This paper analyzes the Logical Key Hierarchy (LKH) secure multicast protocol focusing on the reliability of the re-keying authentication process. We show that the key management in the LKH model is subject to some attacks. In particular, these attacks can be performed by entities external to the multicast group, as well as from internal users of the multicast group. The spectrum of these attacks is spread from the Denial of Service (DoS) to the session hijack, that is the attacker is able to have legitimate users to commit on a session key that is provided by the attacker. The contributions of this paper are: (1) the definition of the threats the LKH key management is subject to; and (2) a reliable key authentication scheme that solves the weaknesses previously identified. This objective is achieved without resorting to public key signatures.