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.

Keywords

• neural network
• neural network end rings
• a neural network with feedback
• the synaptic weight
• modular number system
• modular arithmetic
• reducing the scheme of reduction of bit numbers
• the table method