I’m looking for a one-way accumulator which can safely add new members (deletion is not necessary) and does not rely on a trusted party in any way. Unfortunately it appears that it does not exist yet.
My project has an authentication based on a block chain (like Bitcoin) so it's manually initialized and after that it runs on its own. If I put a hash in every block, nodes relay special packets only for the authenticated users, hence the need for a simple authentication scheme without a group manager, no one is to be trusted more than yourself in his honesty. After a round of votes all the nodes agree on the entrance of a new member and the hash is changed accordingly (or witnesses depending on the scheme) and the ban of a member is simply another "black list" hash (or some other method depending on the scheme).