Messages are frequently addressed to a group of people, e.g., board of directors. Conventional and public key systems (in the sense of Diffie and Hellman [4]) are not adapted when messages are intended for a group instead of for an individual. To deeply understand the lack of usefulness of the above cryptmystems in the case that messages are intended for (or are originating from) a group of people, let u s now nevertheless attempt to use these systems. When conventional and public key systems are used to protect privacy, the legitimate receiver(s) has (have) to know the secret key to decrypt. This means that, a first solution could be, to send the message to dl members of the group, e.g., using their public keys. A second is that the secret key is known to all membexs and that the message is sent only once. All other solutions using a conventional or public key system, are combinations of the above two solutions. We now explain briefly why these two obvious solutions are not adapted to security needs specific to the protection of information intended for groups.