New Algebraic Structure Based on Cyclic Geometric Progressions over Polynomial Ring Applied for Cryptography

Currently, there are many methods for constructing cryptosystems based on various algebraic structures. This paper presents a proposed cryptosystem that based on a new algebraic structure with simple and flexible properties. This cryptosystem is constructed from Cyclic Geometric Progressions over polynomial ring in finite field, in which it is considered as a polyalphabetic cipher. Simple scheme for cryptosystem using the cyclic geometric progression over polynomial ring is described. The new structure of multiplicative group and Cyclic over polynomial ring is also mentioned in this paper.