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In this book, the security algorithms for wireless communications were discussed. Then different algorithms of global system for mobile communications (GSM) and their work have been analysed using qualitative method that we conducted our research which was the research methodology we used for this study.GSM was one of the first digital mobile phone systems to follow the analogue era. Widely known problems with GSM's analogue counter parts were the possibility of phone fraud through cloning phones and thus calling in someone else's expense, and the possibility of someone intercepting the phone call over the air and eavesdropping on the discussion. The GSM system was supposed to correct these problems by implementing strong authentication and encryption. A part of the security in GSM comes from the fact that it is a digital system employing speech coding and channel coding algorithms, GMSK (Gaussian Minimum Shift Keying) modulation, slow frequency hopping and time division multipleaccess (TDMA) timeslot architecture. Finally the authentication and encryption algorithms for GSM were tested using GSM network server and mobile station