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Encryption is used in a communication system to safeguard information in the transmitted messages from anyone other than the intended receiver(s). To perform the encryption and decryption the transmitter and receiver(s) ought to have matching encryption and decryption keys. A clever way to generate these keys is to use the public key distribution system invented by Diffie and Hellman. That system, however, admits only one pair of communication stations to share a particular pair of encryption and decryption keys, The public key distribution system is generalized to a conference key distribution system (CKDS) which admits any group of stations to share the same encryption and decryption keys. The analysis reveals two important aspects of any conference key distribution system. One is the multitap resistance, which is a measure of the information security in the communication system. The other is the separation of the problem into two parts: the choice of a suitable symmetric function of the private keys and the choice of a suitable one-way mapping thereof. We have also shown how to use CKDS in connection with public key ciphers and an authorization scheme.