Abstract: A communication network and its user i has a device for implementing a common key cryptosystem, an identifier of the user i represented by ID.sub.i which is made public in the network, an authentication key of a user i represented by S.sub.i is known only to the network and the user i and these identifiers and authentication keys of all the users are stored in a database of the network. Data for authentication and encrypted data of a cipher key for the subsequent privacy communication are sent from the network to the user, the user presents his identifier (ID) to the network, after which up to three interactions take place between the network and the user to perform the required authentications and distribution of the cipher key.