Clustered-Support HE-PFL: Coarsening the Sparsity Side Channel for Cheap Encrypted Personalized Federated Learning

Homomorphic encryption (HE) secure aggregation requires coordinate-aligned updates, whereas personalized federated learning (PFL) lets each client share a different parameter subset. Top-k sparsification widens this gap: per-client supports must be unioned and re-packed, exposing a data-dependent cleartext index. We propose Clustered-Support HE-PFL (CSS-FL), a two-phase protocol that clusters clients by their already-exposed Top-k support via k-means on binary indicator vectors. In an index phase, each cluster agrees on one shared sparse support by majority vote; in a value phase, clients encrypt exactly the agreed coordinates, which are aligned by construction and sum directly under CKKS, while non-shared coordinates remain local. Relative to full-union HE, the aggregation server gains no new information (clustering consumes only the routing indices Top-k already exposes), the only values ever decrypted are multi-client cluster means, and every party downstream of the server observes a coarse cluster-level index rather than per-client indices. On MNIST, Fashion-MNIST, and CIFAR-10 with K∈{2,4,8} clusters, LeNet (three seeds; five at the most heterogeneous setting) and ResNet-18 (three seeds), CSS-FL reduce CKKS encryption cost by 5.3–7.3× relative to a constructed Full-Union baseline at 0.25–0.5 the downstreamcleartext index footprint for K≤4 (the server-visible index footprint is unchanged), with personalized accuracy comparable to established PFL baselines (though below Ditto on CIFAR-10), and transmits 5–7× fewer end-to-end bytes including ciphertext expansion. An aggregation-width sensitivity study shows that averaging ≥4 updates, a width the protocol enforces via a minimum-cluster-size merge floor, collapses single-sample DLG reconstruction from 34.5 dB to ≈6 dB.