Development and Research of Highly Efficient Architectures of Special Purpose Computer System for Implementing Computing in Finite Fields

The modified method window exponentiation elements of field GF(p), four algorithms implementing this method and software was proposed. The idea of the proposed method can be applied to the problem of scalar multiplication of points of an elliptic curve over an arbitrary finite field.
The developed software has shown that the proposed method gives performance gains compared to the existing 15%, both for exponentiation in a finite field, and scalar multiplication on elliptic curve defined over a finite field. The proposed methods, algorithms and software to perform modulo 2m – 1. Developed tabular method of operations over the elements of the field GF(2m). The method should be used for m ≤ 20. The software and hardware to implement tabular method of operations over the elements of the field GF(2m) was created. A method of storing sparse table of elements of the field GF(2m), which reduces the amount of memory required to store the elements of the field GF(2m).
The project is the creation of a specialized processor architecture that is aimed at performing calculations in Galois fields, the increase in speed compared to the universal computer system 2.4 – 3 times. The processor command system and software implementation Galois compiler was develop.

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