The objective need to improve information security systems in the conditions of information-telecommunication technologies developing is shown. A new area of NP-complete promplems of diophantine analisys is firstly researched, namely Tarry–Escott multigrade diophantine equation systems (MDES) of given dimension and degree. The theorems, that describe parametrical MDES parametric solution properties, required for the development of the algorythm of building of dissymmetric bigram cryptosystem, are given in the article. The author's theorem, which allows to develop information protection system (IPS) mathematical model as a cortege, containing diophantine probleme. A new approach to develop dissymmetric bigram cryptosystem(DBC) on the base of two-parametrical MDES solution, which generalize open key cryptosystem, is considered. Forward and reverse conversions based on parametrical solution are suggested tyo realize on such algorythm. A new concept of equivalence of ordered sets of numbers (parameters) of a given dimension and order is introduced to build DBC mathematical model, using two-parametrical MDES solution. Described mathematical model demonstrates application potential of diophantine equations for IPS with a high degree of reliability.

Keywords: NP-complete probleme, information protection system, symmetric (dissymmetric) cryptosystem, open key cryptosystem, forward and reverse information conversions, Tarry–Escott multigrade diophantine equation system, parametrical solution

The problem of searching over encrypted data using homomorphic encryption in distributed software systems is addressed. The paper considers the application of the approach developed by the authors for the implementation of a distributed system prototypes for issuing digital diplomas and certificates for obtaining competencies with recording in IPFS and an Ethereum smart contract and a search engine for recruiting personnel. The prototype of the system presented in the article demonstrates the use of homomorphic encryption, which allows the search engine and users to interact with the directly transformed data in public blockchain networks without performing the reverse transformation, ensuring their security.

Keywords: blockchain, distributed software systems, cloud computing, homomorphic encryption, mathematical model, transactions, smart contracts, digital diploma, recruiting