Healthcare federated learning requires strong privacy guarantees while maintaining computational efficiency across resource-constrained medical institutions. This paper presents MedHE, a novel framework combining adaptive gradient sparsification with CKKS homomorphic encryption to enable privacy-preserving collaborative learning on sensitive medical data. Our approach introduces a dynamic threshold mechanism with error compensation for top-k gradient selection, achieving 97.5 percent communication reduction while preserving model utility. We provide formal security analysis under Ring Learning with Errors assumptions and demonstrate differential privacy guarantees with epsilon less than or equal to 1.0. Statistical testing across 5 independent trials shows MedHE achieves 89.5 percent plus or minus 0.8 percent accuracy, maintaining comparable performance to standard federated learning (p=0.32) while reducing communication from 1277 MB to 32 MB per training round. Comprehensive evaluation demonstrates practical feasibility for real-world medical deployments with HIPAA compliance and scalability to 100 plus institutions.

翻译：医疗健康领域的联邦学习需要在资源受限的医疗机构之间提供强隐私保障的同时保持计算效率。本文提出MedHE，一种将自适应梯度稀疏化与CKKS同态加密相结合的新型框架，以实现对敏感医疗数据的隐私保护协同学习。我们的方法引入了一种带误差补偿的动态阈值机制用于top-k梯度选择，在保持模型效用的同时实现了97.5%的通信量削减。我们在环上容错学习假设下提供了形式化的安全性分析，并证明了ε≤1.0的差分隐私保障。基于5次独立试验的统计检验表明，MedHE达到了89.5%±0.8%的准确率，在保持与标准联邦学习相当性能（p=0.32）的同时，将每轮训练的通信量从1277 MB降低至32 MB。综合评估证明了该框架在实际医疗部署中符合HIPAA规范、可扩展至100+机构的可行性。