Patent ID: 7333617

Claim:
A method for establishing a common key for a group of at least three subscribers for transmitting messages over a communication channel, the method comprising the steps of: generating, by each subscriber T j , a respective message N j =(g zj mod p) from a publicly known element g of large order of a publicly known mathematical group G and a respective random number zj, j=1 to n, where n is the number of subscribers in the group of at least three subscribers; sending the respective message Nj, by each subscriber, to each of the other subscribers T j ; encrypting, by a first subscriber T 1 , the received messages N j of the other subscribers T j , j≠1, with the random number z1 to form a respective transmission key k 1j for each subscriber T j , j≠1; computing, by each subscriber T j , j≠1, a symmetrical counterpart k j1 of the respective transmission key k 1j using the received message N 1 ; sending, by the first subscriber T 1 , the random number z1 to all other subscribers T j , j≠1 in encrypted form by generating a message M 1j according to M 1j :=E(k 1j , z1), E(k 1j , z1) being a symmetrical encryption algorithm in which the random number z1 is encrypted with the transmission key k 1j ; decrypting, by each subscriber T j , the message M 1j ; determining a common key k, by each subscriber Tj, using an assignment k:=h(z1, g x2 , . . . , g zn ), h(x1, x2, . . . , xn) being a function which is symmetrical in the arguments x2, . . . , xn; encrypting, by one of the subscribers T i , a transmission message using the common key k; and transmitting the encrypted transmission message to at least one of the other subscribers T j , j≠i.