Martynenko S. Method and tools for reducing the computational complexity, cryptography RSA-transformations on the basis of modular number system

Object of research - process of cryptographic information processing in the modular number system. Research objective - The models and method development to reduce RSA cryptotransformation computation complexity through the use of additive-multiplicative propertied of Galois fields. Research methods are based on analysis and synthesis, theory of numbers during development methods and tools of arithmetic operations in the Galois fields by applying modular number system using the principle of circular shift and method of bases choice in the modular number system, probability theory and reliability theory during the study methods of increasing reliability of the special processor handling cryptographic information (SPHCI) which operates in the modular number system. Equipment - the personal computer. Theoretical and practical results of research - the developed in the dissertation method of reducing RSA cryptotransformation computation complexity and improved methods of performing arithmetic operations in the modular number system by considering the properties of Galois fields is a scientific and methodological basis for practical creation of SPHCI in the modular number system.. Scientific novelty - for the first time developed a method for processing of cryptotrasformations, which is based on the use of a modular system by using the principle of circular shift, which reduces the computational complexity of the RSA cryptographic; improved mathematical model of the fail-safe for the special processor handling cryptographic information which is different considering the reliability of the control tracts, which makes it possible to assess the reliability of special processor handling of cryptographic information; improved method for performing integer arithmetic in the modular number system, which is unlike analogues takes into account the additive-multiplicative properties of Galois fields, thus increasing the speed of processing special processor cryptographic information Results of dissertational work are introduced in the closed joint-stock company. "Institute of information technologies" (Kharkov) and Public Enterprise Kharkov Instrumental Factory T.Shevchenko (Kharkov). Scientific theoretical and practical results of the dissertation can be used in the research, design and development special processor handling cryptographic information that implements operations of addition, subtraction, multiplication, and squaring numbers by modulo.