| Issue |
SHS Web Conf.
Volume 141, 2022
IV International Scientific and Practical Conference “Modern Management Trends and Digital Economy: from Regional Development to Global Economic Growth” (MTDE 2022)
|
|
|---|---|---|
| Article Number | 01020 | |
| Number of page(s) | 11 | |
| Section | Digital Technologies in the Management of Socio-Economic Systems | |
| DOI | https://doi.org/10.1051/shsconf/202214101020 | |
| Published online | 24 June 2022 | |
Research and development of the mathematic models of cryptosystems based on the universal Diophantine language
Kuban State University, Krasnodar, Russia
* Corresponding author: v.osippyan@gmail.com
This paper shows the objective necessity of improving the information security systems under the development of information and telecommunication technologies. The paper for the first time involves a new area of NP-complete problems from Diophantine analysis, namely, multi-degree systems of Diophantine equations of a given dimension and degree of Tarry-Escott type. Based on a fundamentally new number-theoretic method, a mathematical model of an alphabetic information security system (ISS) has been developed that generalizes the principle of building cryptosystems with a public key – the so called dissymmetric bigram cryptosystem. This implies to implement direct and inverse transformations according to a given algorithm based on a two-parameter solution of a multi-degree system of Diophantine equations. A formalized algorithm has been developed for the specified model of a dissymmetric bigram cryptosystem and a training example based on a normal multi-degree system of Diophantine equations of the fifth degree is presented.
© The Authors, published by EDP Sciences, 2022
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