Research and development of the mathematic models of cryptosystems based on the universal Diophantine language

Abstract

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.