A method and apparatus for negotiating a shared secret among members of a multicast group are disclosed. A tree that represents the group is created and stored in a memory. Each node of the tree is associated with a group member. The shared secret is generated by traversing the tree in post-order, and at each node of the tree, recursively generating a partial key value for use in the shared secret and a base value for use in subsequent recursive partial key value generation. At each node, a partial key value is computed by accumulating the exponent portion of the Diffie-Hellman key equation and computing a new base value for use in subsequent computations. If a particular node has a left or right child sub-tree, each sub-tree is also recursively traversed in post-order fashion. When traversal of the entire tree is complete, all nodes have the shared secret key.