Open Access

ARTICLE

A Privacy-Preserving Aggregation Mechanism with Multi-Key Support and Short Ciphertexts for Federated Learning

Hongzhen Liu¹, Liang Xie¹, Zhiqiang Ru^2,*, Yuan Wan¹, Zhe Zhang¹, Xi Fang^1,*

1 School of Mathematics and Statistics, Wuhan University of Technology, Wuhan, China
2 Xi’an Jiaotong University-China Mobile Communications Group Co., Ltd. Digital Government Joint Research Institute, Xi’an, China

* Corresponding Authors: Zhiqiang Ru. Email: ; Xi Fang. Email:

Computers, Materials & Continua 2026, 88(3), 29 https://doi.org/10.32604/cmc.2026.082755

Received 22 March 2026; Accepted 08 May 2026; Issue published 23 July 2026

Abstract

Federated learning is a privacy-preserving machine learning framework that facilitates model training directly on decentralized data that, due to privacy concerns or transmission costs, cannot be centralized on a server for traditional model training. To prevent adversaries from reconstructing the original data via parameters transmitted during the process, homomorphic encryption is a commonly adopted method. However, it introduces significant communication and computation costs and risks total security failure if any secret key is compromised. This paper proposes a privacy-preserving aggregation mechanism that enables each client to independently generate partial keys for encryption while allowing decryption after homomorphic operations using an aggregated key. Key aggregation for the proposed algorithm is realized through secret sharing. Incorporating these components into a standard federated learning framework yields a novel method that enhances communication efficiency and offers robustness against privacy breaches from internal collusion. The algorithm’s resistance to linear and differential attacks is formally demonstrated by algebraically modeling the encryption procedure. Based on this analysis, the overall security of the method is likewise established. Experiments on the privacy-preserving aggregation mechanism demonstrate that the generated ciphertext exhibits favorable statistical properties and sensitivity. Simulation results of the federated learning method further indicate that, compared to existing encryption schemes, our proposed encryption method reduces communication cost by 77%∼93% with acceptable computational cost, thereby enabling lightweight encryption in federated learning.

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Keywords

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