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.
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