АЛГОРИТМИ ПОШУКУ ЗАЛИШКІВ ДОВГИХ ЧИСЕЛ ДЛЯ ЗАДАЧ АСИМЕТРИЧНОЇ КРИПТОГРАФІЇ

At the present stage of providing information security of the state, it is important to make secret military communication networks. One of the key areas to secret a network is the use of cryptographic methods for information protection, in particular, asymmetric cryptography. To improve asymmetric cryptography algorithms we can find the remains of long numbers. The implementation of known algorithms for finding the remains of long numbers has a number of significant drawbacks. The paper analyzes two new methods of finding long-numbered residues, their drawbacks, and computational complexities. The method proposed by the authors is described, its algorithm and block diagram are presented. The computational complexities of the three researched methods are studied. The numerical complexity evaluation experiment shows that when performing modular operations used in asymmetric cryptographic algorithms, when transferring numbers from the decimal system to the system of the numbers of residual classes, the proposed method should be used. The method has less complexity. There are two ways of further consideration. It is well-known that the algorithm effectiveness gain is equal to the ratio of computational complexity and equal 2. The application developed in the high-level programming language C ++ allows us to investigate the time characteristics of the two methods. In this paper, we give a fragment of the testing of the application for double Mersenne numbers and a graphic representation of the dependence of the time of finding the remnants of large numbers from the prime number for which the remainder is. The developed algorithm for finding the remnants of large numbers allowed to increase the speed compared to the known due to the use of the properties of residues and the numerical basis of Rademacher. This reduced the computational complexity and increased the efficiency of the algorithm compared with the known twice, which proves the expediency of its use in processing long numbers in asymmetric cryptographic information security systems to increase the speed of encryption and cryptanalysis. [ABSTRACT FROM AUTHOR]