Originally designed to protect the Neighbor Discovery Protocol (NDP) (part of the IPv6 protocol suite), the Cryptographically Generated Addresses (CGA) and the Secure Neighbor Discovery (SEND) now need to be adapted to the context of Mobility and extended to new functionalities. The term "Mobility" encompasses many aspects, among them : node mobility (Mobile IPv6, MIPv6), router mobility (Network Mobility, NEMO) and network-based mobility management (Proxy Mobile IPv6, PMIPv6). Numerous changes need to be operated on the SEND protocol in order to comply with the Mobility : the cryptographic operations need to be adapted to operate on low power mobile nodes, the incompatibilities between the address sharing model of the mobile protocol and the address protections offered by SEND need to be fixed, etc. Firstly, we present the Neighbor Discovery protocol, the CGA addresses and the SEND protocol. We study their limitations, and, in order to improve their performances, we propose to replace the signature algorithm used in SEND (RSA) by the elliptic curves cryptography (ECC). We then evaluate the performances of our proposal. Subsequently, we modify the SEND protocol to include a signature algorithm selection mechanism. Secondly, we solve incompatilities between the SEND protocol and the mobility protocols (e.g. MIPv6) and between the SEND protocol and the anycast addresses. Finally, we present our contributions containing a derivate use of the CGA addresses and the SEND protocol.