Kerberos is an authentication service, which provides security over the network. It assumes that the messages can be read, modified and fabricated by an intruder. It does not provide any security against breaches caused by buggy software or poor passwords. The original design and implementation of Kerberos V1 through V4 was the work of three former Athena Project staff members, Steve Miller of Digital Equipment Corporation and Clifford Neuman along with Jerome Saltzer, Technical Director of Project Athena, and Jeffrey Schiller, MIT Campus Network [1][8][10]. It is designed to provide strong authentication for client/server applications by using secret-key cryptography. The Kerberos protocol uses Data Encryption Standard (DES) so that a client can prove its identity to a server (and vice versa) across an insecure network connection. Authentication is one of the important network security aspects nowadays in internet activity, a more secure application for authentication is fairly useful. Kerberos is an authentication service developed as part of Project Athena at MIT. In this paper, three proposed extensions to integrate public-key cryptography into Kerberos in cross realm are outlined and some basic performance comparisons are made between them and also comments were made on the major security issues related to public-key enhancements introduced to the Kerberos Authentication Protocol trust model. Here the authors have given brief introduction to Kerberos and, public-key cryptography is provided for those unfamiliar with these security systems.