Currently, group membership management in IP Multicast and Anycast can be abused in order to launch denial-of- service (DoS) attacks. The root of the problem is that routers cannot determine if a given host is authorized to join a group (this is sometimes referred to as the Proof-of-Membership Problem [1]). We propose a solution for IPv6 based on Group Cryptographically Generated Addresses (G-CGA). These addresses have characteristics of statistical uniqueness and cryptographic verifiability that lend themselves to severely limiting certain classes of DoS attacks. Our scheme is fully distributed and does not require any trusted third party or pre-established security association between the routers and the hosts. This is not only a huge gain in terms of scalability, reliability and overhead, but also in terms of privacy.