A method for establishing a common key for a group of at least three subscribers includes using a publicly known mathematical number group and a higher order element of the group g.epsilon.G. In the first step, a message corresponding to Ni:=g.sup.zi mod p is sent by each subscriber to all other subscribers (Tj), (zi) being a random number chosen from the set (1, . . . , p-2) by a random number generator. In the second step, each subscriber (Ti) selects a transmission key kij:=(g.sup.zj).sup.zi for each other subscriber (Tj) from the received message (g.sup.zj), with i.noteq.j, for transmitting their random number (zi) to the subscribers (Tj). In the third step, the common key k is calculated as k:=f(z1, z2, . . . , zn) for each subscriber Ti.