Implementation

 

TREE_API is a group key agreement API implementing the cryptographic primitives of TGDH. The underlying communication system is assumed to deal with group communication and network events such as merges, partitions, failures and other abnormalities. TREE_API is small and it contains only the following three function calls:

• tree_new_user generates a group context for a new group member (including its secret share).
• tree_merge_req is called by each sponsor when a merge occurs. The output (new key tree) is then broadcast to the merging group. This function performs no cryptographic operations.
• tree_cascade is the core function of TREE_API. Every group member calls this function following a membership event. The function is called repeatedly until the group key is computed.

As mentioned in section 6, tree_cascade provides robustness against cascaded network events. Since TREE_API does not provide its own communication facility, the robustness of the API was tested by simulating random events on a single machine running all group members.

We use OpenSSL 0.9.4 [12] as the underlying cryptographic library. Note that we set $f(x)\; =\; (xp)\; q$ where $x\; \in Z$_q so as to enhance the efficiency of our protocol.