We revisit the password-based group key exchange protocol due to Lee et al. (2004), which carries a claimed proof of security in the Bresson et al. model under the intractability of the Decisional Diffie–Hellman problem (DDH) and Computational Diffie–Hellman (CDH) problem. We reveal a previously unpublished flaw in the protocol and its proof, whereby we demonstrate that the protocol violates the definition of security in the model. To provide a better insight into the protocol and proof failures, we present a fixed protocol. We hope our analysis will enable similar mistakes to be avoided in the future. We also revisit protocol 4 of Song and Kim (2000), and reveal a previously unpublished flaw in the protocol (i.e., a reflection attack).