A network fault can cause a partition of the group. To the remaining members, this actually appears as a concurrent leave of multiple members. With a minor modification, the leave protocol can handle multiple leaving members in a single round. The only difference is the sponsorselection. In case of a partition, the sponsoris the leaf node directly below the lowest-numbered leaving member. (If is the lowest-numbered leaving member, the sponsoris the lowest-numbered surviving member.)
After deleting all leaving nodes, the sponsor refreshes its session random (key share), computes keys and blinded keys going up the tree - as in the plain leave protocol - terminating with the computation of . It then broadcasts the updated key tree containing only blinded values. Each member including can now compute the group key.
The computation and communication complexity of the partition protocol is identical to that of the leave protocol. The same holds for its security properties.