Considering a protocol of Tseng, we show that a group key agreement protocol that resists attacks by malicious insiders in the authenticated broadcast model, loses this security when it is transfered into an unauthenticated point-to-point network with the protocol compiler introduced by Katz and Yung. We develop a protocol framework that allows to transform passively secure protocols into protocols that provide security against malicious insiders and active adversaries in an unauthenticated point-to-point network and, in contrast to existing protocol compilers, does not increase the number of rounds. Our protocol particularly uses the session identifier to achieve the security. By applying the framework to the Burmester-Desmedt protocol we obtain a new 2 round protocol that is provably secure against active adversaries and malicious participants.