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The Session Initiation Protocol (SIP) is a standard for managing IP multimedia sessions in the Internet. Identity management in SIP is a crucial security field that deals with identifying users in SIP networks and controlling their access to the corresponding resources. RFC 4474 describes a mechanism, based on certificates, for dealing with the SIP users identities. This RFC recommends the use of the RSA algorithm as it is currently the most popular public key cryptography system. The proliferation of small and simple devices as well as the need to increase the capacity of the SIP servers to handle the increasing VoIP traffic will make continued reliance on RSA more challenging over time. In this paper, we describe our implementation of the current RFC 4474, our integration of elliptic curves cryptography into this RFC and show that the corresponding performance is much more significant than the one where RSA is used. This paper can be considered as a first step in standardizing the use of elliptic curves in the identity management for SIP.