view to implementing the problem of classification of an input set of binary vectors. The formation of a sequence sorted by the Hamming distance as the proximity measure is based on the conversion of cyclic Hamming codes. The correctness of the synthesis of such an impleme...
Published in Automatic Control and Computer Sciences
This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of n variables whose complexity (in terms of th...
Published in Mathematical Notes
Published in Designs, Codes and Cryptography
In this work, we discuss two notions of differential equivalence on Sboxes. First, we introduce the notion of DDT-equivalence which applies to vectorial Boolean functions that share the same difference distribution table (DDT). Next, we compare this notion to what we call the γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} ...
The growing interest in the Internet of Things (IoT) has led to predictions claiming that by 2020 we can expect to be surrounded by 50 billion Internet connected devices. With more entry points to a network, adversaries can potentially use IoT devices as a stepping stone for attacking other devices connected to the network or the network itself. In...
Published in Cybernetics and Systems Analysis
This article considers problems of partition of a set of vectors with nonnegative integer coordinates into two classes with respect to a threshold value and a threshold relation using adaptable logical networks. The correctness of the corresponding algorithms for implementing such a partition is proved for an arbitrary threshold value and a dimensi...
