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<p>Federated learning (FL) enables distributed model training across multiple clients while keeping local data decentralized, addressing critical data privacy concerns in traditional centralized learning paradigms. However, scaling FL to large-scale distributed systems with high-dimensional data demands supercomputing capabilities for parallel processing, low-latency communication, and real-time aggregation. In previous privacy preservation schemes in FL, numerous schemes rely on homomorphic encryption (HE) or asymmetric encryption techniques to protect clients’ model gradients which incur polynomial multiplication. Even though many existing researchers have devoted themselves into efficient FL scheme, these schemes still impose a significant computational burden on the client side, making them unsuitable for computationally constrained devices. This paper proposes a novel privacy-preserving FL scheme that incorporates a matrix transformation method leveraging magic square (MS) to generate masks for blinding clients’ gradients. The matrix transformation method involves only addition operations and simple index transformations, making it friendly to computationally constrained clients such as mobile phones and IoT devices. Importantly, this lightweight design is inherently parallelizable, enabling seamless integration with HPC frameworks to support large-scale client networks by distributing mask generation across GPU clusters. The properties of MS ensure that even the masked gradients are transmitted in plaintext form, individual clients’ gradients remain computationally indistinguishable. In terms of transmission efficiency, the proposed scheme utilizes a Chinese Remainder Theorem (CRT)-based method to compress gradients. This compression reduces the volume of data to be transmitted, thereby lowering the communication overhead between clients and the server. Overall, the proposed scheme improves both computational and communication efficiency while preserving the privacy of clients’ gradients. The experimental results demonstrate that our scheme achieves an efficiency improvement in gradients blinding.</p>

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A privacy-enhanced federated learning scheme via magic squares

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Yingze Fan,
  • Tianqi Zhou,
  • Wenying Zheng

摘要

Federated learning (FL) enables distributed model training across multiple clients while keeping local data decentralized, addressing critical data privacy concerns in traditional centralized learning paradigms. However, scaling FL to large-scale distributed systems with high-dimensional data demands supercomputing capabilities for parallel processing, low-latency communication, and real-time aggregation. In previous privacy preservation schemes in FL, numerous schemes rely on homomorphic encryption (HE) or asymmetric encryption techniques to protect clients’ model gradients which incur polynomial multiplication. Even though many existing researchers have devoted themselves into efficient FL scheme, these schemes still impose a significant computational burden on the client side, making them unsuitable for computationally constrained devices. This paper proposes a novel privacy-preserving FL scheme that incorporates a matrix transformation method leveraging magic square (MS) to generate masks for blinding clients’ gradients. The matrix transformation method involves only addition operations and simple index transformations, making it friendly to computationally constrained clients such as mobile phones and IoT devices. Importantly, this lightweight design is inherently parallelizable, enabling seamless integration with HPC frameworks to support large-scale client networks by distributing mask generation across GPU clusters. The properties of MS ensure that even the masked gradients are transmitted in plaintext form, individual clients’ gradients remain computationally indistinguishable. In terms of transmission efficiency, the proposed scheme utilizes a Chinese Remainder Theorem (CRT)-based method to compress gradients. This compression reduces the volume of data to be transmitted, thereby lowering the communication overhead between clients and the server. Overall, the proposed scheme improves both computational and communication efficiency while preserving the privacy of clients’ gradients. The experimental results demonstrate that our scheme achieves an efficiency improvement in gradients blinding.