Proving membership of a group without revealing identity?
Look at group signatures (but use one of the more modern schemes; they are proven secure). The signature can be applied to a running counter, or a random challenge. Group signatures also give you a lot of "management" options which can be useful depending on the application. If you don't need them, then you can use ring signatures (but the verifier has to check that the ring includes only members of the set, or someone else can easily join).