Mathematical model of the process of tabular’s implementation of the operation algebraic multiplication in the residues class

doi:10.26565/2519-2310-2019-2-01

Віктор Краснобаєв V. N. Karazin Kharkiv National University
Михайло Зуб V. N. Karazin Kharkiv National University
Олеся Решетняк V. N. Karazin Kharkiv National University
Андрій Д’яченко V. N. Karazin Kharkiv National University
Ірина Локоткова V. N. Karazin Kharkiv National University
Костянтин Мисливцев V. N. Karazin Kharkiv National University

DOI: https://doi.org/10.26565/2519-2310-2019-2-01

Keywords: residues class, tabular’s implementation, mathematical model, operation algebraic multiplication

Abstract

Based on the properties of the class of residues in the article, a mathematical model of the process of tabular implementation of modular multiplication was synthesized, for both positive and negative numerical ranges of information processing by means of integer information processing. This model is recommended for practical application in the development of methods and algorithms for rapid processing of cryptographic information. Finding ways to simplify the structure of the table operating device integer information processing has led to the need to improve the mathematical model, methods and algorithms for modular operations, which increase the efficiency of the use of table arithmetic in the class of residues. A feature of the implementation of this model is the possibility of reducing the number of equipment operating device integer information by reducing the (50-70)% of logical elements "And" in the nodes of the table permanent storage device, directly implement the operation of modular multiplication by arbitrary m_i module residual class. This is possible by using the symmetry properties of the a_ib_i (mod m_i) implementation table of the modular multiplication operation.

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Author Biographies

Віктор Краснобаєв, V. N. Karazin Kharkiv National University

Doctor of Sciences (Engineering), Full Prof.

Михайло Зуб, V. N. Karazin Kharkiv National University

computer science student

Олеся Решетняк, V. N. Karazin Kharkiv National University

computer science student

Андрій Д’яченко, V. N. Karazin Kharkiv National University

computer science student

Ірина Локоткова, V. N. Karazin Kharkiv National University

computer science student

Костянтин Мисливцев, V. N. Karazin Kharkiv National University

computer science student

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