The user authentication service can be used to prevent telecommunications piracy and to demand reliable payment from subscriber. Over the last few years several of the cryptographic systems being used by the IS-41 North American Mobile telephones have been broken. These algorithms included ORYX, CMEA and CAVE. The process of replacing these algorithms is already underway. In this paper we designed a hash function and applied it to the authentication algorithm of IS-95A authentication system. We also analyzed the randomness properties of designed algorithm using statistical analysis and simulated the validity of this algorithm using C programming language.