245 research outputs found

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

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    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

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

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    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

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

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    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

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    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

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    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

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    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.Π£ статті розглянуто ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΠ½Ρ– аспСкти впровадТСння систСми ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Ρ–Π½Π³Ρƒ Π½Π° підприємстві. Π’ΠΈΠ·Π½Π°Ρ‡Π΅Π½ΠΎ основні ΠΏΡ–Π΄Ρ…ΠΎΠ΄ΠΈ Ρ‚Π° ΠΏΡ€ΠΈΠ½Ρ†ΠΈΠΏΠΈ ΠΎΡ€Π³Π°Π½Ρ–Π·Π°Ρ†Ρ–Ρ— Ρ– впровадТСння ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Ρ–Π½Π³Ρƒ. Описано основні ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΠΈ, Π· якими ΡΡ‚ΠΈΠΊΠ°ΡŽΡ‚ΡŒΡΡ підприємства Π² Ρ…ΠΎΠ΄Ρ– ΠΎΡ€Π³Π°Π½Ρ–Π·Π°Ρ†Ρ–Ρ—, Π° ΠΏΠΎΡ‚Ρ–ΠΌ - Ρ– впровадТСння ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Ρ–Π½Π³Ρƒ. Розглянуто ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΠΈ, які Π²ΠΈΠ½ΠΈΠΊΠ°ΡŽΡ‚ΡŒ Π² ΡƒΠΌΠΎΠ²Π°Ρ… впровадТСння слуТби ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Ρ–Π½Π³Ρƒ Π½Π° підприємстві, Ρ‚Π° ΡˆΠ»ΡΡ…ΠΈ Ρ—Ρ… Π²ΠΈΡ€Ρ–ΡˆΠ΅Π½Π½Ρ. Π’Π°ΠΊΠΎΠΆ Ρ€ΠΎΠ·Ρ€ΠΎΠ±Π»Π΅Π½ΠΎ схСму впровадТСння ΠΌΠ΅Ρ…Π°Π½Ρ–Π·ΠΌΡƒ ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Ρ–Π½Π³Ρƒ Π² систСму управління підприємством Ρ‚Π° Π½Π°Π΄Π°Π½ΠΎ характСристику Π΅Ρ‚Π°ΠΏΠ°ΠΌ Ρ€Π΅Π°Π»Ρ–Π·Π°Ρ†Ρ–Ρ— Ρ†Ρ–Ρ”Ρ— схСми. Π‘ΡŒΠΎΠ³ΠΎΠ΄Π½Ρ– систСма ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Ρ–Π½Π³Ρƒ Ρ‰Π΅ Π½Π΅Π΄ΠΎΡΡ‚Π°Ρ‚Π½ΡŒΠΎ Π²ΠΏΡ€ΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π° Π² ΡƒΠΏΡ€Π°Π²Π»Ρ–Π½ΡΡŒΠΊΡƒ ΠΏΡ€Π°ΠΊΡ‚ΠΈΠΊΡƒ підприємств Π£ΠΊΡ€Π°Ρ—Π½ΠΈ, Ρ‚ΠΎΠΌΡƒ Π²Π°Ρ€Ρ‚ΠΎ Π²ΠΈΠ·Π½Π°Ρ‡ΠΈΡ‚ΠΈ ΠΏΡ€Ρ–ΠΎΡ€ΠΈΡ‚Π΅Ρ‚ΠΈ Ρ‰ΠΎΠ΄ΠΎ напряму Π΄Ρ–ΡΠ»ΡŒΠ½ΠΎΡΡ‚Ρ– вітчизняних підприємств, моТливості Ρ—Ρ… ΠΊΠΎΠ½ΠΊΡƒΡ€Π΅Π½Ρ†Ρ–Ρ— Π· Ρ–Π½ΠΎΠ·Π΅ΠΌΠ½ΠΈΠΌΠΈ підприємствами Π² ΠΌΠ°ΠΉΠ±ΡƒΡ‚Π½ΡŒΠΎΠΌΡƒ Ρ‚Π° пСрспСктиви Π΅ΠΊΠΎΠ½ΠΎΠΌΡ–Ρ‡Π½ΠΎΠ³ΠΎ Ρ€ΠΎΠ·Π²ΠΈΡ‚ΠΊΡƒ, які Π΄Π°Ρ” впровадТСння систСми ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Ρ–Π½Π³Ρƒ.Π’ ΡΡ‚Π°Ρ‚ΡŒΠ΅ рассмотрСны ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΠ½Ρ‹Π΅ аспСкты внСдрСния систСмы ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Π»ΠΈΠ½Π³Π° Π½Π° прСдприятии. ΠžΠΏΡ€Π΅Π΄Π΅Π»Π΅Π½Ρ‹ основныС ΠΏΠΎΠ΄Ρ…ΠΎΠ΄Ρ‹ ΠΈ ΠΏΡ€ΠΈΠ½Ρ†ΠΈΠΏΡ‹ ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΈ внСдрСния ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Π»ΠΈΠ½Π³Π°. ΠžΠΏΠΈΡΠ°Π½Ρ‹ основныС ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΡ‹, с ΠΊΠΎΡ‚ΠΎΡ€Ρ‹ΠΌΠΈ ΡΡ‚Π°Π»ΠΊΠΈΠ²Π°ΡŽΡ‚ΡΡ прСдприятия Π² Ρ…ΠΎΠ΄Π΅ ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠΈ, Π° Π·Π°Ρ‚Π΅ΠΌ - ΠΈ внСдрСния ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Π»ΠΈΠ½Π³Π°. РассмотрСны ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΡ‹, Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡŽΡ‰ΠΈΠ΅ Π² условиях внСдрСния ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Π»ΠΈΠ½Π³Π° Π½Π° прСдприятии, ΠΈ ΠΏΡƒΡ‚ΠΈ ΠΈΡ… Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ. Π Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π° схСма внСдрСния ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠ° ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Π»ΠΈΠ½Π³Π° Π² систСму управлСния прСдприятиСм ΠΈ ΠΎΡ…Π°Ρ€Π°ΠΊΡ‚Π΅Ρ€ΠΈΠ·ΠΎΠ²Π°Π½Ρ‹ этапы Ρ€Π΅Π°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ этой схСмы. БСгодня систСма ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Π»ΠΈΠ½Π³Π° Π΅Ρ‰Π΅ нСдостаточно Π²Π½Π΅Π΄Ρ€Π΅Π½Π° Π² ΡƒΠΏΡ€Π°Π²Π»Π΅Π½Ρ‡Π΅ΡΠΊΡƒΡŽ ΠΏΡ€Π°ΠΊΡ‚ΠΈΠΊΡƒ прСдприятий Π£ΠΊΡ€Π°ΠΈΠ½Ρ‹, поэтому слСдуСт ΠΎΠΏΡ€Π΅Π΄Π΅Π»ΠΈΡ‚ΡŒ ΠΏΡ€ΠΈΠΎΡ€ΠΈΡ‚Π΅Ρ‚Ρ‹ ΠΎΡ‚Π½ΠΎΡΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎ направлСния Π΄Π΅ΡΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ отСчСствСнных прСдприятий, возмоТности ΠΈΡ… ΠΊΠΎΠ½ΠΊΡƒΡ€Π΅Π½Ρ†ΠΈΠΈ с иностранными прСдприятиями Π² Π±ΡƒΠ΄ΡƒΡ‰Π΅ΠΌ ΠΈ пСрспСктивы экономичСского развития, ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Π΅ Π΄Π°Π΅Ρ‚ Π²Π½Π΅Π΄Ρ€Π΅Π½ΠΈΠ΅ систСмы ΠΊΠΎΠ½Ρ‚Ρ€ΠΎΠ»Π»ΠΈΠ½Π³Π°
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