Construction of primitive polynomials over finite fields

In this paper, using the polynomial composition methods some computationally simple and explicit ways for constructing higher degrees primitive polynomials from a given primitive polynomial over [Formula: see text] are given.

Public Key Cryptosystem Based on Polynomial Composition

The public key cryptosystem is an extension of an asymmetric key cryptosystem. The public key cryptosystems have been developed based on the concepts of matrix, polynomial and polynomial decomposition. In this study, we will introduce the public key cryptosystem over polynomial composition. This research is a literature study. The results show that the polynomial composition can be used in public-key cryptosystems by modifying special functions to apply commutative properties<em>.</em>

FACTORIZATION OF SOME COMPOSITE POLYNOMIALS OVER FINITE FIELDS

In this paper we study the factorization of composite polynomials, constructed with some polynomial composition methods, into irreducible factors over finite fields. The main aim of this paper is to provide a proof of a useful theorem of Varshamov (1973), which had been stated by him, without proof.