With the rapid development of electric vehicles and energy storage systems, the state of health (SOH) monitoring of power batteries has become a key task to ensure battery safety and extend their service life. However, the traditional centralized battery management system (BMS) faces the dual challenges of computing resources and privacy protection in large-scale applications. To this end, this paper proposes a power battery SOH monitoring BMS architecture based on distributed algorithms and privacy protection mechanisms. First, this paper designs a distributed SOH evaluation algorithm to improve the overall computing efficiency of the system. Then, this paper adopts privacy protection technology and combines the secure multi-party computing (SMC) protocol to complete the integration and sharing of SOH information. This architecture effectively protects the privacy of battery data and realizes the accurate transmission of SOH evaluation results. Finally, the experimental results show that the distributed BMS architecture can significantly improve computing efficiency, reduce system latency, and show excellent security performance in multiple privacy protection attack scenarios. For example, in high-load scenarios, the distributed architecture reduces the computing time by about 88% compared with the traditional centralized BMS. At the same time, in the privacy protection experiment, the risk of data leakage is reduced by more than 60%, showing its strong advantages in battery health management.