To address the challenge of user access authentication under resource-constrained conditions, this paper proposes a fast multi-factor authentication algorithm that integrates ID, password, biometrics, physical unclonable function (PUF), and challenge-response mechanisms. The algorithm leverages a dynamic biometric key-based challenge-response mechanism to enhance user authentication security. PUF authentication is performed on user devices, with the security further strengthened by associating PUF with the authentication gateway and user biometrics. The algorithm employs lightweight operations such as hashing, XOR, and symmetric encryption, with lower communication overhead and computational overhead. It meets essential security requirements, demonstrating resistance to replay attacks, impersonation attacks, DDoS attacks, and other common threats.