


À. À. Kolyada, D. Sc., Associate Professor; Email: razan@tut.by, P. V. Kuchynski, D. Sc., Associate Professor Director of IAPP "Institute of Applied Physics Problems of À. N. Sevchenko" Belarusian State University (IAPP of À. N. Sevchenko), Minsk, 220045, Belarus, Kurchatov St., 7; Email: niipfp@bsu.by, N. I. Chervyakov, D. Sc., Professor, Head of Department, Federal State Autonomous Educational Institution of Higher Professional Education "NorthCaucasus Federal University", Stavropol, 355029, Russian Federation; Email: Chervyakov@yandex.ru, whbear@yandex.ru Reducing Method of PositionalModular Converting Large Numbers for Neural Networks to the End Rings The article is devoted to the problem of constructing neural networks of a finite ring (NNFR), which serve as the basis for neural network modular computing structures for highperformance cryptographic applications. The methodological basis of the NNFR of the investigated class is the modified reduction method of positionmodular transformation of weighted large numbers. The authors give a mathematical formalization of the method, was obtained estimates for the range of change and the number of elements of the residue sequence formed by the reduction scheme of the recursive type, the nature and speed of its convergence are investigated, a flexible tabular mechanism for reducing the number of iterations of the scheme is proposed. Synthesized general reducing algorithm of positionmodular code conversion, was developed the parallel structure of the NNFR which performs a basic transformation in one iteration — during the time of order ( [log_{2}b] + 2)t_{cë}, where b is the number of the input number;t_{cë} is the duration of the twofold addition operation. 