# Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels

arXiv: https://arxiv.org/abs/2605.30123 · HTML: https://mlsanity.com/paper/2605.30123/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 9 of 9)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Privacy-preserving Federated Learning based on Multi-key Homomorphic Encryption](https://mlsanity.com/paper/2104.06824/) (2021)
- [TeraHertz Band Communication: An Old Problem Revisited and Research Directions for the Next Decade](https://mlsanity.com/paper/2112.13187/) (2021)
- [The Evolution of Applications, Hardware Design, and Channel Modeling for Terahertz (THz) Band Communications and Sensing: Ready for 6G?](https://mlsanity.com/paper/2406.06105/) (2024)
- [Communication-Efficient Zero-Order and First-Order Federated Learning Methods over Wireless Networks](https://mlsanity.com/paper/2508.08013/) (2025)

## Abstract (arXiv)

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/√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.