NEURAL NETWORKS OF THE FINAL RING BASED ON THE REDUCTION SCHEME OF THE POSITION-MODULAR-CODE TRANSFORMATION
Abstract
The article studies the problem of creating a neural network of modular computing structures for highperformance expressions in the field of information security. The main attention is paid to the reduction technology of position-modular transformation of scalable integers, which serves as the basis for constructing the so-called neural networks of the finite ring (NNFR). To increase the speed of convergence of the reduction scheme used to reduce the number of elements of the generated sequence of residues, an effective tabular method is proposed. The developed approach makes it possible to reduce the number of iterations of the reduction process to a theoretical minimum. This is achieved through flexible adaptive mechanism check botheration deductions to a special range, allowing a tabular decomposition of its elements into pairs of residues in modules of the modular number system. On the basis of a modified reduction method there was synthesized a fast algorithm and a parallel structure of the NNFR with feedback, which ensures the implementation of the reduction scheme in a time order (S(⌈log2b⌉+1) +2)tsum, were S – the number of iterations, b – the bit width of the input number, – the duration of the addition operation of two deductions.
About the Authors
N. I. Chervyakov
North-Caucasus Federal University, Stavropol
Belarus
D. Sc. (Engineering), Professor
Belarus
D. Sc. (Engineering), Professor
A. A. Kolyada
Scientific Research Institution "Institute of Applied Physical Problems named after A. N. Sevchenko" of the Belarusian State University, Minsk
Belarus
D. Sc. (Physics and Mathematics), Chief Researcher of the Laboratory of Specialized Computational Systems
Belarus
D. Sc. (Physics and Mathematics), Chief Researcher of the Laboratory of Specialized Computational Systems
N. A. Kolyada
Scientific Research Institution "Institute of Applied Physical Problems named after A. N. Sevchenko" of the Belarusian State University, Minsk
Belarus
Researcher, Laboratory of Specialized Computing Systems
Belarus
Researcher, Laboratory of Specialized Computing Systems
V. A. Kuchukov
North-Caucasus Federal University, Stavropol
Belarus
Patent Holder of the Department of Scientific and Technical Information, Sciencemetry and Export Control, Professor
Belarus
Patent Holder of the Department of Scientific and Technical Information, Sciencemetry and Export Control, Professor
S. U. Protasenia
Scientific Research Institution "Institute of Applied Physical Problems named after A. N. Sevchenko" of the Belarusian State University, Minsk
Belarus
Junior Scientific Employee, Laboratory of Specialized Computational Systems
Belarus
Junior Scientific Employee, Laboratory of Specialized Computational Systems
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Review
For citations:
Chervyakov N.I., Kolyada A.A., Kolyada N.A., Kuchukov V.A., Protasenia S.U. NEURAL NETWORKS OF THE FINAL RING BASED ON THE REDUCTION SCHEME OF THE POSITION-MODULAR-CODE TRANSFORMATION. Informatics. 2018;15(2):98-110. (In Russ.)
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