SIM card has an important role in mobile communications. It contains the user's private key, which is used in COMP128 algorithm for user authentication to the mobile network and generating session keys to encrypt communications.
In this thesis a detailed description of COMP128 algorithm is presented. A brute force attack on the algorithm is described, which exploits a weakness in the structure of COMP128 algorithm, and is based on birthday paradox. As a result the user's private key can be obtained in real time. The attack on COMP128 algorithm was also implemented and tested. A separate chapter provides the necessary cryptographic concepts such as authentication, hash functions and birthday paradox.