Complete decompositions of dihedral groups and group based key exchange protocol

Abstract

This research is about the group coverings of subsets of finite non-abelian groups and its application in the field of cryptography. Group coverings of finite abelian groups has been researched over the years and it has many applications in various fields. The popularity of internet has increased rapidly and the application of cryptography become more important as it ensures the privacy and security of the users in the network. A cryptosystem is a structure consisting of several cryptographic primitives. Key exchange protocol is one of the cryptographic primitives that parties used to exchange a shared key. The group covering that we investigate in this paper is the complete decompositions of order t in dihedral group. Let D2n be dihedral group of order 2 for positive integer n≥3. We show some constructions of complete decompositions of D2n of order t for t∈{2,3,…,n}. Since D2n is a non-abelian group, the hardness of the mathematical problems will be increased in designing a secure cryptosystem. By using the computational complete decomposition of dihedral group of order t search problem, two parties key exchange protocol is proposed without sharing any keys directly. Finally, we show that the proposed scheme is a secure communication between the authorized parties and protect the data from being disclosed to the third parties or hackers.