Diffie-Hellman key exchange protocol, its generalization and nilpotent groups

This dissertation has two chapters. In the first chapter we talk about the discrete logarithm problem, more specifically we concentrate on the Diffie-Hellman key exchange protocol. We survey the current state of security for the Diffie-Hellman key exchange protocol. We also motivate the reader to think about the Diffie-Hellman key exchange in terms of group automorphisms.; In the second chapter we study two key exchange protocols similar to the Diffie-Hellman key exchange protocol using an abelian subgroup of the automorphism group of a non-abelian group. We also generalize group no. 92 of the Hall-Senior table, for arbitrary prime p and study the automorphism group of these generalized group. We show that for those groups, the group of central automorphisms is an abelian group. We use these central automorphisms for the key exchange we are studying. We also develop a signature scheme.