A basic idea according to the invention is to enhance or update the basic cryptographic security algorithms by an algorithm-specific modification of the security key information generated in the normal key agreement procedure of the mobile communication system. For communication with the mobile terminal, the network side normally selects an enhanced version of one of the basic cryptographic security algorithms supported by the mobile, and transmits information representative of the selected algorithm to the mobile terminal. The basic security key resulting from the key agreement procedure (AKA, 10) between the mobile terminal and the network is then modified (22) in dependence on the selected algorithm to generate an algorithm-specific security key. The basic security algorithm (24) is then applied with this algorithm-specific security key as key input to enhance security for protected communication in the mobile communications network.