FedPHE: A Secure and Efficient Federated Learning via Packed Homomorphic Encryption

Cross-silo federated learning (FL) enables multiple institutions (clients) to collaboratively build a global model without sharing private data. To prevent privacy leakage during aggregation, homomorphic encryption (HE) is widely used to encrypt model updates, yet incurs high computation and communication overheads. To reduce these overheads, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">packed</i> HE (PHE) has been proposed to encrypt multiple plaintexts into a single ciphertext. However, the original design of PHE assumes all clients share a single private key, making the system vulnerable to security threats of ciphertexts being intercepted and decrypted by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">honest-but-curious clients</i>. Also, it does not consider the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heterogeneity</i> among different clients, resulting in undermined training efficiency with slow convergence and stragglers. To address these challenges, we propose FedPHE, a secure and efficient FL framework with PHE by jointly exploiting contribution-aware secure aggregation and straggler-resistant client selection. Using CKKS with sparsification and blinding, FedPHE achieves efficient secure aggregation that allows clients to only provide <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">obscured</i> encrypted updates while the server can perform aggregation by accounting for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">contributions</i> of local updates. To mitigate the straggler effect, we devise a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">perturbed sketch</i>-based selection to cherry-pick representative clients with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heterogeneous models and computing capabilities</i> in a communication-efficient and privacy-preserving manner. We show, through rigorous security analysis and extensive experiments, that FedPHE can efficiently safeguard clients' privacy, achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.45-6.56\times$</tex-math></inline-formula> training speedup, cut the communication overhead by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.32-24.85\times$</tex-math></inline-formula>, and reduce straggler effects by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.89-2.78\times$</tex-math></inline-formula>.