Formal Verification of Divide and Conquer Key Distribution Protocol Using ProVerif and TLA+

We conduct formal verification of the divide and conquer key distribution scheme (DC DHKE)-a contributory group key agreement that uses a quasilinear amount of exponentiations with respect to the number of communicating parties. The verification is conducted using both ProVerif and TLA⁺ as tools. ProVerif is used to verify the protocol correctness as well as its security against passive attacker; while TLA⁺ is utilized to verify whether all participants in the protocol retrieve the mutual key simultaneously. We also verify the ING and GDH.3 protocol for comparative purposes. The verification results show that the ING, GDH.3, and DC DHKE protocols satisfy the pre-meditated correctness, security, and liveness properties. However, the GDH.3 protocol does not satisfy the liveness property stating that all participants obtain the mutual key at the same time.