无线联邦学习中用多密钥加密实现无信道估计的隐私聚合
Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels
- 采用xMK-CKKS多密钥加密，通过重传公钥和密文使大模数项代数抵消
- 在低速直达波信道下，通信开销与模型维度无关，收敛速率保持O(1/√K)
- 适合对客户端隐私要求高、服务器不可信的边缘联邦学习场景
同态加密（HE）可在不解密的情况下实现联邦学习中的隐私保护聚合。现有无线同态加密方法多依赖单密钥方案，需信道估计或预均衡来补偿无线衰落。但单密钥方案对持有共享密钥的诚实但好奇（HBC）客户端仍不安全；多密钥同态加密通过为每台设备分配独立密钥，提供更强的客户端级安全。本文提出一种四阶段协议，在无需信道估计的共享无线信道上实现xMK-CKKS的聚合。该协议通过同一信道实现公钥与密文的重传，使得解密时主导的大模数加密项可代数相消。将该协议与缓慢变化的直射波主导信道上的零阶联邦学习结合，每轮仅需设备发送一个加密标量，通信与加密开销与模型维度无关。理论表明，加密与无线聚合引入的残余噪声仅导致可忽略的噪声底限，收敛速率仍保持标准的O(1/√K)，其中K为通信轮数。协议假设服务器不可信，可抵御HBC客户端，防止任一客户端恢复其他参与者的本地更新。基于MNIST与CIFAR-10的数值结果验证了理论分析。
原文摘要 · Abstract (English)
Homomorphic encryption (HE) enables privacy-preserving aggregation in federated learning (FL) by allowing the server to operate on encrypted data without decryption. Existing HE-over-the-air (OTA) methods mainly rely on single-key HE schemes and require channel estimation or pre-equalization to compensate for wireless fading. However, single-key HE remains vulnerable to honest-but-curious (HBC) clients holding the shared secret key, while multi-key HE provides stronger client-level security by assigning each device its own secret key. We propose a four-phase protocol that enables the aggregation of xMK-CKKS over a shared wireless channel without channel estimation. The protocol retransmits partial public keys and ciphertexts through the same channel realization, so that the dominant large-modulus encryption terms cancel algebraically during decryption. We integrate this protocol with zero-order FL over slowly varying LoS-dominant channels, where each device transmits a single encrypted scalar per round and the communication/encryption overhead is independent of the model dimension. We show that the residual noise induced by encryption and wireless aggregation preserves the standard convergence rate \(O(1/\sqrt{K})\) up to a negligible noise floor, where $K$ is the number of communication rounds. The protocol assumes a non-trusted server and is secure against HBC clients, preventing any client from recovering the local updates of other participants. Numerical results on MNIST and CIFAR-10 validate the theoretical analysis.
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