Finite field transforms applicatons to cryptography and error free polynimial matrix computation

Abstract

In this dissertation, we have presented the properties of finite field transforms and a few of their applications. We do not consider our study exhaustive, and we expect other applications to be developed soon. The most important applications are likely to occur in the formulation of exact computational procedures for selected problems. In this connection, we would like to point out that the exact Smith Form algorithm of Chapter 3 will find use in an exact computational procedure for the spectral factorization of a rational polynomial matrix.