A method for generating a cryptographic key by players in a dynamic group, where: 1) a first player U.sub.1 initiates an upflow to the next player, the upflow based on a random value x.sub.1, a random value v.sub.1, and "g", a generator of a finite cyclic group where a computational solution to a Diffie-Hellman problem is hard; 2) each player after the first U.sub.p sends an upflow Fl.sub.p, comprising information based on a random value x.sub.p, a random value v.sub.p, and the previous upflow Fl.sub.p-1; 3) the last player U.sub.p sends a downflow Fl.sub.n to all other players in the dynamic group, where the downflow Fl.sub.n comprises information based on a random value x.sub.n, a random value v.sub.n, and the previous upflow Fl.sub.n-1. New players may join the dynamic group in a similar fashion. Players may be removed from the dynamic group by adjusting the downflow to the remaining players. The dynamic group may be refreshed by adjusting the downflow to establish a new cryptographic key.
 This invention was made with U.S. Government support under Contract Number DE-AC03-76SF00098 between the U.S. Department of Energy and The Regents of the University of California for the management and operation of the Lawrence Berkeley National Laboratory. The U.S. Government has certain rights in this invention.