Onai M.V.

Hardware Implementation Computations in Finite Fields Characteristics of Two

The article substantiates the need for hardware implementation of computational procedures in finite fields of the form GF(2m) with a high rate of speed. Analysis of different forms of the field elements GF(2m) representation was performed and showed that there is a need (in the process of computation) to move from one form of presentation elements to another, namely provide isomorphism field in hardware implementation. It was specified that for Galois fields with never-exceed 220 capacities it is expedient to use tabular method of elements field storage.

Hardware Implementation of Multiplication and Division Operations for Polynomials in Finite Fields

In this paper we prove it is necessary to implement hardware or hardware-software operations in Galois fields. Specifically, we demonstrate that hardware implementation is preferable for multiplication and division operations on polynomials with coefficients that belong to the finite field. It is also feasible to run these operations on separate functional units. We develop formulas that allow skipping summation cycles if the bars being summed contain zero values.