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Advancing Privacy-Preserving Federated Learning: Innovative Frameworks and Protocols

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 31 July 2026 | Viewed by 1899

Special Issue Editors

Cybersecurity Research Institute, National Institute of Information and Communications Technology (NICT), Koganei, Tokyo 184-8795, Japan
Interests: applied cryptography; privacy-preserving machine learning; secure data utilization

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Guest Editor
School of Computing, Queen's University, Kingston, ON K7L 2N8, Canada
Interests: privacy enhancing technologies; IoT-big data security and privacy; applied cryptography
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Special Issue Information

Dear Colleagues,

The increasing demand for data privacy and secure machine learning has fueled interest in federated learning (FL)—a paradigm that enables the training of machine learning models across distributed devices and servers without centralized data collection. This aligns closely with the core themes of Entropy, including information-theoretic security, uncertainty quantification, and the trade-offs among privacy, utility, and efficiency. Despite its promise, federated learning still faces critical challenges in guaranteeing robust privacy in the context of realistic adversarial models. This Special Issue invites high-quality, original research that advances the theoretical foundations and practical implementations of privacy-preserving federated learning, grounded in information theory, entropy-based analysis, and cryptographic mechanisms. We especially welcome interdisciplinary contributions that explore the intersection of machine learning, cryptography, and information theory. Studies that provide measurable security guarantees, resource-efficient protocols, and scalable system designs are of particular interest. 
Topics of interest include, but are not limited to, the following:

  • Novel protocols for privacy-preserving federated learning;
  • Information-theoretic and entropy-based approaches to privacy in FL;
  • Practical frameworks combining distributed machine learning and cryptography;
  • Integration of homomorphic encryption, secure multiparty computation, and differential privacy in decentralized learning;
  • Blockchain and distributed ledger technologies for enhancing trust and accountability in FL;
  • Theoretical analysis of privacy–utility trade-offs;
  • Secure aggregation and model update strategies;
  • System architectures and real-world deployments of privacy-preserving FL;
  • Benchmarking, evaluation metrics, and performance analysis of privacy-enhanced federated systems;
    The submission of manuscripts that address related advancements in privacy-preserving techniques for other distributed or collaborative learning paradigms is also encouraged. We look forward to receiving your contributions.

Dr. Lihua Wang
Prof. Dr. Rongxing Lu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • federated learning
  • privacy preserving
  • homomorphic encryption
  • differential privacy
  • secure multiparty computation
  • privacy-enhancing technologies
  • distributed AI
  • applied cryptography

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Published Papers (2 papers)

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Research

18 pages, 639 KB  
Article
Efficient Non-Interactive Discrete ReLU over CKKS Using Interpolation Look-Up Table
by Zhigang Chen, Xinxia Song and Liqun Chen
Entropy 2026, 28(5), 542; https://doi.org/10.3390/e28050542 - 11 May 2026
Viewed by 203
Abstract
Deploying neural networks on encrypted data requires efficient evaluation of nonlinear activations, especially the ReLU function, without decryption. While the CKKS homomorphic encryption scheme supports packed arithmetic over approximate numbers efficiently, its approximate semantics make direct nonlinear evaluation difficult, and polynomial surrogates often [...] Read more.
Deploying neural networks on encrypted data requires efficient evaluation of nonlinear activations, especially the ReLU function, without decryption. While the CKKS homomorphic encryption scheme supports packed arithmetic over approximate numbers efficiently, its approximate semantics make direct nonlinear evaluation difficult, and polynomial surrogates often introduce approximation error and non-discrete outputs. In this work, we present a task-specific, non-interactive construction for discrete ReLU evaluation in CKKS by combining modulus-switch-based discretization with interpolation-driven lookup-table (LUT) evaluation. We instantiate this design in two complementary schemes. The first uses trigonometric Hermite interpolation and functional bootstrapping to compute a discrete sign indicator, which is then combined with the encrypted input through conditional multiplication to obtain the ReLU output; this variant is compact and suitable for lightweight settings. The second uses iterative most-significant-bit (MSB) bootstrapping to support larger plaintext moduli and higher-precision regimes through repeated digit extraction. A common enabler of both schemes is a discretization step that maps approximate CKKS plaintexts to a finite integer representation; exactness in our setting therefore refers to exact evaluation over this discretized representation, while the deviation from the original CKKS plaintext is governed by the discretization error analyzed in Lemma 1. Experiments on encrypted MNIST inference and the accompanying LUT/storage analysis indicate that the proposed schemes preserve competitive accuracy relative to polynomial-approximation baselines while maintaining manageable auxiliary storage under the reported parameter settings. These results suggest that interpolation-based discrete activation is a promising alternative to polynomial approximation for selected CKKS-based encrypted inference tasks. Full article
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29 pages, 473 KB  
Article
FedHGPrompt: Privacy-Preserving Federated Prompt Learning for Few-Shot Heterogeneous Graph Learning
by Xijun Wu, Jianjun Shi and Xinming Zhang
Entropy 2026, 28(2), 143; https://doi.org/10.3390/e28020143 - 27 Jan 2026
Viewed by 697
Abstract
Learning from heterogeneous graphs under the constraints of both data scarcity and data privacy presents a significant challenge. While graph prompt learning offers a pathway for efficient few-shot adaptation, and federated learning provides a paradigm for decentralized training, their direct integration for heterogeneous [...] Read more.
Learning from heterogeneous graphs under the constraints of both data scarcity and data privacy presents a significant challenge. While graph prompt learning offers a pathway for efficient few-shot adaptation, and federated learning provides a paradigm for decentralized training, their direct integration for heterogeneous graphs is non-trivial due to structural complexity and the need for rigorous privacy guarantees. This paper proposes FedHGPrompt, a novel federated framework that bridges this gap through a cohesive architectural design. Our approach introduces a three-layer model: a unification layer employing dual templates to standardize heterogeneous graphs and tasks, an adaptation layer utilizing trainable dual prompts to steer a frozen pre-trained model for few-shot learning, and a privacy layer integrating a cryptographic secure aggregation protocol. This design ensures that the central server only accesses aggregated updates, thereby cryptographically safeguarding individual client data. Extensive evaluations on three real-world heterogeneous graph datasets (ACM, DBLP, and Freebase) demonstrate that FedHGPrompt achieves superior few-shot learning performance compared to existing federated graph learning baselines (including FedGCN, FedGAT, FedHAN, and FedGPL) while maintaining strong privacy assurances and practical communication efficiency. The framework establishes an effective approach for collaborative learning on distributed, heterogeneous graph data where privacy is paramount. Full article
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