Browsing by Author "Kostyk, Andrii"
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Item Features of multiplication execution of operations in binary and ternary Galois fields(Lviv Polytechnic Publishing House, 2015) Kostyk, Andrii; Hlukhov, Valerii; Zholubak, Ivan; Lviv Polytechnic National UniversityConsider the proposed method of construction serial ternary multiplier element Galois field GF (3m). The described method of verification operations on elements of the Galois field GF (2m) and GF (3m) use mathematical package Maple.Item Galois fields elements processing units for cryptographic data protection in cyber-physical systems(Lviv Politechnic Publishing House, 2017-12-03) Hlukhov, Valerii; Kostyk, Andrii; Zholubak, Ivan; Rahma, Mohammed; Lviv Polytechnic National UniversityCurrently, elliptic curves are the mathematical basis for digital signature processing. Elliptic curve points processing is based on the performance of operations in Galois field GF(2m) in normal or polynomial bases. Characteristics of multipliers for these bases are different. In this paper, the time complexity of software multipliers for binary Galois fields GF(2m) and fields GF(dn) was investigated. Fields with approximately the same number of elements were investigated. Elements of these fields were represented in a polynomial basis. It is established that the Galois field GF(3т) provides the greatest time complexity of software multiplication, and the prime Galois field GF(P) has the least time complexity. It is also shown that the use of polynomial basis allows, in contrast to the normal basis, to realize larger part of multiplier on FPGA chip.Item The research of multiplication in the ternary Galois fields(Видавництво Львівської політехніки, 2017-12-23) Kostyk, Andrii; Hlukhov, Valerii; Berezko, Leonid; Lviv Polytechnic National UniversityThe research of multiplication in the ternary Galois fields Calculation and finding irreducible polynomials for Galois field GF(pm). Consider the proposed method of construction serial ternary multiplier element Galois field GF (3m).Item The research of the binary codes program complication and application in Cyber Physical Systems(Lviv Polytechnic Publishing House, 2016) Kostyk, Andrii; Hlukhov, Valerii; Zholubak, Ivan; Lviv Polytechnic National UniversityThe research of the binary codes program complication and application in Cyber Physical Systems. Calculation and finding irreducible polynomials for Galois field GF(pm).