In the Internet of Things (IoT) systems, the central server distributes core information to multiple IoT devices, which need collaboratively process sensitive data upon reception and conduct device authentication. The federated learning frameworks based on Paillier homomorphic encryption encrypts the distributed core information, and uploads the model gradient encryption trained by each device, effectively reducing the risk of core information and sensitive data leakage. However, due to the different computational capabilities of IoT devices and the high computational complexity of Paillier encryption, this process results significant time overhead. Additionally, during device authentication, IoT devices are vulnerable to impersonation attack, and multi-device collaboration may lead to single-point failures under malicious attacks. To address these, this paper proposes a PUF-Paillier dual-factor encryption secret sharing federated learning frameworks (PP-SSFL). In this frameworks, the core information is first partitioned into multiple fragments using the secret sharing scheme, and each IoT device encrypts its received fragment using the PUF-Paillier dual-factor mechanism. Meanwhile, the system integrates a Bayesian reputation-based game auction mechanism to dynamically select a sufficient number of suitable devices to meet the information recovery threshold and employs a Q-Learning algorithm to adaptively adjust the auction strategy, thereby enhancing system efficiency and security. Moreover, Newton interpolation is adopted in place of the Lagrange interpolation used in the Shamir scheme to further accelerate information recovery in multi-device authentication environments. Experimental results show that, compared with original method, the proposed method effectively reduces time overhead and improves system efficiency.