As we are entering the third generation of mobile technology (3G) the number of services needing security grows larger. To assess if the security provided by 3G is sufficient, we take a closer look at the security mechanisms and their building blocks. Within the 3G security environment the Kasumi block cipher plays an important role in the integrity and confidentiality provided. Thus the security of Kasumi, the integrity mode ($9) and confidentiality mode (f8) is vital. In this thesis the published attacks, the provable security and the pseudo-randomness of Kasumi are examined in order to consider whether Kasumi, f8 and f9 are secure. Also described are the authentication and key agreement example set Milenage and it's kernel function Rijndael (AES). In addition, background theory is provided for the reader to better understand the proofs and cryptanalytic techniques used. The results of this thesis show no threat to the security of the Milenage, f8 or f9 functions. The security of Kasumi is also preserved as it is a family of pseudo-random permutations and provable secure against linear and differential cryptanalysis.