245 research outputs found
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
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
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.Π£ ΡΡΠ°ΡΡΡ ΡΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½Ρ Π°ΡΠΏΠ΅ΠΊΡΠΈ Π²ΠΏΡΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π½Ρ ΡΠΈΡΡΠ΅ΠΌΠΈ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π³Ρ Π½Π° ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ²Ρ. ΠΠΈΠ·Π½Π°ΡΠ΅Π½ΠΎ ΠΎΡΠ½ΠΎΠ²Π½Ρ ΠΏΡΠ΄Ρ
ΠΎΠ΄ΠΈ ΡΠ° ΠΏΡΠΈΠ½ΡΠΈΠΏΠΈ ΠΎΡΠ³Π°Π½ΡΠ·Π°ΡΡΡ Ρ Π²ΠΏΡΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π½Ρ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π³Ρ. ΠΠΏΠΈΡΠ°Π½ΠΎ ΠΎΡΠ½ΠΎΠ²Π½Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠΈ, Π· ΡΠΊΠΈΠΌΠΈ ΡΡΠΈΠΊΠ°ΡΡΡΡΡ ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ²Π° Π² Ρ
ΠΎΠ΄Ρ ΠΎΡΠ³Π°Π½ΡΠ·Π°ΡΡΡ, Π° ΠΏΠΎΡΡΠΌ - Ρ Π²ΠΏΡΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π½Ρ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π³Ρ. Π ΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠΈ, ΡΠΊΡ Π²ΠΈΠ½ΠΈΠΊΠ°ΡΡΡ Π² ΡΠΌΠΎΠ²Π°Ρ
Π²ΠΏΡΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π½Ρ ΡΠ»ΡΠΆΠ±ΠΈ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π³Ρ Π½Π° ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ²Ρ, ΡΠ° ΡΠ»ΡΡ
ΠΈ ΡΡ
Π²ΠΈΡΡΡΠ΅Π½Π½Ρ. Π’Π°ΠΊΠΎΠΆ ΡΠΎΠ·ΡΠΎΠ±Π»Π΅Π½ΠΎ ΡΡ
Π΅ΠΌΡ Π²ΠΏΡΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π³Ρ Π² ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΏΡΠ°Π²Π»ΡΠ½Π½Ρ ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ²ΠΎΠΌ ΡΠ° Π½Π°Π΄Π°Π½ΠΎ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΡ Π΅ΡΠ°ΠΏΠ°ΠΌ ΡΠ΅Π°Π»ΡΠ·Π°ΡΡΡ ΡΡΡΡ ΡΡ
Π΅ΠΌΠΈ. Π‘ΡΠΎΠ³ΠΎΠ΄Π½Ρ ΡΠΈΡΡΠ΅ΠΌΠ° ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π³Ρ ΡΠ΅ Π½Π΅Π΄ΠΎΡΡΠ°ΡΠ½ΡΠΎ Π²ΠΏΡΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π° Π² ΡΠΏΡΠ°Π²Π»ΡΠ½ΡΡΠΊΡ ΠΏΡΠ°ΠΊΡΠΈΠΊΡ ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ² Π£ΠΊΡΠ°ΡΠ½ΠΈ, ΡΠΎΠΌΡ Π²Π°ΡΡΠΎ Π²ΠΈΠ·Π½Π°ΡΠΈΡΠΈ ΠΏΡΡΠΎΡΠΈΡΠ΅ΡΠΈ ΡΠΎΠ΄ΠΎ Π½Π°ΠΏΡΡΠΌΡ Π΄ΡΡΠ»ΡΠ½ΠΎΡΡΡ Π²ΡΡΡΠΈΠ·Π½ΡΠ½ΠΈΡ
ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ², ΠΌΠΎΠΆΠ»ΠΈΠ²ΠΎΡΡΡ ΡΡ
ΠΊΠΎΠ½ΠΊΡΡΠ΅Π½ΡΡΡ Π· ΡΠ½ΠΎΠ·Π΅ΠΌΠ½ΠΈΠΌΠΈ ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ²Π°ΠΌΠΈ Π² ΠΌΠ°ΠΉΠ±ΡΡΠ½ΡΠΎΠΌΡ ΡΠ° ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²ΠΈ Π΅ΠΊΠΎΠ½ΠΎΠΌΡΡΠ½ΠΎΠ³ΠΎ ΡΠΎΠ·Π²ΠΈΡΠΊΡ, ΡΠΊΡ Π΄Π°Ρ Π²ΠΏΡΠΎΠ²Π°Π΄ΠΆΠ΅Π½Π½Ρ ΡΠΈΡΡΠ΅ΠΌΠΈ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π³Ρ.Π ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΡΠ΅ Π°ΡΠΏΠ΅ΠΊΡΡ Π²Π½Π΅Π΄ΡΠ΅Π½ΠΈΡ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Π»ΠΈΠ½Π³Π° Π½Π° ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΠΈ. ΠΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Ρ ΠΈ ΠΏΡΠΈΠ½ΡΠΈΠΏΡ ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π²Π½Π΅Π΄ΡΠ΅Π½ΠΈΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Π»ΠΈΠ½Π³Π°. ΠΠΏΠΈΡΠ°Π½Ρ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ, Ρ ΠΊΠΎΡΠΎΡΡΠΌΠΈ ΡΡΠ°Π»ΠΊΠΈΠ²Π°ΡΡΡΡ ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΡ Π² Ρ
ΠΎΠ΄Π΅ ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ, Π° Π·Π°ΡΠ΅ΠΌ - ΠΈ Π²Π½Π΅Π΄ΡΠ΅Π½ΠΈΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Π»ΠΈΠ½Π³Π°. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ, Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡΡΠΈΠ΅ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π²Π½Π΅Π΄ΡΠ΅Π½ΠΈΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Π»ΠΈΠ½Π³Π° Π½Π° ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΠΈ, ΠΈ ΠΏΡΡΠΈ ΠΈΡ
ΡΠ΅ΡΠ΅Π½ΠΈΡ. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° ΡΡ
Π΅ΠΌΠ° Π²Π½Π΅Π΄ΡΠ΅Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° ΠΊΠΎΠ½ΡΡΠΎΠ»Π»ΠΈΠ½Π³Π° Π² ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΠ΅ΠΌ ΠΈ ΠΎΡ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΠΎΠ²Π°Π½Ρ ΡΡΠ°ΠΏΡ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΡΠΎΠΉ ΡΡ
Π΅ΠΌΡ. Π‘Π΅Π³ΠΎΠ΄Π½Ρ ΡΠΈΡΡΠ΅ΠΌΠ° ΠΊΠΎΠ½ΡΡΠΎΠ»Π»ΠΈΠ½Π³Π° Π΅ΡΠ΅ Π½Π΅Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎ Π²Π½Π΅Π΄ΡΠ΅Π½Π° Π² ΡΠΏΡΠ°Π²Π»Π΅Π½ΡΠ΅ΡΠΊΡΡ ΠΏΡΠ°ΠΊΡΠΈΠΊΡ ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΠΉ Π£ΠΊΡΠ°ΠΈΠ½Ρ, ΠΏΠΎΡΡΠΎΠΌΡ ΡΠ»Π΅Π΄ΡΠ΅Ρ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ ΠΏΡΠΈΠΎΡΠΈΡΠ΅ΡΡ ΠΎΡΠ½ΠΎΡΠΈΡΠ΅Π»ΡΠ½ΠΎ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π΄Π΅ΡΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΠΎΡΠ΅ΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΡ
ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΠΉ, Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΈΡ
ΠΊΠΎΠ½ΠΊΡΡΠ΅Π½ΡΠΈΠΈ Ρ ΠΈΠ½ΠΎΡΡΡΠ°Π½Π½ΡΠΌΠΈ ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΡΠΌΠΈ Π² Π±ΡΠ΄ΡΡΠ΅ΠΌ ΠΈ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Ρ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ°Π·Π²ΠΈΡΠΈΡ, ΠΊΠΎΡΠΎΡΡΠ΅ Π΄Π°Π΅Ρ Π²Π½Π΅Π΄ΡΠ΅Π½ΠΈΠ΅ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Π»ΠΈΠ½Π³Π°
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