Secure group key management (GKM) schemes typically operate under a passive adversary model to evaluate the requirements for forward and backward secrecy. In this model, the adversary can join and leave the group at will. In contrast, the strong adversary model is known as the strong active outsider adversary (SAOA) model, where the adversary is permitted to compromise a legitimate user within the group. Research has shown that all schemes based on the Chinese Remainder Theorem (CRT) are vulnerable to an SAOA adversary. One of the open problems is the design of a secure GKM scheme that can withstand an SAOA adversary without introducing significant complexity. In this work, we propose a first-of-its-kind CRT-based GKM scheme that remains secure against an SAOA adversary while maintaining a rekeying complexity comparable to that of existing CRT-based GKM schemes designed for passive adversaries. Our proposed method can be applied to enhance the security of all current CRT-based key management schemes against SAOA adversaries.