Abstract: A method for generating a cryptographic key by players in a dynamic group, where: 1) a first player U1 initiates an upflow to the next player, the upflow based on a random value x1, a random value v1, 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 Up sends an upflow Flp, comprising information based on a random value xp, a random value vp, and the previous upflow Flp?1; 3) the last player Up sends a downflow Fln to all other players in the dynamic group, where the downflow Fln comprises information based on a random value xn, a random value vn, and the previous upflow Fln?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.