Reinforcement learning (RL) has been increasingly adopted in IoT systems for tasks such as resource allocation and control. However, in privacy-critical and resource-constrained environments, existing privacy-preserving RL schemes suffer from high computational cost, slow convergence, and limited scalability due to the use of homomorphic encryption or differential privacy. We propose a distributed privacy-preserving Q-learning framework that enables secure and efficient policy updates across multiple clients. Each client independently trains a local Q-table and encrypts it using a sparse matrix transformation combined with additive secret sharing of structured perturbations. The encrypted Q-tables are uploaded to a cloud server for aggregation and averaging without decryption. The encrypted global Q-table is then returned and decrypted locally using the inverse sparse matrix. Experimental results on four benchmark environments (CartPole-v1, MountainCar-v0, Acrobot-v1, and LunarLander-v3) show that our scheme achieves up to 92% reduction in computation time compared to the FHE-based method, while maintaining comparable reward performance and faster convergence.

Machine learning algorithm for multi-modal image segmentation is extensively employed in medical analysis and diagnosis. Clustering represents a mainstream approach for image segmentation, with the fuzzy c-means and particle swarm optimization (FCM-PSO) algorithm garnering significant attention. As image segmentation tasks have substantial computational costs, the outsourcing scheme offers an effective solution by leveraging cloud servers to execute complex computations. Given that medical images contain sensitive patient information, the image segmentation outsourcing scheme must ensure data privacy and confidentiality. In this paper, we propose a secure outsourcing scheme for the FCM-PSO based image segmentation algorithm through a novel sparse matrix encryption method. By analyzing each stage of the image segmentation algorithm, we delegate the computationally intensive task of calculating the Euclidean distance to an untrusted cloud server. We utilize sparse matrices to obscure the private image data. These matrices are created by incorporating multiple small-sized random invertible matrices, thereby circumventing the local storage of generation factors. Additionally, we implement a lightweight verification method to verify the correctness of returned results. Experimental results show that our scheme improves the efficiency of the image segmentation task by 29.99% to 49.50% with the increasing of image set, compared to the original algorithm executed locally.

In this work, we propose a privacy-preserving face recognition scheme based on secure similarity comparison on encrypted data. We innovatively split sensitive face embeddings into two shares and encrypt them to guarantee data privacy. We present a novel matrix blinding method to conduct face similarity computation on encrypted face embeddings. Furthermore, we design an effective re-encryption method to achieve non-local secure data update, which reduces the risk of data leakage. Simulation experiments demonstrate that the proposed scheme completes face recognition tasks securely and efficiently. With different size of datasets, scale of embeddings, and number of queries, our scheme accomplishes face recognition tasks at low costs without obvious accuracy penalty.

With the rapid development of artificial intelligence and big data technologies, gait recognition has become a key method for identity authentication. As a unique biometric characteristic, gait is difficult to counterfeit and supports long-distance, non-contact authentication, making it ideal for security, surveillance, and health monitoring. However, traditional gait authentication faces privacy and efficiency challenges. This paper presents a privacy-preserving gait authentication scheme based on partial Euclidean distance calculation, and the scheme encrypts gait features using block-diagonal orthogonal matrices and random perturbation vectors, enabling efficient encrypted computation on the cloud. Experimental results demonstrate that the proposed scheme improves processing efficiency and matching accuracy while protecting privacy. For instance, on the CASIA-B dataset, it reduces computation time by approximately 30% without compromising accuracy.

Saber, as one of the candidates of the NIST Post Quantum Cryptography (PQC) Standardization, is a post-quantum Key Encapsulation Mechanism (KEM) that provides strong security guarantees against quantum adversaries. Due to the high computational complexity, enhancing its efficiency is essential for real-world deployment. In practical applications, the high computational cost of polynomial multiplication remains a major bottleneck to its performance. To address this, we propose a novel optimization method for Saber by introducing a Fermat number transform (FNT) as a key algorithmic improvement. By leveraging a Fermat prime as one of the moduli, the modular multiplications are efficiently implemented by bitshift operations, thereby reducing the arithmetic complexity in negacyclic convolutions. We integrate FNT with a K-reductionbased modular reduction scheme which eliminates the need for precomputation or multiplications and enables reduction to be completed using only shifts and additions. To fully exploit the Intel hardware architecture, we design a high-performance AVX2-based vectorized implementation by utilizing 256-bit SIMD instructions. Specifically, FNT is optimized by using shift-based butterfly operations tailored to the structure of Fermat primes, while the modular reduction is accelerated by bitwise and shift instructions, ensuring high throughput and memory efficiency. Our experimental evaluation shows that the proposed polynomial multiplication scheme achieves a speedup of 14.7 % and reduces cycle counts by up to 8 % compared to previous state-of-the-art implementations. These improvements highlight the efficacy of our method, making it highly suitable for high-performance cryptographic applications.

In the field of machine learning, PCA based face recognition is widely applied in identity authentication and access control. Due to limited storage and computational capabilities, the client often needs to outsources face recognition tasks to cloud servers, which brings privacy leakage risks. Existing privacy-preserving schemes calculate the inner product of encrypted vectors to perform face matching, but they involve complex operations, making efficient recognition challenging and lacking in automatic verification of computational integrity. In this paper, we propose a blockchain-aided privacy-preserving PCA based face recognition scheme. Our approach uses sparse matrices to construct keys, reducing the number of non-zero elements in matrix operations. The scheme also introduces a blockchainaided verification and payment mechanism based on hash commitments to verify the integrity of computation tasks. This mechanism allows encrypted face images and face recognition results to be uploaded to the blockchain, effectively reducing the number of interactions between the client and the cloud server. Experimental results demonstrate that this scheme reduces the overall execution time by 43% without compromising recognition accuracy, achieving a recognition accuracy rate of 99.35%.

In the Internet of Things (IoT) scenarios, edge computing assists in completing machine learning on resource-constrained terminal devices. As one of the most significant operations, large-scale matrix multiplication remains a huge efficiency bottleneck. Existing distributed computation approaches typically decompose the matrix computation into subtasks of the same scale, overlooking edge computing environments with unbalanced computing resources. In this paper, we propose a secure distributed matrix multiplication outsourcing scheme in edge computing with unbalanced resources. Specifically, the large-scale matrix multiplication is decomposed into several subtasks of varying scales according to unbalanced edge computing resources, which achieves better distributed computational performance. A novel matrix blinding method is presented by employing perturbation matrices and permutation matrices to guarantee input and output privacy. Experimental results demonstrate that our scheme improves the efficiency by 51.13% to 98.79% compared to traditional matrix multiplication without outsourcing. Additionally, our scheme outperforms state-of-the-art outsourcing schemes, with an average improvement of 9.36% in edge computing with balanced resources and 14.83% in unbalanced environments.

For the huge amount of data from the Internet of Things (IoT) devices, multiple kernel learning is a widely concerned issue in data analyzing, among which the multiple kernel fuzzy clustering (MKFC) algorithm is an effective approach for extracting linear features in high-dimensional space. For a time-consuming multiple kernel clustering task, it is meaningful to find a secure and efficient outsourcing scheme in the edge-end collaborative architecture, which utilizes edge computing resources while resisting untrusted edge servers. However, existing secure outsourcing schemes cannot align well with the distributed and real-time characteristics of edge computing due to their complex encryption processes. In this article, we propose a secure MKFC outsourcing scheme based on a novel matrix blinding method. The proposed novel matrix blinding method conducts two related encryption operations with disturbance terms, which avoids specific disturbance elimination computations, to reduce the computational burdens in the decryption phase. Additionally, we introduce a sampling verification method to detect the server’s deceptive behaviors. The theoretical analysis demonstrates that our scheme guarantees data privacy and has the capability to verify incorrect results. The experimental results indicate that our scheme is 6.73% superior to other schemes on average when conducting matrix outsourcing computation and enhances the efficiency of conducting the MKFC algorithm by 10.44% to 55.70% on different datasets.

Lattice-based Post-Quantum Cryptography (PQC) can effectively resist the quantum threat to blockchain's underlying cryptographic algorithms. Blockchain node decryption is one of the most commonly used cryptographic computations in blockchain systems, and polynomial multiplication, a time-consuming operation for decryption, is one of the factors limiting blockchain efficiency. This paper proposes a novel distributed computing algorithm for polynomial multiplication, applicable in blockchain decryption. By splitting polynomials into lower-degree terms and delegating tasks to distributed nodes, our approach reduces computation time. A novel verification strategy based on the Karatsuba algorithm ensures result accuracy. The experimental results demonstrate that our proposed scheme improves the execution efficiency of NTT and INTT operations by approximately 47.8% and 52.4%, and reduces Kyber decryption time by up to 23.5%.

With the advancement of the Internet of Things (IoT), numerous machine learning applications on IoT are encountering performance bottlenecks. Graph embedding is an emerging type of machine learning that has achieved commendable results in areas such as network anomaly detection, malware detection, IoT device management, and service recommendation within the Internet of Things. However, for some resource-constrained IoT devices, computing graph embedding algorithms is highly complex and time-consuming. In this paper, we introduce an efficient and secure distributed outsourcing scheme, employing four non-colluding cloud servers to facilitate the computation of graph embedding for IoT devices. Our scheme utilizes a novel blinding factor generated through QR decomposition to blind matrices containing sensitive information. We partition the blinded matrix into several segments, distributing different small matrix blocks across four servers, each of which executes only a portion of the computational tasks. The proposed outsourcing solution ensures the privacy of input and output information is not compromised. In our scheme, we utilize an effective verification method that can detect the erroneous behaviors of cloud servers with a probability close to one. Theoretical analysis and experimental results indicate that our solution achieves a computational efficiency of (35m2+2m)/(3m3) compared to the original algorithm.

Large-scale matrix multiplication is a computational bottleneck in various applications including artificial intelligence and machine learning. Given the time complexity of O(n3) for matrix multiplication, large matrix computation is exceedingly time-consuming for the client-side user. By outsourcing this task to cloud servers with substantial computational resources, we can significantly reduce the client-side computational time. This paper presents a parallel matrix multiplication outsourcing scheme based on Cannon’s algorithm. By distributing the matrix across multiple cloud servers for parallel computation, we can get a significant efficiency speedup. Our scheme employs multiple cloud servers to perform parallel matrix computation, reducing the computational load by 89-97% when utilizing 4-16 servers as opposed to using a single server. We provide a comprehensive analysis of the scheme’s correctness, security, and verifiability, substantiating the benefits of our approach through the experimental data.

The proliferation of Internet of Things (IoT) devices has led to the generation of massive amounts of data that require efficient aggregation for analysis and decision-making. However, multi-tier IoT systems, which involve multiple layers of devices and gateways, face more complex security challenges in data aggregation compared to ordinary IoT systems. In this paper, we propose an efficient privacy-preserving multi-functional data aggregation scheme for multi-tier IoT architecture. The scheme supports privacy-preserving calculation of mean, variance, and anomaly proportion. The scheme uses the Paillier cryptosystem and the BLS algorithm for encryption and signature, and uses blinding techniques to keep the size of the IoT system secret. In order to make the Paillier algorithm more suitable for the IoT scenario, we also improve its efficiency of encryption and decryption. The performance evaluation shows that the scheme improves encryption efficiency by 43.7% and decryption efficiency by 45% compared to the existing scheme.

With the popularity of Internet of Things (IoT) and 5G, privacy-preserving message transmission and authentication have become an indispensable part in the field of data collection and analysis. There exist many protocols based on the public key cryptosystem, which allow the users to utilize their own identity as the public key to carry out data encryption and digital signature, which is very suitable for applying in the IoT environment with a large number of terminal devices. However, these protocols usually involve some complex cryptographic operations, which hinder their application on the resource-constrained IoT devices. In this paper, we design a privacy-preserving and verifiable outsourcing message transmission and authentication protocol, which allows the resource-constrained users to delegate some complex operations to the two untrusted edge servers and reduce the computational burden on the users side. The designed protocol contains several secure and novel outsourcing algorithms for modular exponentiation, bilinear pairing and scalar multiplication. For the different operations in the different situations, we design several different blinding techniques and verification methods, which not only protect the users’ private information, but also ensure the users can verify the correctness of results. Finally, we carry out some experiments to show that our proposed protocol is efficient.

Data security and privacy have become an important problem while big data systems are growing dramatically fast in various application fields. Paillier additive homomorphic cryptosystem is widely used in information security fields such as big data security, communication security, cloud computing security, and artificial intelligence security. However, how to improve its computational performance is one of the most critical problems in practice. In this paper, we propose two modifications to improve the performance of the Paillier cryptosystem. Firstly, we introduce a key generation method to generate the private key with low Hamming weight, and this can be used to accelerate the decryption computation of the Paillier cryptosystem. Secondly, we propose an acceleration method based on Hensel lifting in the Paillier cryptosystem. This method can obtain a faster and improved decryption process by showing the mathematical analysis of the decryption algorithm.