Privacy-preserving hierarchical federated learning via CKKS homomorphic encryption

Hierarchical federated learning (HFL) reduces cloud-facing traffic by aggregating client updates at intermediate edge servers, but plaintext aggregation exposes model updates to honest-but-curious infrastructure. This paper studies a client–edge–cloud HFL architecture protected by the Cheon–Kim–Kim–Song (CKKS) approximate homomorphic-encryption scheme and evaluated under wireless impairments. Clients encrypt packed model updates, edge servers aggregate ciphertexts, and the cloud completes the second aggregation stage without accessing plaintext updates. A trusted key holder alone decrypts the global update. The wireless model accounts for heterogeneous bandwidth, fading, packet loss, retransmissions, and deadline-based client admission. Experiments on Fashion-MNIST use 20 clients, four edge servers, Dirichlet non-IID partitioning with concentration α = 0.5 , and 100 global rounds. Four variants are compared: plaintext HFL, CKKS-HFL, wireless plaintext HFL, and wireless CKKS-HFL. Under reliable links, plaintext and CKKS curves nearly overlap and exceed 91% final accuracy, while CKKS relative aggregation error remains below approximately 6 × 1 0 − 10 in the ideal-link case. Wireless plaintext HFL remains close to the reliable-link baseline because almost all clients are received each round. In contrast, wireless CKKS-HFL admits only about one to seven clients per round because encrypted updates are much larger, causing noisier convergence and lower final accuracy of approximately 89%. HFL nevertheless reduces encrypted edge-to-cloud traffic from roughly 670 MB at the client tier to about 470 MB in the ideal CKKS case, with larger reductions when wireless admission limits participation. These results show that CKKS numerical error is negligible, whereas ciphertext-induced communication pressure is the dominant practical bottleneck.