Development of information security system mathematical models by the solutions of the multigrade Diophantine equation systems

Abstract

In this paper there are theorems that demonstrate the validity of using Diophantine equations parametric solutions properties for information security system mathematical models. For this the proof of a generalization of the known Frolov's theorem has been done and represented. Also we present new theorem as a mathematical model of information security system containing Diophantine problems.On the basis of two particular solutions a new method of parameterization of multigrade systems of Diophantine equations has been invented and presented in this paper. Particulary, on the basis of two equations with less variables this method allows to get general parametric solutions for multigrade Diophantine equations. On the example of the fifth degree equation, the parametric solutions of the multigrade system of Diophantine equations have been used as a mathematical model of a new cryptosystem.The new approach has been proposed for the development of information security system. It generalizes the principle of construction public key cryptosystems: one part of the conditional identity is used for the direct transformation of an original message, and other part is used for the inverse transformation.The represented mathematical models demonstrate the potential of using Diophantine equations for the development of information security system with a high degree of reliability. These models give an ability to build both a symmetrical system and an public key system. Such systems allow an existence of a countable set of equally probable keys that leads to Diophantine problems.