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Keywords = learning homomorphisms with noise

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29 pages, 3212 KB  
Article
Secure Hierarchical Asynchronous Federated Learning with Shuffle Model and Mask–DP
by Yonghui Chen, Daxiang Ai and Linglong Yan
Sensors 2026, 26(2), 617; https://doi.org/10.3390/s26020617 - 16 Jan 2026
Viewed by 192
Abstract
Hierarchical asynchronous federated learning (HAFL) accommodates more real networking and ensures practical communications and efficient aggregations. However, existing HAFL schemes still face challenges in balancing privacy-preserving and robustness. Malicious training nodes may infer the privacy of other training nodes or poison the global [...] Read more.
Hierarchical asynchronous federated learning (HAFL) accommodates more real networking and ensures practical communications and efficient aggregations. However, existing HAFL schemes still face challenges in balancing privacy-preserving and robustness. Malicious training nodes may infer the privacy of other training nodes or poison the global model, thereby damaging the system’s robustness. To address these issues, we propose a secure hierarchical asynchronous federated learning (SHAFL) framework. SHAFL organizes training nodes into multiple groups based on their respective gateways. Within each group, the training nodes prevent inference attacks from the gateways and committee nodes via a mask–DP exchange protocol and employ homomorphic encryption (HE) to prevent collusion attacks from other training nodes. Compared with conventional solutions, SHAFL uses noise that can be eliminated to reduce the impact of noise on the global model’s performance, while employing a shuffle model and subsampling to enhance the local model’s privacy-preserving level. At global model aggregation, SHAFL considers both model accuracy and communication delay, effectively reducing the impact of malicious and stale models on system performance. Theoretical analysis and experimental evaluations demonstrate that SHAFL outperforms state-of-the-art solutions in terms of convergence, security, robustness, and privacy-preserving capabilities. Full article
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23 pages, 1101 KB  
Article
A Reinforcement Learning-Based Optimization Strategy for Noise Budget Management in Homomorphically Encrypted Deep Network Inference
by Chi Zhang, Fenhua Bai, Jinhua Wan and Yu Chen
Electronics 2026, 15(2), 275; https://doi.org/10.3390/electronics15020275 - 7 Jan 2026
Viewed by 217
Abstract
Homomorphic encryption provides a powerful cryptographic solution for privacy-preserving deep neural network inference, enabling computation on encrypted data. However, the practical application of homomorphic encryption is fundamentally constrained by the noise budget, a core component of homomorphic encryption schemes. The substantial multiplicative depth [...] Read more.
Homomorphic encryption provides a powerful cryptographic solution for privacy-preserving deep neural network inference, enabling computation on encrypted data. However, the practical application of homomorphic encryption is fundamentally constrained by the noise budget, a core component of homomorphic encryption schemes. The substantial multiplicative depth of modern deep neural networks rapidly consumes this budget, necessitating frequent, computationally expensive bootstrapping operations to refresh the noise. This bootstrapping process has emerged as the primary performance bottleneck. Current noise management strategies are predominantly static, triggering bootstrapping at pre-defined, fixed intervals. This approach is sub-optimal for deep, complex architectures, leading to excessive computational overhead and potential accuracy degradation due to cumulative precision loss. To address this challenge, we propose a Deep Network-aware Adaptive Noise-budget Management mechanism, a novel mechanism that formulates noise budget allocation as a sequential decision problem optimized via reinforcement learning. The core of the proposed mechanism comprises two components. First, we construct a layer-aware noise consumption prediction model to accurately estimate the heterogeneous computational costs and noise accumulation across different network layers. Second, we design a Deep Q-Network-driven optimization algorithm. This Deep Q-Network agent is trained to derive a globally optimal policy, dynamically determining the optimal timing and network location for executing bootstrapping operations, based on the real-time output of the noise predictor and the current network state. This approach shifts from a static, pre-defined strategy to an adaptive, globally optimized one. Experimental validation on several typical deep neural network architectures demonstrates that the proposed mechanism significantly outperforms state-of-the-art fixed strategies, markedly reducing redundant bootstrapping overhead while maintaining model performance. Full article
(This article belongs to the Special Issue Security and Privacy in Artificial Intelligence Systems)
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24 pages, 1537 KB  
Article
Privacy-Aware Hierarchical Federated Learning in Healthcare: Integrating Differential Privacy and Secure Multi-Party Computation
by Jatinder Pal Singh, Aqsa Aqsa, Imran Ghani, Raj Sonani and Vijay Govindarajan
Future Internet 2025, 17(8), 345; https://doi.org/10.3390/fi17080345 - 31 Jul 2025
Cited by 3 | Viewed by 2420
Abstract
The development of big data analytics in healthcare has created a demand for privacy-conscious and scalable machine learning algorithms that can allow the use of patient information across different healthcare organizations. In this study, the difficulties that come with traditional federated learning frameworks [...] Read more.
The development of big data analytics in healthcare has created a demand for privacy-conscious and scalable machine learning algorithms that can allow the use of patient information across different healthcare organizations. In this study, the difficulties that come with traditional federated learning frameworks in healthcare sectors, such as scalability, computational effectiveness, and preserving patient privacy for numerous healthcare systems, are discussed. In this work, a new conceptual model known as Hierarchical Federated Learning (HFL) for large, integrated healthcare organizations that include several institutions is proposed. The first level of aggregation forms regional centers where local updates are first collected and then sent to the second level of aggregation to form the global update, thus reducing the message-passing traffic and improving the scalability of the HFL architecture. Furthermore, the HFL framework leveraged more robust privacy characteristics such as Local Differential Privacy (LDP), Gaussian Differential Privacy (GDP), Secure Multi-Party Computation (SMPC) and Homomorphic Encryption (HE). In addition, a Novel Aggregated Gradient Perturbation Mechanism is presented to alleviate noise in model updates and maintain privacy and utility. The performance of the proposed HFL framework is evaluated on real-life healthcare datasets and an artificial dataset created using Generative Adversarial Networks (GANs), showing that the proposed HFL framework is better than other methods. Our approach provided an accuracy of around 97% and 30% less privacy leakage compared to the existing models of FLBM-IoT and PPFLB. The proposed HFL approach can help to find the optimal balance between privacy and model performance, which is crucial for healthcare applications and scalable and secure solutions. Full article
(This article belongs to the Special Issue Security and Privacy in AI-Powered Systems)
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25 pages, 2838 KB  
Article
BHE+ALBERT-Mixplus: A Distributed Symmetric Approximate Homomorphic Encryption Model for Secure Short-Text Sentiment Classification in Teaching Evaluations
by Jingren Zhang, Siti Sarah Maidin and Deshinta Arrova Dewi
Symmetry 2025, 17(6), 903; https://doi.org/10.3390/sym17060903 - 7 Jun 2025
Viewed by 1017
Abstract
This study addresses the sentiment classification of short texts in teaching evaluations. To mitigate concerns regarding data security in cloud-based sentiment analysis and to overcome the limited feature extraction capacity of traditional deep-learning methods, we propose a distributed symmetric approximate homomorphic hybrid sentiment [...] Read more.
This study addresses the sentiment classification of short texts in teaching evaluations. To mitigate concerns regarding data security in cloud-based sentiment analysis and to overcome the limited feature extraction capacity of traditional deep-learning methods, we propose a distributed symmetric approximate homomorphic hybrid sentiment classification model, denoted BHE+ALBERT-Mixplus. To enable homomorphic encryption of non-polynomial functions within the ALBERT-Mixplus architecture—a mixing-and-enhancement variant of ALBERT—we introduce the BHE (BERT-based Homomorphic Encryption) algorithm. The BHE establishes a distributed symmetric approximation workflow, constructing a cloud–user symmetric encryption framework. Within this framework, simplified computations and mathematical approximations are applied to handle non-polynomial operations (e.g., GELU, Softmax, and LayerNorm) under the CKKS homomorphic-encryption scheme. Consequently, the ALBERT-Mixplus model can securely perform classification on encrypted data without compromising utility. To improve feature extraction and enhance prediction accuracy in sentiment classification, ALBERT-Mixplus incorporates two core components: 1. A meta-information extraction layer, employing a lightweight pre-trained ALBERT model to capture extensive general semantic knowledge and thereby bolster robustness to noise. 2. A hybrid feature-extraction layer, which fuses a bidirectional gated recurrent unit (BiGRU) with a multi-scale convolutional neural network (MCNN) to capture both global contextual dependencies and fine-grained local semantic features across multiple scales. Together, these layers enrich the model’s deep feature representations. Experimental results on the TAD-2023 and SST-2 datasets demonstrate that BHE+ALBERT-Mixplus achieves competitive improvements in key evaluation metrics compared to mainstream models, despite a slight increase in computational overhead. The proposed framework enables secure analysis of diverse student feedback while preserving data privacy. This allows marginalized student groups to benefit equally from AI-driven insights, thereby embodying the principles of educational equity and inclusive education. Moreover, through its innovative distributed encryption workflow, the model enhances computational efficiency while promoting environmental sustainability by reducing energy consumption and optimizing resource allocation. Full article
(This article belongs to the Section Computer)
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24 pages, 380 KB  
Article
Pseudorandom Function from Learning Burnside Problem
by Dhiraj K. Pandey and Antonio R. Nicolosi
Mathematics 2025, 13(7), 1193; https://doi.org/10.3390/math13071193 - 4 Apr 2025
Viewed by 926
Abstract
We present three progressively refined pseudorandom function (PRF) constructions based on the learning Burnside homomorphisms with noise (Bn-LHN) assumption. A key challenge in this approach is error management, which we address by extracting errors from the secret key. Our first [...] Read more.
We present three progressively refined pseudorandom function (PRF) constructions based on the learning Burnside homomorphisms with noise (Bn-LHN) assumption. A key challenge in this approach is error management, which we address by extracting errors from the secret key. Our first design, a direct pseudorandom generator (PRG), leverages the lower entropy of the error set (E) compared to the Burnside group (Br). The second, a parameterized PRG, derives its function description from public parameters and the secret key, aligning with the relaxed PRG requirements in the Goldreich–Goldwasser–Micali (GGM) PRF construction. The final indexed PRG introduces public parameters and an index to refine efficiency. To optimize computations in Burnside groups, we enhance concatenation operations and homomorphisms from Bn to Br for nr. Additionally, we explore algorithmic improvements and parallel computation strategies to improve efficiency. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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21 pages, 1553 KB  
Article
Bootstrapping Optimization Techniques for the FINAL Fully Homomorphic Encryption Scheme
by Meng Wu, Xiufeng Zhao and Weitao Song
Information 2025, 16(3), 200; https://doi.org/10.3390/info16030200 - 5 Mar 2025
Cited by 2 | Viewed by 3368
Abstract
With the advent of cloud computing and the era of big data, there is an increasing focus on privacy computing. Consequently, homomorphic encryption, being a primary technique for achieving privacy computing, is held in high regard. Nevertheless, the efficiency of homomorphic encryption schemes [...] Read more.
With the advent of cloud computing and the era of big data, there is an increasing focus on privacy computing. Consequently, homomorphic encryption, being a primary technique for achieving privacy computing, is held in high regard. Nevertheless, the efficiency of homomorphic encryption schemes is significantly impacted by bootstrapping. Enhancing the efficiency of bootstrapping necessitates a dual focus: reducing the computational burden of outer product operations integral to the process while rigorously constraining the noise generated by bootstrapping within predefined threshold limits. The FINAL scheme is a fully homomorphic encryption scheme based on the number theory research unit (NTRU) and learning with errors (LWE) assumptions. The performance of the FINAL scheme is better than that of the TFHE scheme, with faster bootstrapping and smaller bootstrapping and key-switching keys. In this paper, we introduce ellipsoidal Gaussian sampling to generate keys f and g in the bootstrapping of the FINAL scheme, so that the standard deviations of keys f and g are different and reduce the bootstrapping noise by 76%. However, when q is fixed, the boundary for bootstrapping noise remains constant. As a result, larger decomposition bases are used in bootstrapping to reduce the total number of polynomial multiplications by 47%, thus improving the efficiency of the FINAL scheme. The optimization scheme outperforms the original FINAL scheme with 33.3% faster bootstrapping, and the memory overhead of blind rotation keys is optimized by 47%. Full article
(This article belongs to the Section Information Security and Privacy)
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26 pages, 1339 KB  
Article
A Novel Data Obfuscation Framework Integrating Probability Density and Information Entropy for Privacy Preservation
by Haolan Cheng, Chenyi Qiang, Lin Cong, Jingze Xiao, Shiya Liu, Xingyu Zhou, Huijun Wang, Mingzhuo Ruan and Chunli Lv
Appl. Sci. 2025, 15(3), 1261; https://doi.org/10.3390/app15031261 - 26 Jan 2025
Cited by 2 | Viewed by 1443
Abstract
Data privacy protection is increasingly critical in fields like healthcare and finance, yet existing methods, such as Fully Homomorphic Encryption (FHE), differential privacy (DP), and federated learning (FL), face limitations like high computational complexity, noise interference, and communication overhead. This paper proposes a [...] Read more.
Data privacy protection is increasingly critical in fields like healthcare and finance, yet existing methods, such as Fully Homomorphic Encryption (FHE), differential privacy (DP), and federated learning (FL), face limitations like high computational complexity, noise interference, and communication overhead. This paper proposes a novel data obfuscation method based on probability density and information entropy, leveraging a probability density extraction module for global data distribution modeling and an information entropy fusion module for dynamically adjusting the obfuscation intensity. In medical image classification, the method achieved precision, recall, and accuracy of 0.93, 0.89, and 0.91, respectively, with a throughput of 57 FPS, significantly outperforming FHE (0.82, 23 FPS) and DP (0.84, 25 FPS). Similarly, in financial prediction tasks, it achieved precision, recall, and accuracy of 0.95, 0.91, and 0.93, with a throughput of 54 FPS, surpassing traditional approaches. These results highlight the method’s ability to balance privacy protection and task performance effectively, offering a robust solution for advancing privacy-preserving technologies. Full article
(This article belongs to the Special Issue Cloud Computing: Privacy Protection and Data Security)
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25 pages, 813 KB  
Review
Exploring Homomorphic Encryption and Differential Privacy Techniques towards Secure Federated Learning Paradigm
by Rezak Aziz, Soumya Banerjee, Samia Bouzefrane and Thinh Le Vinh
Future Internet 2023, 15(9), 310; https://doi.org/10.3390/fi15090310 - 13 Sep 2023
Cited by 77 | Viewed by 16649
Abstract
The trend of the next generation of the internet has already been scrutinized by top analytics enterprises. According to Gartner investigations, it is predicted that, by 2024, 75% of the global population will have their personal data covered under privacy regulations. This alarming [...] Read more.
The trend of the next generation of the internet has already been scrutinized by top analytics enterprises. According to Gartner investigations, it is predicted that, by 2024, 75% of the global population will have their personal data covered under privacy regulations. This alarming statistic necessitates the orchestration of several security components to address the enormous challenges posed by federated and distributed learning environments. Federated learning (FL) is a promising technique that allows multiple parties to collaboratively train a model without sharing their data. However, even though FL is seen as a privacy-preserving distributed machine learning method, recent works have demonstrated that FL is vulnerable to some privacy attacks. Homomorphic encryption (HE) and differential privacy (DP) are two promising techniques that can be used to address these privacy concerns. HE allows secure computations on encrypted data, while DP provides strong privacy guarantees by adding noise to the data. This paper first presents consistent attacks on privacy in federated learning and then provides an overview of HE and DP techniques for secure federated learning in next-generation internet applications. It discusses the strengths and weaknesses of these techniques in different settings as described in the literature, with a particular focus on the trade-off between privacy and convergence, as well as the computation overheads involved. The objective of this paper is to analyze the challenges associated with each technique and identify potential opportunities and solutions for designing a more robust, privacy-preserving federated learning framework. Full article
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19 pages, 818 KB  
Article
Secure Convolution Neural Network Inference Based on Homomorphic Encryption
by Chen Song and Ruwei Huang
Appl. Sci. 2023, 13(10), 6117; https://doi.org/10.3390/app13106117 - 16 May 2023
Cited by 8 | Viewed by 5650
Abstract
Today, the rapid development of deep learning has spread across all walks of life, and it can be seen in various fields such as image classification, automatic driving, and medical imaging diagnosis. Convolution Neural Networks (CNNs) are also widely used by the public [...] Read more.
Today, the rapid development of deep learning has spread across all walks of life, and it can be seen in various fields such as image classification, automatic driving, and medical imaging diagnosis. Convolution Neural Networks (CNNs) are also widely used by the public as tools for deep learning. In real life, if local customers implement large-scale model inference first, they need to upload local data to the cloud, which will cause problems such as data leakage and privacy disclosure. To solve this problem, we propose a framework using homomorphic encryption technology. Our framework has made improvements to the batch operation and reduced the complexity of layer connection. In addition, we provide a new perspective to deal with the impact of the noise caused by the homomorphic encryption scheme on the accuracy during the inference. In our scheme, users preprocess the images locally and then send them to the cloud for encrypted inference without worrying about privacy leakage during the inference process. Experiments show that our proposed scheme is safe and efficient, which provides a safe solution for users who cannot process data locally. Full article
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17 pages, 364 KB  
Article
Privacy Preserving Classification of EEG Data Using Machine Learning and Homomorphic Encryption
by Andreea Bianca Popescu, Ioana Antonia Taca, Cosmin Ioan Nita, Anamaria Vizitiu, Robert Demeter, Constantin Suciu and Lucian Mihai Itu
Appl. Sci. 2021, 11(16), 7360; https://doi.org/10.3390/app11167360 - 10 Aug 2021
Cited by 34 | Viewed by 5719
Abstract
Data privacy is a major concern when accessing and processing sensitive medical data. A promising approach among privacy-preserving techniques is homomorphic encryption (HE), which allows for computations to be performed on encrypted data. Currently, HE still faces practical limitations related to high computational [...] Read more.
Data privacy is a major concern when accessing and processing sensitive medical data. A promising approach among privacy-preserving techniques is homomorphic encryption (HE), which allows for computations to be performed on encrypted data. Currently, HE still faces practical limitations related to high computational complexity, noise accumulation, and sole applicability the at bit or small integer values level. We propose herein an encoding method that enables typical HE schemes to operate on real-valued numbers of arbitrary precision and size. The approach is evaluated on two real-world scenarios relying on EEG signals: seizure detection and prediction of predisposition to alcoholism. A supervised machine learning-based approach is formulated, and training is performed using a direct (non-iterative) fitting method that requires a fixed and deterministic number of steps. Experiments on synthetic data of varying size and complexity are performed to determine the impact on runtime and error accumulation. The computational time for training the models increases but remains manageable, while the inference time remains in the order of milliseconds. The prediction performance of the models operating on encoded and encrypted data is comparable to that of standard models operating on plaintext data. Full article
(This article belongs to the Special Issue Applied Cognitive Sciences)
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17 pages, 6208 KB  
Article
Speckle Reduction on Ultrasound Liver Images Based on a Sparse Representation over a Learned Dictionary
by Mohamed Yaseen Jabarulla and Heung-No Lee
Appl. Sci. 2018, 8(6), 903; https://doi.org/10.3390/app8060903 - 31 May 2018
Cited by 19 | Viewed by 9551
Abstract
Ultrasound images are corrupted with multiplicative noise known as speckle, which reduces the effectiveness of image processing and hampers interpretation. This paper proposes a multiplicative speckle suppression technique for ultrasound liver images, based on a new signal reconstruction model known as sparse representation [...] Read more.
Ultrasound images are corrupted with multiplicative noise known as speckle, which reduces the effectiveness of image processing and hampers interpretation. This paper proposes a multiplicative speckle suppression technique for ultrasound liver images, based on a new signal reconstruction model known as sparse representation (SR) over dictionary learning. In the proposed technique, the non-uniform multiplicative signal is first converted into additive noise using an enhanced homomorphic filter. This is followed by pixel-based total variation (TV) regularization and patch-based SR over a dictionary trained using K-singular value decomposition (KSVD). Finally, the split Bregman algorithm is used to solve the optimization problem and estimate the de-speckled image. The simulations performed on both synthetic and clinical ultrasound images for speckle reduction, the proposed technique achieved peak signal-to-noise ratios of 35.537 dB for the dictionary trained on noisy image patches and 35.033 dB for the dictionary trained using a set of reference ultrasound image patches. Further, the evaluation results show that the proposed method performs better than other state-of-the-art denoising algorithms in terms of both peak signal-to-noise ratio and subjective visual quality assessment. Full article
(This article belongs to the Special Issue Ultrasound B-mode Imaging: Beamforming and Image Formation Techniques)
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