If you know who posted it, you look up their identity in an LDAP directory or something, and find their public key. The public key would decode the encrypted message, as well as authenticating that the person who signed it is the same one that's in the LDAP directory.
Because only the holder of the private key for that (public key, private key) pair could have encrypted the message that is decryptable by their public key. The private key cannot be derived from the public key.