Abstract: The encryption key based on a blocking set cryptosystem includes knowledge of the blocking set, and ciphers (usually independent) on the blocking set and its complement. In order to decipher, a legitimate receiver needs to know only the blocking set and the cipher used on it. Thus it is not necessary for the sender to transmit to anyone the cipher on the complement of the blocking set. The fact that part of the encryption key need not be transmitted is the fundamental difference between the proposed cryptosystem and the so-called private key system, where both the sender and receiver know, but keep secret, the encryption and decryption keys. Particularly useful applications of this scheme are two situations where a central person, institution or computer send out confidential information to several parties, but where none of the parties has the authority to transmit information to the group. This might apply to the main branch of a company, or to a certification authority in a cryptographic protocol.