Under a system referred to as GAA in the 3G protocol, authentication of devices in a network that is usually performed by a home subscriber server can be transferred to a third party element known as a bootstrapping server function. However, the use of a bootstrapping server function does not completely address the problem of reducing authentication traffic at the home subscriber server. Such a problem is alleviated by utilizing the original session key generated under GAA and using that key in a recursive process to authenticate and generate further session keys at other network elements. This generation of further keys can be performed independently of the home subscriber server, and thus reduces traffic at the home subscriber server.