How can the Diffie-Hellman key exchange be extended to three parties? Possible Duplicate:
  Can one generalize the Diffie-Hellman key exchange to three or more parties?  




How can Alice, Bob, and Charlie share a common secret key using an extended version of the Diffie-Hellman key exchange protocol?

a=3, b=4, c=5
g=2
p=5
Alice computes $A=g^a$, Bob computes $B=g^b$ and Charlie computes $C=g^c$.
$A,B$ and $C$ are published.
Alice computes $AC=C^a$ and $AB=B^a$ and Bob computes $BC=C^b$.
$AB,AC$ and $BC$ are published.
Alice computes $ABC=BC^a$, Bob computes $ABC=AC^b$ and Charlie
computes $ABC=AB^c$.
Everybody shares $ABC=g^{abc}$.


This can be generalized for any number of participants in a tree construction, however it becomes increasingly inefficient, because the number of rounds increases.