Method for establishing a common key for a group of at least three subscribers

Procedure for establishing a common key for a group of at least three participants using a mathematical group G and a known publicly element gG group of higher order, characterized in that a) each participant Ti, from the g element of group G and one zi number chosen by the participant or randomly generated, generates a message Ni = (GZI mod p) and sends the message to all other participants Tj, because b) each Ti participant from the Nj messages received from other participants Tj, with ji, and his zi random number and according to kij = Njzi = (gzj) function zi generates a transmission key kij which is known by the participant Tj thanks to the relationship kij = KJI, because c) each Ti participant sends encrypted the random number zi to each of the other participants Tj by generating the message Mij as Mij = E (k ij, zi), where E (k ij, zi) a symmetric encryption algorithm in which the dataset zi is encrypted with the key common transmission kij, and that d) each Ti participant determines the common key ka establish, from its own random number zi and random numbers zj, with ji, received from other participants as the formula k = f (z1, ..., zn) in which f must be an invariant symmetric function when their arguments are interchanged.