With the quantum threat looming, IoT deployments urgently require post-quantum cryptographic solutions that deliver strong security within tight resource limits. Lattice-based schemes, including NTRU-type encryption(IEEE Std 1363.1) and fully homomorphic encryption (FHE), are attractive in this setting because they can combine quantum resistance with relatively low computational overhead. However, accurate security assessment of these schemes is important for parameter selection in resource-constrained IoT deployments. This work addresses the ternary Learning With Errors (LWE) problem that underpins these cryptosystems by adapting cryptographic puncturing to lattice attacks. In this paper, we revisit the randomized dimension reduction (RDR) technique originally proposed by May to assess the security of the original NTRU cryptosystem. More specifically, we study how the LWE sample dimension can be reduced while preserving the effective secret-error search space through an explicit puncturing threshold, replacing ad hoc sample-selection rules with a single distribution-aware criterion. We also study LWE with side-channel hints, using elimination-based linear equation solving to construct the reduced hint lattice more transparently before the final embedding step, which is relevant in settings where devices may be physically exposed to leakage. Experimental results demonstrate 41% threshold embedding-dimension reduction for NTRU-like schemes (n, log2q,h) = (100, 12, 50) and FHE parameters (n, log2q,h, σe) = (128, 14, 12, 3.2). Relative to standard lattice-estimator evaluations, our refined analysis tightens representative security estimates by 1–3 bits: a CKKS/HEAAN-style parameter set (n, q,w) = (1024, 216, 64) with sparse ternary secret is reduced by 3 bits, while NTRU-Prime (n, q,w) = (653, 4621, 288) and LAC (n, q,w) = (512, 251, 128) parameters are reduced by 1 bit. Additional coefficient-hint experiments on Kyber/ML-KEM parameter settings and representative hint counts from May–Nowakowski show that applying RDR after hint elimination can further reduce the estimated BKZ block size in hint-assisted regimes. These refined estimates provide a more concrete basis for parameter assessment in IoT-style settings.

Driven by the growing demand for clean and high-velocity transportation, maglev car systems have emerged as promising solutions. Precise velocity control is crucial for the safe and stable operation of maglev cars. However, strong nonlinearities and underdamped dynamics of these systems make accurate modeling difficult, which limits the performance of traditional model-based controllers. Therefore, research in this area remains limited. While Model-Free Adaptive Control (MFAC) offers a potential solution, standard algorithms with fixed parameters that struggle to balance response velocity and stability. To overcome these limitations, this paper proposes an MFAC framework integrated with error gain scheduling (EGS). The EGS dynamically adjusts the controller’s parameters based on real-time tracking error regions, thereby mitigating the trade-off between transient response rate and overshoot. The MFAC‑EGS scheme preserves low computational complexity and real‑time adaptability, requiring neither a precise model nor extensive offline training. The primary contributions of this work include: (1) A velocity control scheme for maglev cars is developed to ensure stable velocity regulation under complex conditions, which is essential for operational safety and stability; (2) A data-driven MFAC-EGS paradigm is established, which enhances MFAC robustness against disturbances without increasing structural complexity; (3) Experimental results demonstrate that the maglev car velocity control function is achieved under various controllers, among which MFAC-EGS shows the superior control performance. Specifically, the proposed method reduces the root mean square error (RMSE) by 20.9% in steady-state tracking and 22.9% under disturbed conditions. It also achieves reductions of 50.5% and 21.5% for triangular and square-wave signals, respectively, alongside faster response and lower overshoot. This work offers valuable insights into the future high-speed operation of maglev cars.

The integration of smart medical technology has revolutionized personal health management, with devices like smartwatches and smartphones facilitating efficient data collection and analysis. However, the exponential growth in medical data has heightened privacy concerns, underscoring the need for a robust and secure transmission system. Traditional encryption, while effective, is limited by its resource-intensive nature, hindering its application in IoT devices. Our research delves into the application of compressed sensing for medical image privacy, addressing challenges such as high resource consumption, security vulnerabilities, and the need for robust watermarking. We have designed the Lightweight Quantum-resistant Medical Image Transmission (LQRMIT) model, which combines a 3D chaotic system with the Learning With Errors (LWE) theory, offering a key space of up to$2^{700}$, significantly enhancing security. Additionally, we have designed a watermark embedding algorithm compatible with compressed sensing, which ensures high invisibility and high-quality watermark extraction. The model also employs a meaningful image hiding strategy within encrypted transmissions to improve stealth. Extensive experimental and theoretical analysis has validated the effectiveness of our solution, providing a promising approach for secure and efficient medical image transmission in the digital medical era.

In this paper, we study the physical layer message authentication and encryption scheme for wireless networks, based on the Advanced Encryption Standard(AES)-based authentication encryption scheme. Specifically, we first propose an efficient and feasible authentication encryption scheme built upon the GCM-SIV mode and utilizing the AES algorithm. Secondly, we propose a novel physical layer security scheme that seamlessly integrates precoding-based message authentication and encryption with the AGSP algorithm by strategically leveraging the unique characteristics of wireless channels. By integrating encryption and authentication at the physical layer, our protocol offers a promising approach to scalable and secure communication in the 6G era.

The Learning With Errors (LWE) problem serves as the security foundation for many post-quantum cryptographic schemes. Its various variants, including the sparse and small LWE problem, also play a key role in post-quantum cryptography. Accurately evaluating the computational complexity of solving LWE and its variants is important for understanding the security of related cryptographic schemes. In this paper, we propose an improved Dropping Meet-in-the-Middle (MitM) algorithm for LWE instances with sparse and small secrets. The core idea is to reduce the dimension of the MitM phase by pre-guessing τ components of the secret vector s, and to balance the additional guessing overhead against the reduction in the MitM phase, thereby achieving an overall optimization of computational cost. Experimental results show that our proposed method exhibits better performance compared with other attacks.

Pseudo‐random number generator (PRNG) is a type of algorithm that generates a sequence of random numbers using a mathematical formula, which is widely used in computer science, such as simulation, modeling applications, data encryption, et cetera. The efficiency and security of PRNG are closely related to its output bits at each iteration. Especially, we have recently found that linear congruential generator (LCG) is commonly used as the underlying PRNG in short message service (SMS) app, fast knapsack generator (FKG), and programming languages such as Python, while the quadratic generator plays an important role in Monte Carlo method. Therefore, in this paper, we revisit the security of these two number‐theoretic pseudo‐random generators and obtain the best results for attacking these two kinds of PRNGs up to now. More precisely, we prove that when the mapping function of LCG and the quadratic generator is unknown, if during each iteration, generators only output the most significant bits of v i , one can also recover the seed of PRNG when enough consecutive or nonconsecutive outputs are obtained. The primary tool of our attack is the Coppersmith method which can find small roots on polynomial equations. Our advantage lies in applying the local linearization technique to the polynomial equations to make them simple and easy to solve and applying the analytic combinatorics method to simplify the calculation of solution conditions in the Coppersmith method. Experimental data validate the effectiveness of our work.

In the context of connected vehicles, encrypted image search technologies have gained significant importance. However, existing techniques are plagued by several limitations, including high resource consumption, lack of flexibility, insufficient security evaluation, and absence of hierarchical security mechanisms. These constraints render them inadequate for meeting the diverse resource requirements and multi-level security needs of different devices within the connected vehicle ecosystem. Therefore, improvements are urgently needed to enhance efficiency and security. In light of these issues, we introduce a novel framework designed for the secure retrieval of k-nearest Neighbor (kNN) images, leveraging cloud-based storage. This framework is underpinned by a Self-Adaptive Asymmetric Scalar Product Homomorphic Encryption algorithm (SA-ASPE). It incorporates an adaptive block mechanism to generate a suite of encryption keys tailored for images of diverse dimensions. Additionally, a security hierarchy, facilitated by a recursive split tree, is established to provide a selection of multi-tiered security options suitable for a variety of IoT contexts. To further augment the security of image feature vectors, we have integrated chaotic encryption techniques, which serve to thoroughly randomize these vectors, thereby significantly enhancing their unpredictability. To rigorously assess the robustness of the ASPE protocol against potential security threats, we have devised a comprehensive four-tier attack model coupled with an Amplified Attack (AA) strategy. Ultimately, through an extensive comparative analysis of existing and proposed schemes, we demonstrate that our framework adeptly satisfies the efficiency and security demands of a multitude of IoT device privacy protection scenarios.

The Internet of Things (IoT) technology, through the deployment of sensors and intelligent traffic cameras, facilitates the collection, processing, and analysis of traffic flow, vehicle density, and road conditions. However, traffic image data contains a substantial amount of personal sensitive information. Therefore, implementing hierarchical encryption on images is crucial for preventing the leakage of personal privacy and ensuring data is used in compliance with regulations. Moreover, the rise of quantum computing poses a substantial threat to existing key distribution systems, especially for resource-constrained IoT devices. To address these challenges, this article presents a lightweight hierarchical privacy protection scheme for traffic images that addresses key adaptability, quantum threats, and hierarchical privacy protection. The scheme includes a lattice-based public-key algorithm with updatable public and private keys to ensure quantum-resistant and forward security. It also introduces, for the first time, a hierarchical tree-structured encryption scheme based on the SHA3 hash function and the homomorphic property of compressed sensing, allowing high-permission users to generate keys for low-permission users without compromising the quality of image decryption. Additionally, the scheme includes a compressed sensing public-key encryption algorithm based on chaotic systems and the difficulty of matrix factorization, which supports sampling of images of any size, enhancing adaptability and reducing resource consumption. Tests indicate that this image encryption algorithm can resist various statistical analyses, achieving a high number of pixel change rate of 99.6277%. In summary, our research significantly contributes to the effective safeguarding of personal data security in resource-constrained IoT environments, particularly in the face of potential quantum computing threats.

Designing secure outsourcing schemes enables resource-constrained Internet of Things (IoT) devices to perform highly complex computational tasks. Solving the quadratic congruence problem is one of the core components in the construction of cryptographic algorithms for IoT. Recently, Rangasamy designed an outsourcing scheme for solving quadratic congruence equations. Interestingly, we find that the scheme has the risk of secret information being cracked. We propose two lattice attack algorithms in this article. In the first attack algorithm, we prove that there is a possibility of leaking secret information in the public parameters of the outsourcing scheme. Specifically, by intercepting the parameters transmitted between the client and the server, and combining the ideas from Fermat’s Little Theorem and the Euclidean algorithm, the attacker can obtain multiples of the secret parameter p. Furthermore, after recover the value of p, our attack algorithm is capable of recovering all secret parameters in the quadratic congruence equation. In the second attack algorithm, we note that the authors recommend the randomly chosen value of k to be small in the original outsourcing scheme. However, in this article, we point out that the random value k should not be too small, otherwise, the outsourcing scheme would be wrecked. More precisely, we use the Coppersmith method to provide an approach that can recover all the secret information. Our attack algorithm will succeed once k satisfied$|k| \lt \sqrt {p}$, so in order to ensure the security of the outsourcing scheme, we propose the recommended selection length of the random value k. Finally, we experimentally verified the two proposed attack algorithms.

Homomorphic Encryption (HE) is a kind of algorithm which provides data processing but not data access. Since it was proposed in 1978, as one of the important tools in cryptography, it is broadly used in many scenarios, like privacy protection, cloud computing, federated learning, and so on. Especially in the association rules mining privacy protection schemes, it often used as a key technology to ensure data security. Recently, Li et al. and Rajasekaran et al. introduced a kind of symmetric HE algorithm in their privacy protection scheme. However, in this paper, we find that this symmetric HE algorithm has the possibility to recover its secret key in practical applications. We propose two attacking algorithms based on lattice to recover its secret key SK=(sd,q). The core of our attack is to construct a lattice basis using the transformation relation between ciphertexts so that the short vector in the lattice contains the secret key SK. Then we can use the LLL algorithm to recover the secret key. We prove the feasibility of our attacking algorithms with experiments and the experimental results suggest that all of our algorithms can recover the key within 0.1s. Besides, we also give some improvements for this symmetric HE algorithm so that the new HE algorithm can resist our attacking algorithms.

The swift progression of Web3 and the proliferation of Decentralized Applications (DApps) have ushered in an era where data services are seamlessly integrated with blockchain technology. Despite this integration, the highly esteemed Quality of Service (QoS) service recommendation methodologies from the Web2.0 era face challenges in achieving seamless compatibility due to their centralized nature. In this paper, we introduce an innovative hybrid approach that bridges the on-chain and off-chain realms for service evaluation and recommendation, which we term as QoBS. This method leverages the power of ring signatures to safeguard identity data, thereby ensuring an efficient and secure framework for decentralized blockchain governance in the Web3 ecosystem. Through rigorous experimentation within the Ethereum environment, we validate the practical viability of our proposed solution, showcasing its robustness and effectiveness in the evolving landscape of decentralized services.

Solving quadratic congruence equations is an expensive operation widely employed in cryptographic constructions for secure Internet of Things applications. Recently, two outsourcing algorithms were proposed by Zhanget al.to solve quadratic congruence equations by employing Cippolla’s algorithm. It was claimed that all the inputs and outputs can be obscured in these two algorithms. However, we present two passive attacks in this article to show that all the inputs and outputs can be recovered efficiently by just a curious server, which implies the two outsourcing algorithms are insecure. To fix them, we further propose an improved outsourcing algorithm to solve quadratic congruence equations, which is more efficient and the privacy of actual inputs and outputs can be protected very well.

The decisional version and computational version of the subset sum problem are known to be NP‐complete and NP‐hard. At International Symposium on Information Theory and its Applications 2012, Yasuyuki Murakami, Shinsuke Hamasho and Masao Kasahara presented a knapsack scheme based on the decisional version of the odd order subset sum problem. They claimed that the public sequence is indistinguishable from uniformly distributed sequences. In this study, the authors present an equivalent key attack against this scheme. More precisely, they firstly observe that there are many groups of equivalent keys, which satisfy several necessary conditions. Subsequently, they show that one can recover a group of equivalent keys by using the orthogonal lattice technique. The feasibility of the attack is validated by the experimental data when the bit length of secret keys is not too large. Hence, the security of the proposed scheme is overestimated.

We present a deterministic $2^{O(t)}q^{\frac{t-2}{t-1}+o(1)}$ algorithm to decide whether a univariate polynomial $f$, with $t$ monomial terms and degree $

We present a deterministic 2O(t)qt-2/t-1 +o(1) algorithm to decide whether a univariate polynomial f, with exactly t monomial terms and degree

At ISIT 2008, Aguilar Melchor, Castagnos and Gaborit presented a lattice-based homomorphic encryption scheme (abbreviated as MCG). Its security is based on the Computational Knapsack Vector Problem. In this paper, we explore a secret linear relationship between the public keys and the secret keys, which can be used to construct a reduced-dimension lattice, and then we obtain a group of equivalent private keys by solving the Closest Vector Problem of the lattice. Moreover, our attack is practical on all the three settings of recommended parameters, and the running time to recover the equivalent private keys is only several hours on a single PC.

In this paper, we present an improvement of the Nguyen-Vidick heuristic sieve algorithm for shortest vector problem in general lattices, which time complexity is 20.3836n polynomial computations, and space complexity is 20.2557n. In the new algorithm, we introduce a new sieve technique with two-level instead of the previous one-level sieve, and complete the complexity estimation by calculating the irregular spherical cap covering.