Elliptic curve cryptography , a new and most improved cryptographic algorithm of the era. This book concern about how efficiently one can imposed this algorithm in GSM network. Unlike any wired telephone network GSM is most widely used telephone network in which security is always a great issue. So this book contains detailed discussion about RSA and ECC and some codes for developing programming ideas and corresponding output for better understanding of reader. The book shows with the help of one of the most powerful algorithms : elliptic curve cryptography whether GSM security will be more improved or not.