The Omura-Massey Cryptosystem is an asymmetric key cryptosystem (public-key cryptosystem) that is mainly studied on the discrete logarithm problem in finite field GF(p). Based on recent research results on the equivalence of some polynomial rings with two cyclic cyclotomic cosets with Galois Field GF(p), the paper proposes the method of constructing the Omura-Massey cryptosystem that is also based on the discrete logarithm problem but in some special polynomial rings with two cyclotomic cosets. In addition, on the basic of additive groups and multiplicative groups of polynomial rings with two cyclotomic cosets, the article also proposes two new variants of the Omura-Massey cryptosystem.
Keyword
Public-key cryptography, Omura-Massey cryptosystem, polynomial ring, finite field
