Golub V.I.

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.

The Compression of the Alphanumeric Information in its Graphic Coding Representation

We devise the compression method of alphanumeric information in its graphic coding representation. The method of data compression is based on converting data from one alphabet to another – from the alphabet of characters into alphabet of graphic coding symbols. The method provides the data compression on average by 20 % for digit data and by 12 % for text sequences. Furthermore, this method provides the storage of a large information content (over 1000 alphanumerical characters) in the form of graphical codes on a limited area of carrier.