Metrical properties of the set of bent functions in view of duality

In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n + 2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n > 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered

Cryptographic properties of a simple S-box construction based on a Boolean function and a permutation

We propose a simple method of constructing S-boxes using Boolean functions and permutations. Let n be an arbitrary permutation on n elements, f be a Boolean function in n variables. Define a vectorial Boolean function Fn : F^ F^ as Fn(x) = = (f (x), f (n(x)), f (n2(x)),..., f (nn-1(x))). We study cryptographic properties of Fn such as high nonlinearity, balancedness, low differential 5-uniformity in dependence on properties of f and n for small n

On one-to-one property of a vectorial Boolean function of the special type

S-boxes are widely used in cryptography. In particular, they form important components of SP and Feistel networks. Mathematically, S-box is a vectorial Boolean function F : Fn Fm that should satisfy several cryptographic properties. Usually n = m. We study one-to-one property of a vectorial Boolean function constructed in a special way on the base of a Boolean function and a permutation on n elements. The number of all one-to-one functions of this type is calculated

Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography

The mathematical problems and their solutions of the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technology, etc. Two open problems in mathematical cryptography are also discussed and a solution for one of them proposed by a participant during the Olympiad is described. It was the first time in the Olympiad history

On the number of unsuitable boolean functions in constructions of filter and combining models of stream ciphers

It is well known that every stream cipher is based on a good pseudorandom generator. For cryptographic purposes, we are interested in generation of pseudorandom sequences of the maximal possible period. A feedback register is one of the most known cryptographic primitives that is used in construction of stream generators. We analyze periodic properties of pseudorandom sequences produced by filter and combiner generators equipped with nonlinear Boolean functions. We determine which nonlinear functions in these schemes lead to pseudorandom sequences of not maximal possible period. We call such functions unsuitable and count the exact number of them for an arbitrary n

Problems and prospects of implementation controlling as a modern enterprise management tool

The article includes problematic aspects implementation of the introduction of controlling in the enterprise. Identified the basic approaches and principles of organizations and implementation controlling. Described the basic problem faced by enterprises in the during organization and implementation controlling. Considered problems arising in case of implementing controlling service in the enterprise, and ways of solutions. Also developed the scheme implementing a mechanism for controlling in management system and provided characteristics of the stages of implementation of this scheme. Today controlling system is not implemented in administrative practice of Ukraine, so you should prioritize the direction of domestic enterprises, the possibility of their competition with foreign enterprises in the future and prospects of economic development, which allows the introduction of controlling.У статті розглянуто проблемні аспекти впровадження системи контролінгу на підприємстві. Визначено основні підходи та принципи організації і впровадження контролінгу. Описано основні проблеми, з якими стикаються підприємства в ході організації, а потім - і впровадження контролінгу. Розглянуто проблеми, які виникають в умовах впровадження служби контролінгу на підприємстві, та шляхи їх вирішення. Також розроблено схему впровадження механізму контролінгу в систему управління підприємством та надано характеристику етапам реалізації цієї схеми. Сьогодні система контролінгу ще недостатньо впроваджена в управлінську практику підприємств України, тому варто визначити пріоритети щодо напряму діяльності вітчизняних підприємств, можливості їх конкуренції з іноземними підприємствами в майбутньому та перспективи економічного розвитку, які дає впровадження системи контролінгу.В статье рассмотрены проблемные аспекты внедрения системы контроллинга на предприятии. Определены основные подходы и принципы организации и внедрения контроллинга. Описаны основные проблемы, с которыми сталкиваются предприятия в ходе организации, а затем - и внедрения контроллинга. Рассмотрены проблемы, возникающие в условиях внедрения контроллинга на предприятии, и пути их решения. Разработана схема внедрения механизма контроллинга в систему управления предприятием и охарактеризованы этапы реализации этой схемы. Сегодня система контроллинга еще недостаточно внедрена в управленческую практику предприятий Украины, поэтому следует определить приоритеты относительно направления деятельности отечественных предприятий, возможности их конкуренции с иностранными предприятиями в будущем и перспективы экономического развития, которые дает внедрение системы контроллинга