Cryptosystems mathematical models design based on NP-complete problems containing Diophantine difficulties
UDC
519.72+004DOI:
https://doi.org/10.31429/vestnik-19-4-20-26Abstract
A new area of NP-complete problems from Diophantine analysis is involved in the manuscript: multistep systems of Tarry-Escott type Diophantine equations. Mathematical models of cryptosystems based on known NP-complete problems using a universal Diophantine language are presented. The described models demonstrate the potential of using Diophantine equations for the development of SPI with a high degree of reliability. A mathematical model of an alphabetic information security system has been developed that generalizes the principle of constructing cryptosystems with a public key - the so-called dissymmetric trigram cryptosystem. In it, forward and reverse transformations are implemented according to a given algorithm based on a multiparametric solution of a multi-stage system of Diophantine equations.
Keywords:
NP-complete problem, multi-degree system of Diophantine equations, key generation, symmetric (dissymmetric) cryptosystem, parametric solution, Diophantine difficultiesReferences
- Shannon, C., Communication theory of secrecy systems. Bell System Techn. J., 1949, vol. 28, iss. 4., pp. 656–715.
- Dorwart, H.L., Brown, O.E., The Tarry-Escott problem. Amer. Math. Monthly, 1937, vol. 44, iss. 10, pp. 613–626.
- Матиясевич, Ю.В., Десятая проблема Гильберта. Наука, Москва, 1993. [Matiyasevich, Yu.V., Desyataya problema Gil'berta = Hilbert's tenth problem. Nauka, Moscow, 1993.]
- Carmichael, R.D., The theory of numbers and diophantine analysis. New York, 1959.
- Саломаа, А., Криптография с открытым ключом. Мир, Москва, 1995. [Salomaa, A., Kriptografiya s otkrytym klyuchom = Public key cryptography. Mir, Moscow, 1995. (in Russian)]
- Осипян, В.О., Разработка математической модели дисимметричной биграммной криптосистемы на основе параметрического решения многостепенной системы диофантовых уравнений. Сетевой научный журнал "Инженерный вестник Дона", 2020, № 6. [Osipyan, V.O., Development of a mathematical model of a dissymmetric bigram cryptosystem based on the parametric solution of a multi-degree system of Diophantine equations. Setevoy nauchnyy zhurnal "Inzhenernyy vestnik Dona" = Web Scientific Journal "Engineering Bulletin of the Don", 2020, no. 6. (in Russian)] URL: http://ivdon.ru/ru/magazine/archive/N6y2020/6534
- Осипян, В.О., Разработка математических моделей систем защиты информации, содержащих диофантовы трудности. Кубанский гос. ун-т, Краснодар, 2021. [Osipyan, V.O., Razrabotka matematicheskikh modeley sistem zashchity informatsii, soderzhashchikh diofantovy trudnosti = Development of mathematical models of information security systems containing Diophantine difficulties. Kuban State University, Krasnodar, 2021. (in Russian)]
- Koblitz, N.A., Course in number theory and cryptography. Springer-Verlag, New York, 1987.
- Осипян, В.О., Литвинов, К.И., Жук, А.С., Разработка математических моделей систем защиты информации на основе многостепенных систем диофантовых уравнений. Экологический вестник научных центров Черноморского экономического сотрудничества, 2019, т. 16, № 3, с. 6–15. [Osipyan, V.O., Litvinov, K.I., Zhuk, A.S., Development of mathematical models of information security systems based on multi-degree systems of Diophantine equations. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva = Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2019, vol. 16, no. 3, pp. 6–15. (in Russian)] DOI 10.31429/vestnik-16-3-6-15
Downloads
Submitted
Published
How to Cite
Copyright (c) 2022 Osipyan V.O., Al Gharib E.J.
This work is licensed under a Creative Commons Attribution 4.0 International License.
