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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.30123 |
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| _version_ | 1866918529690763264 |
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| author | Ayli, Anthony Harris, Khalil Fahs, Jihad Assaad, Mohamad |
| author_facet | Ayli, Anthony Harris, Khalil Fahs, Jihad Assaad, Mohamad |
| contents | 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 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 clients sharing the same secret key. In addition, compromising a single client may compromise the security of the entire network, while multi-key HE schemes provide stronger client-level security by assigning each device its own secret key. We propose a four-phase protocol that enables xMK-CKKS, a famous multi-key HE scheme, aggregation 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 prove that the decoded encryption noise preserves the \(O(1/\sqrt{K})\) convergence rate up to a negligible noise floor. The protocol is secure against an honest-but-curious server colluding with up to \(N-1\) clients, and numerical results on MNIST validate the analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30123 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels Ayli, Anthony Harris, Khalil Fahs, Jihad Assaad, Mohamad Cryptography and Security Machine Learning 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 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 clients sharing the same secret key. In addition, compromising a single client may compromise the security of the entire network, while multi-key HE schemes provide stronger client-level security by assigning each device its own secret key. We propose a four-phase protocol that enables xMK-CKKS, a famous multi-key HE scheme, aggregation 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 prove that the decoded encryption noise preserves the \(O(1/\sqrt{K})\) convergence rate up to a negligible noise floor. The protocol is secure against an honest-but-curious server colluding with up to \(N-1\) clients, and numerical results on MNIST validate the analysis. |
| title | Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels |
| topic | Cryptography and Security Machine Learning |
| url | https://arxiv.org/abs/2605.30123 |