SON CONSTRUCTION OF CRYPTOGRAPHIC SYSTEMS OVER UNITS OF GROUP RINGS

Abstract

Encryption schemes can be derived from the units which are known as invertible elements in a group ring. Besides there are many studies on units in group rings in the literature, we can also see some studies of units in terms of applicability to cryptography and coding theory. In this work, we shall establish the relations between units and RSA problem. Our motivation is to construct a much stronger public key cryptosystem. It is clear that we must consider a mathematical hard problem to do this. Thus, we investigate some interesting properties of units which are no deterministic algorithm in general. Our notations follow (8).