Kronus, David
Published in
Annals of Operations Research

Every k-interval Boolean function f can be represented by at most k intervals of integers such that vector x is a truepoint of f if and only if the integer represented by x belongs to one of these k (disjoint) intervals. Since the correspondence of Boolean vectors and integers depends on the order of bits an interval representation is also specifie...

Zgurovsky, M. Z. Boldak, A. A. Pomerantseva, T. N.
Published in
Cybernetics and Systems Analysis

Bayesian Belief Networks are used to establish qualitative causal relations between global threats and indicators of sustainable development. The method of belief network synthesis and a method of generalization of final results are proposed. This made it possible to obtain a holistic understanding of effects of global threats on the sustainable de...

Sun, Guanghong Wu, Chuankun
Published in
Applicable Algebra in Engineering, Communication and Computing

The r-th order nonlinearity of Boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers. It is also very useful in coding theory, since it is related to the covering radii of Reed-Muller codes. By investigating the lower bound of the nonlinearity of the derivative of the function f, this pap...

Tan, C.-H. Goh, S.-T.

10.1587/transfun.E94.A.165 / IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences / E94-A / 1 / 165-171 / IFESE

Tokareva, N. N.
Published in
Journal of Applied and Industrial Mathematics

Bent functions (Boolean functions with extreme nonlinearity properties) are actively studied for their numerous applications in cryptography, coding theory, and other fields. New statements of problems lead to a large number of generalizations of the bent functions many of which remain little known to the experts in Boolean functions. In this artic...

Merle, Guillaume Roussel, Jean-Marc Lesage, Jean-Jacques

This paper presents an algebraic approach allowing to perform the analysis of any Dynamic Fault Tree (DFT). This approach is based on the ability to formally express the structure function of DFTs. We first present the algebraic framework that we introduced to model dynamic gates and hence be able to determine the structure function of DFTs. Then, ...

Rychkov, K. L.
Published in
Journal of Applied and Industrial Mathematics

A generalization of the concept of parallel-sequential switching circuits (π-circuits) to the case when the variables assigned to contacts can take not two, as in the Boolean case, but a greater number of values. The conductivity of the contact is still two-valued (the contact is either closed or open). A lower bound is obtained on the complexity o...

Smyshlyaev, Stanislav V.
Published in
Journal of Cryptology

In the current paper we consider the following properties of filters: perfect balancedness of a filter function (i.e. preserving pure randomness of the input sequence) and linearity of a filter function in the first or the last essential variable. Previous results on this subject are discussed, including misleading statements in Gouget and Sibert (...

Chugunova, V. V.
Published in
Mathematical Notes

We prove that, in the basis {x1 & x2 & x3, x1 ∨ x2 ∨ x3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar x_1 $$\end{document}}, for inverse faults at the inputs o...

Parriaux, Jérémy Guillot, Philippe Millérioux, Gilles
Published in
Cryptography and Communications

This paper addresses the problem of characterizing the functions that can be used in the design of self-synchronizing stream ciphers. We propose a general framework based on a spectral characterization through correlation matrices or equivalently through Walsh matrices. Two modes of self-synchronization are discussed: the finite time one and the st...