Long Term Evolution (LTE) is the first technology that provides exclusively packet-switched data and modifies the security architecture of the 2G (Second Generation) and 3G systems. The LTE security architecture offers confidentiality, access control, a kind of obscurity and mutual authentication. However, numerous types of attacks can be encountered during the mutual authentication process which is a challenge-response based technique. Therefore, a high secure public key algorithm can be implemented to improve the network security services.