Is it possible to accomplish the following scheme?
There is a Server (S) and many clients.
Each client enrolls with S, exposing its real identity; S saves the real identity information in its database and executes some keys/identifiers exchange with each client (could be something like DHE or RSA).
Then, someone sends to S a claim such that S would be able to tell that this claim comes from one of the enrolled clients, but not being able to identify from which one (inability similar to factoring large prime numbers). At the same time S should be able to save it and only accept 2 more claims from the remaining clients (i.e. the client that have sent a claim can't send it again).
No client should have such information that, if leaked, could invalidate the entire scheme. In other words, any exposure of the identifier of a single client should only put in danger the ability of this client to make its claim.
A case: 3 clients (X, Y and Z) enroll with S.
X makes a claim to S.
S verifies that it comes from one of the clients and saves it, notifying the client that the claim was accepted. S does NOT know that the claim came from X. At this point, S only knows that 2 of the 3 claims remain.
Z makes its claim. S verifies and accepts it.
At this point S knows that only 1 claim remains.
X sends its claim again. S finds that it was already claimed and rejects it.
Y sends it claim. S verifies and accepts it.
At this point, S knows that all the claims were made.