Development of disymmetric information security system mathematical model by the parametric solution of the multigrade Diophantine equations system
Abstract
Development of disymmetric information security system mathematical model by the parametric solution of the multigrade Diophantine equations system
Incoming article date: 07.06.2020The paper demonstrates the objective need of improvment of information security systems in terms of development of information and telecommunications equipment. The theorems that describe the properties of parametric solutions of multigrade diophantine equation systems (MDES) is presented. The properties are used to develop information security system mathematical models. Also the paper demonstrate generalized Frolov's theorem and author's theorem to enable development information security system mathematical models with Diophantine problems. Author's alphabetical information security system mathematical model in form of tuple is given. Approch to develop disymmetric bigramm information security system (DBISS) based on two-parametric solutions is given. The approach generalize establishing open-key information security system. The direct and inverse transformations is realized through parametric solution that provisionally divided into two parts - for direct transformation and inverse transformation. Also author introduces new concept of equity of number ordered set or set of parameter with given dimension and grade. The DBISS mathematical model is given in the paper. The model is based on the MDES two-parametric solution with given dimension and grade. The decribed mathematical model demonstrate the potentil of diophantine equations to development of information security systems with high reliability.
Keywords: information security system, symmetric cryptosystem, disymmetric cryptosystem, open-key cryptosystem, ecncryption, decryption, multigrade diophantine equation system, parametirc solution, diophantine problems