Extended diffie-hellman group key generation
View Patent ↗Described are group key generation and distribution mechanisms that offer efficient protection for multi-party communication applications. A network includes a key distribution center (KDC) and m relay stations (RS). The KDC and each RS choose their own secret number. Each RS encodes its secret number and sends it to the KDC. The KDC uses the secret numbers from all the RS's, as well as its own secret number, to generate a random group key RGK. Then, to each RS, the KDC sends a partial key, which is a mathematical combination of the RGK with that RS's secret number. Each RS can then combine its secret number with the received partial key to deduce the RGK. Once all RS have deduced the RGK, the RGK can be used for further key exchange and encryption procedures and encrypted data transfer.
1. A method for use in a network of m members comprising the steps of:
arranging the network such that one member is a key distribution center (KDC) and the other m members are relay stations (RS), wherein RS(i) denotes the ith RS;
sending by each RS(i) a random number K(i) based on g^r(i) to the KDC, wherein g is a generator and r(i) is a random integer picked by the RS(i);
generating by the KDC a random group key RDK based on g^(r( 1 )r( 2 ) . . . r(m))R, wherein g is the generator, and R is a random number generated by the KDC;
sending by the KDC back to each RS(i) a partial key g^((r( 1 )r( 2 ) . . . r(m))Rr(i) −1 ); generating by each RS(i) from the received partial key the RDK based on g^(r( 1 )r( 2 ) . . . r(m)R)r(i); and
using the RDK by all m members of the group to secure communications between the members of the group.
2. The method of claim 1 further comprising the steps of:
adding a new relay station RS(o) to the network;
sending by RS(o) a random number K(o) based on g^r(o) to the KDC, wherein g is a generator and r(o) is a random integer picked by the RS(o);
generating by the KDC a random group key RDK′ based on g^(r( 1 )r( 2 ) . . . r(m)r(o))R;
sending by the KDC back to RS(o) a partial key g^((r( 1 )r( 2 ) . . . r(m)r(o)R)r(o) −1− );
sending by the KDC back to each RS(i) a partial key g^((r( 1 )r( 2 ) . . . r(m)r(o))Rr(i) 1 ); and
using the RDK′ by all m members of the group and RS(o) to secure communications between the members of the group including RS(o).
3. A method for use by a node in a relay network comprising the steps of:
sending by a relay station RS( 1 ) a random number K( 1 ) based on g^r( 1 ) to a key distribution center (KDC), wherein g is a generator and r 1 is a random integer picked by RS 1 , RS 1 being one of group of m relay stations wherein RS(i) notes the ith RS and each RS(i) sends a K(i) based on g^r(i) to the KDC;
receiving by RS( 1 ) partial key g^((r( 2 ) . . . r(m))Rr( 1 ) −1 ), the partial key generated and sent by the KDC, the KDC first generating a random group key RDK based on g^(r( 1 )r( 2 ) . . . r(m))R, wherein g is the generator, and R is a random number generated by the KDC, the KDC then generating the partial key;
generating by RS( 1 ) from the received partial key the RDK based on g^(r( 2 ) . . . r(m)R)r( 1 ); and
using by RS( 1 ) the RDK for secure communications between RS 1 and the other relay stations of the group.
4. A network comprising:
a group including m relay stations RS, wherein RS(i) denotes the ith RS;
a key distribution center KDC;
wherein each RS(i) sends a random number K(i) based on g^ r(i) to the KDC;
wherein the KDC generates a random group key RDK based on g^(r( 1 )r( 2 ) . . . r(m))R, wherein g is a generator, R is a random number generated by the KDC, and r( 1 ), r( 2 ) . . . r(m) are random numbers generated by each RS(i) RS( 1 ), RS( 2 ) . . . RS(m) respectively;
wherein the KDC sends back to each RS(i) a partial key based on g^((r( 1 )r( 2 ) . . . r(m))Rr(i) −1 );
wherein each RS(i) uses the received partial key to generate the RDK based on g^(r( 1 )r( 2 ) . . . r(m)R)r(i); and
wherein the RDK is used by all m members of the group to secure communications between the members of the group.
5. The network of claim 4 comprising:
a new relay station RS(o) added to the network;
wherein RS(o) sends a random number K(o) based on g^r(o) to the KDC, wherein g is a generator and r(o) is a random integer picked by the RS(o);
wherein the KDC generates a random group key RDK′ based on g^(r( 1 )r( 2 ) . . . r(m)r(o))R;
wherein the KDC sends back to RS(o) a partial key g^((r( 1 )r( 2 ) . . . r(m)r(o)R)r(o) −1 );
wherein the KDC sends back to each RS(i) a partial key g^((r( 1 )r( 2 ) . . . r(m)r(o))Rr(i) −1 ); and
wherein the RDK′ is used by all m members of the group and RS(o) to secure communications between the members of the group including RS(o).