Mobile wireless networks are more vulnerable to unauthorised access and eavesdropping when compared with the traditional fixed wired networks due to the mobility of users, the transmission of signals through open-air and the requirement of low power consumption by a mobile user. This paper focuses on the security techniques used within the GSM standard. First, current GSM security system vulnerabilities are given. Securing evaluations of two new security protocol proposals for GSM, using private and public key techniques, are also presented. Next, a new GSM security protocols which uses the Elliptic Curve Public Key Cryptography (ECC) technique is proposed. This is followed by a security analysis of the proposed protocols.