For example in my course there is this protocol :
Initialisation: A and B are sharing a symmetric key S.
(1) A -> B: Ra ; A generates a random number and sends it to A
(2) A <- B: Rb ; B does the same
A and B computes the session key K := E_S(Ra XOR Rb).
Why A and B would establish a new key K if they already have the key S ?
I don't get it.
For me, the Diffie-Hellman protocol is coherent because it establishes a key between 2 entities that have never talked before.