The current development of IP based 4G system is the Long Term Evolution-Advanced (LTE-A), which focuses on the integration of existing wireless technologies in order to provide an extended service for all mobile users. LTE-A system uses the Evolved Packet System Authentication and Key Agreement (EPS-AKA) protocol to mitigate the security issues and the cloning problem. However, there exist vulnerabilities like Redirection, Denial of Service and Man-in-the-Middle attacks which may lead the eavesdroppers to utilize and misuse the subscriber's resources. Therefore, in this paper an enhanced authentication and key agreement protocol namely DSAKA is developed to ensure the security and provide solutions to the vulnerabilities present in the exiting AKA authentication schemes. DS-AKA uses ElGamal Digital signature and Diffie-Hellman key exchange algorithm to establish authentication in all stages between the User Equipment (UE) and Evolved NodeB (eNB). DS-AKA protocol is designed in such a way that it reduces the bandwidth utilization and the number of transactions for the authentication process, thereby it provides greater scalability. The proposed protocol is simulated using NS3 with LENA LTE module and the performances are compared with the existing AKA schemes. The proposed protocol was extensively analyzed and formal verifi cation was carried out using ProVerif and found that DS-AKA is more secured against various malicious attacks.