* King Of Fun:

> All clients have the public key of the server, and the server has all of the 
> public keys of the clients.
> The client can only use its private key for signing. In particular, the 
> client cannot decrypt data that has been encrypted with that client's public 
> key.

TLS with client certificate authentication might fit your needs.  The
server decrypts a challenge sent by the client, and the client signs
most of the handshake messages (including a server-supplied
challenge).
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