In this paper, we present a novel key-indexed channel phase permutation method designed to enhance the security of physical-layer (PHY) authentication in the presence of correlated sub-channels. In wireless communication, secret keys should be protected from eavesdroppers, as unauthorized access to these keys may compromise user security, expose sensitive information, and allow attackers to impersonate legitimate users, bypassing authentication mechanisms. To avoid the malicious interception of the pre-shared secret keys in wireless communication, the proposed scheme takes advantage of the inherent characteristics of reciprocal radio frequency channel phases and the key indices between authorized users. This ensures the completion of PHY authentication process at the PHY layer without divulging the actual secret key to potential attackers. Channel phase data are permuted based on binary key indices and concealed within phase information, thwarting unauthorized access. Through extensive testing using a Universal Software Radio Peripheral testbed, we validate the robustness of our scheme to various attacks, ensuring the confidentiality of secret keys and distinguishing legitimate users from attackers attempting illicit authentication. This method strengthens PHY layer security, offering practical applicability in wireless communication scenarios.