For large-scale Internet of Things (IoT) scenarios, edge caching is required to alleviate backhaul bandwidth pressure while balancing user privacy and security investment costs. A federated learning-based secure edge caching optimization framework is proposed, in which a conversation-based secure aggregation (CSA) protocol is designed, and caching space, backhaul bandwidth, and security investment are jointly modeled within a Stackelberg game. During federated learning training, session windows are adopted as the minimal synchronization unit in CSA. By leveraging long-term session seeds and a dual-masking mechanism, handshake and decryption overhead across multiple training rounds are compressed to the window level while client gradient privacy is preserved. Subsequently, the service provider acts as the leader to price three types of resources, and edge nodes optimize cache shares, backhaul bandwidth, and security investments in parallel under the alternating direction method of multipliers (ADMM) framework, thereby forming a federated learning optimized caching (FLOC) mechanism. Experimental results on the EMNIST and CIFAR-100 datasets show that CSA reduces end-to-end training time by approximately 50% compared with SecAgg with negligible model accuracy loss, approaching non-privacy-preserving FedAvg. In typical edge caching scenarios, FLOC achieves up to 15% higher cache hit rates and 20% lower total backhaul overhead than MP, LRU, LFU, and Greedy strategies. Furthermore, ADMM converges within about a dozen iterations even when the number of users and edge nodes increases by an order of magnitude, demonstrating a favorable balance among privacy protection, resource coordination, and computational complexity.