Abstract: The network and each user i share an encryption algorithm EK.sub.i () using his authentication key K.sub.i as a cipher key, its inverse function EK.sub.i.sup.-1 (), a specific function F() and its inverse function F.sup.-1 (), and a function G(). The network calculates C.sub.1 =EK.sub.i (F(r.sub.n, r.sub.u)), using a random number r.sub.n generated by the user and a random number by the network, and sends it to the user. The user calculates (d.sub.1, d.sub.2)=F.sup.-1 (EK.sub.i.sup.-1 (C.sub.1)) and, if d.sub.1 =r.sub.n, judges the network to be an authorized one. The user generates a random number r.sub.c and sends C.sub.2 =EK.sub.i (F(d.sub.2, r.sub.c)) to the network. The network calculates (d.sub.3, d.sub.4)=F.sup.-1 (EK.sub.i.sup.-1 (C.sub.2)) and, if d.sub.3 =r.sub.u, judges the user to be an authorized one.

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.