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Search Results (193)

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Keywords = applied cryptography

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15 pages, 582 KB  
Article
Dynamic Asymmetric Group Key Agreement Based on SM9 Signature
by Guanglu Wei, Tiecheng Bai, Zehua Fan, Gang Wu, Wenxu Chen, Peng Qin and Kai Fan
Cryptography 2026, 10(3), 37; https://doi.org/10.3390/cryptography10030037 - 12 Jun 2026
Viewed by 122
Abstract
In 2021, the SM9 identity-based cryptographic algorithm became an ISO/IEC international standard, marking a significant advancement in China’s commercial cryptography technology and international standardization capabilities. The SM9 key exchange protocol, a component of the SM9 algorithm suite, provides secure communication by establishing a [...] Read more.
In 2021, the SM9 identity-based cryptographic algorithm became an ISO/IEC international standard, marking a significant advancement in China’s commercial cryptography technology and international standardization capabilities. The SM9 key exchange protocol, a component of the SM9 algorithm suite, provides secure communication by establishing a shared symmetric key between two parties. However, in a group of n users, directly applying this key exchange protocol requires each user to perform O(n) encryption operations and transmit an O(n)-sized ciphertext to ensure confidentiality, which becomes highly inefficient for large groups. To enable efficient secure group communication, we first develop a batch multi-signature algorithm based on SM9, and then we propose a dynamic asymmetric group key agreement (SMDAGKA) protocol based on this method. Our protocol reduces the required encryption operations and ciphertext size to O(1), significantly improving efficiency. Security proofs demonstrate that our scheme achieves a high level of security, and performance analysis shows that it incurs relatively lower computational overhead than related protocols. Full article
(This article belongs to the Special Issue Information and Communications Security—ICICS 2025)
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58 pages, 8495 KB  
Article
Detection and Mitigation of Mythos-Class Frontier Model Capabilities: A Layered Reference Architecture
by Robert Campbell
Computers 2026, 15(6), 331; https://doi.org/10.3390/computers15060331 - 22 May 2026
Viewed by 556
Abstract
Anthropic’s April 2026 Claude Mythos Preview release established a new operational threat category: frontier AI systems whose extended-context reasoning, recursive self-correction, native system-tool integration, and agentic scaffolding render dominant AI safety paradigms—RLHF, output filtering, contractual access vetting, human-in-the-loop supervision—insufficient as sole controls. This [...] Read more.
Anthropic’s April 2026 Claude Mythos Preview release established a new operational threat category: frontier AI systems whose extended-context reasoning, recursive self-correction, native system-tool integration, and agentic scaffolding render dominant AI safety paradigms—RLHF, output filtering, contractual access vetting, human-in-the-loop supervision—insufficient as sole controls. This paper develops a defense-in-depth reference architecture against that category, structured around four named contributions: a five-indicator operational definition of the Mythos-class (capability conjoined with scaffold, access pattern, autonomy depth, and persistence); the Mythos-Class Posture Rubric (MCPR), a three-tier detection framework spanning evaluation, deployment, and runtime with explicit routing to mitigation layers; a four-layer mitigation stack comprising the Vetted-Access Operational Pattern (VAOP), Authority-Bound Output Release (ABOR) cryptographically grounded in FIPS 203/204/205 post-quantum primitives, and the Compute-Plane Isolation Profile (CPIP); and an integrated architecture that crosswalks to the NIST AI Risk Management Framework, NIST Cybersecurity Framework 2.0, and CISA Zero Trust Maturity Model 2.0. The architecture is applied to three deployment surfaces—post-quantum cryptography migration, federal AI supply-chain assurance, and critical-infrastructure operational technology defense—demonstrating that the four contributions generalize across heterogeneous operational contexts. The contribution is a reference design rather than a deployed system; limitations, falsifiability criteria, and a research agenda for empirical refinement are developed. Full article
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28 pages, 6202 KB  
Review
Freeform Micro-Optical Elements—Recent Production Techniques, Opportunities and Challenges
by Tomasz Blachowicz, Guido Ehrmann, Johannes Fiedler, Reinhard Kaschuba and Andrea Ehrmann
Micro 2026, 6(2), 35; https://doi.org/10.3390/micro6020035 - 11 May 2026
Viewed by 632
Abstract
Freeform optics belong to the increasingly important elements in optical research and industry, which pose several challenges regarding design and highly precise manufacturing. First being used in cameras and for focusing, nowadays freeform optics are used in a broad range of applications, from [...] Read more.
Freeform optics belong to the increasingly important elements in optical research and industry, which pose several challenges regarding design and highly precise manufacturing. First being used in cameras and for focusing, nowadays freeform optics are used in a broad range of applications, from lighting to LiDAR, from endoscopy to photovoltaics, and from astronomical instruments to quantum cryptography. Designing freeform optics can be based on different theories and methods. Fabrication is possible by mechanical methods, such as diamond turning or high-precision milling, often followed by different polishing techniques, as well as laser-based techniques, mainly applying different lithographic techniques. Here, we give an overview of recent design and optimization methods, production methods used during the last years, and applications of freeform optics, including the possibility to combine freeform optics with tunability for different applications. We describe the opportunities of new applications as well as common problems and give an outlook towards future directions of research and development. Full article
(This article belongs to the Section Analysis Methods and Instruments)
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25 pages, 617 KB  
Article
A Multiple User Cryptography Approach Using a One-Time User Key Model and a (1, n) Threshold Polynomial Secret Sharing
by Alessandro Caniglia, Felice Franchini, Stefano Galantucci, Giuseppe Pirlo and Gianfranco Semeraro
Cryptography 2026, 10(2), 26; https://doi.org/10.3390/cryptography10020026 - 14 Apr 2026
Viewed by 486
Abstract
Classical approaches to cryptography exhibit several limitations when applied to scenarios involving more than two users. The One-Time User Key (OTUK) meta-cryptographic model addresses these limitations by enabling multi-user encryption that is flexible, applicable to any cryptographic algorithm, and designed for systematic deployment [...] Read more.
Classical approaches to cryptography exhibit several limitations when applied to scenarios involving more than two users. The One-Time User Key (OTUK) meta-cryptographic model addresses these limitations by enabling multi-user encryption that is flexible, applicable to any cryptographic algorithm, and designed for systematic deployment without compromising system security. Each user possesses an individual key from which One-Time keys are derived; these keys feed a secret-sharing function (ω) that establishes the multi-user encrypted channel. In this paper, we present a polynomial-based implementation of the ω function under a (1,n) threshold model. The generated polynomial has roots at points corresponding to valid user keys and is mapped to the real encryption key. We provide a formal threat model, pseudocode for the complete protocol, and a detailed computational analysis across the numerical domains N, Z, and R. Furthermore, we present experimental benchmarks measuring encryption/decryption speed, scalability up to 30 users, parameter sensitivity, and a comparative evaluation against Shamir’s Secret Sharing scheme. A systematic security analysis examines partial-information attacks, derivative-root distance margins, and brute-force resistance, demonstrating that the effective security margin remains above 245 bits for configurations of up to 30 users with 256-bit keys. The proposed method offers a concrete, efficient, and secure foundation for multi-user encrypted communication in domains such as IoT, public administration, and e-health. Full article
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10 pages, 246 KB  
Entry
Grover Quantum Algorithm: Applications and Limits
by David R.C. Hill
Encyclopedia 2026, 6(4), 89; https://doi.org/10.3390/encyclopedia6040089 - 13 Apr 2026
Viewed by 2899
Definition
The Grover algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems, requiring O(√N) queries instead of O(N) classically. It works by repeatedly applying an oracle and a diffusion operator to amplify the probability of marked states. This [...] Read more.
The Grover algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems, requiring O(√N) queries instead of O(N) classically. It works by repeatedly applying an oracle and a diffusion operator to amplify the probability of marked states. This advantage makes it relevant to cryptography, optimization, and constraint satisfaction and as a general primitive via amplitude amplification in areas like quantum machine learning and simulation. However, practical implementations are severely constrained by current noisy intermediate-scale quantum (NISQ) machines with limited coherence, deep oracle circuits, and lack of scalable Quantum RAM, restricting demonstrations to small-scale experiments with reproducibility challenges. Full article
(This article belongs to the Collection Applications of Quantum Mechanics)
24 pages, 1742 KB  
Review
Quantum Encryption in Phase Space
by Randy Kuang
Atoms 2026, 14(3), 23; https://doi.org/10.3390/atoms14030023 - 11 Mar 2026
Viewed by 790
Abstract
Quantum Encryption in Phase Space (QEPS) is a physical-layer encryption framework that harnesses the quantum-mechanical properties of coherent states to secure optical communications against both classical and quantum computational threats. By applying randomized phase shifts, displacements, or their dynamic combinations—implemented as unitary transformations [...] Read more.
Quantum Encryption in Phase Space (QEPS) is a physical-layer encryption framework that harnesses the quantum-mechanical properties of coherent states to secure optical communications against both classical and quantum computational threats. By applying randomized phase shifts, displacements, or their dynamic combinations—implemented as unitary transformations in phase space—QEPS disrupts the phase reference essential for coherent detection, establishing aphase synchronization barrier. This review synthesizes the theoretical foundations, security mechanisms, and experimental progress of the QEPS framework, encompassing its three principal variants: the round-trip Quantum Public Key Envelope (QPKE) protocol—a public-key-like scheme built upon phase randomization (QEPS-p), the symmetric phase-only QEPS-p, and the displacement-based QEPS-d. Experimental validations demonstrate that authorized users achieve bit-error rates (BERs) below the forward-error-correction threshold, whereas eavesdroppers are confined to BERs near 50%, equivalent to random guessing—all while utilizing standard coherent optical transceivers at data rates up to 200 Gb/s over 80 km of fiber. We further examine QEPS’s robustness to channel impairments, its seamless compatibility with existing digital signal processing (DSP) pipelines, and its distinctive position within the post-quantum cryptography landscape. Finally, we outline key challenges and future research directions toward deploying QEPS as a practical, quantum-resistant security layer for next-generation optical networks. Full article
(This article belongs to the Special Issue Quantum Optics and Quantum Information)
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24 pages, 1160 KB  
Article
Enhancing Data Security in Satellite Communication Systems: Integrating Quantum Cryptography with CatBoost Machine Learning
by Mohd Nadeem, Syed Anas Ansar, Sakshi Halwai, Arpita Singh and Rajeev Kumar
Information 2026, 17(3), 220; https://doi.org/10.3390/info17030220 - 25 Feb 2026
Viewed by 911
Abstract
In modern communication networks, particularly satellite-based systems, data security faces significant challenges from vulnerabilities such as signal interception, jamming, and latency during long distance transmissions. Traditional cryptographic methods are increasingly vulnerable to quantum computing threats, underscoring the need for advanced solutions to protect [...] Read more.
In modern communication networks, particularly satellite-based systems, data security faces significant challenges from vulnerabilities such as signal interception, jamming, and latency during long distance transmissions. Traditional cryptographic methods are increasingly vulnerable to quantum computing threats, underscoring the need for advanced solutions to protect data integrity, confidentiality, and availability. This research investigates the fusion of quantum cryptography and Machine Learning (ML) to improve security in satellite communication. The Quantum Key Distribution (QKD), which is grounded in quantum mechanics, enables unbreakable encryption by detecting eavesdropping via quantum state disturbances. The CatBoost ML algorithm is applied to a dataset of 10,000 records featuring categorical attributes for prioritizing security elements such as anomaly detection, encryption types, and access controls. The model yields an accuracy of 89.23% and Area under Curve the Receiver Operating Characteristic (AUC-ROC) score of 94.56%, effectively predicting threat levels. Feature importance reveals anomaly detection (28.5%) and quantum encryption (22.3%) as primary contributors. While hurdles such as high implementation costs and transmission range limitations persist, this quantum ML synergy provides a proactive, adaptive framework for resilient, future-ready communication networks. Full article
(This article belongs to the Special Issue 2nd Edition of 5G Networks and Wireless Communication Systems)
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27 pages, 842 KB  
Article
An Automated Synthesis Framework for Benchmarking Quantum Resource Costs of Symmetric-Key Cryptography
by Chanho Choi, Jinseob Oh, SangMan Lee, Geumhwan Cho and Dooho Choi
Mathematics 2026, 14(4), 719; https://doi.org/10.3390/math14040719 - 19 Feb 2026
Viewed by 595
Abstract
Modern information security relies heavily on symmetric-key cryptography such as AES. As quantum computing advances, these classical schemes face increasing pressure from quantum key-search attacks, most notably Grover’s algorithm. To evaluate and compare quantum security quantitatively, the core components of symmetric-key algorithms must [...] Read more.
Modern information security relies heavily on symmetric-key cryptography such as AES. As quantum computing advances, these classical schemes face increasing pressure from quantum key-search attacks, most notably Grover’s algorithm. To evaluate and compare quantum security quantitatively, the core components of symmetric-key algorithms must be implemented and optimized as quantum circuits. Among them, the S-box is a key source of nonlinearity and often dominates the circuit cost. In this paper, we introduce ADOQ (Automatic Depth Optimizer for Quantum circuits), a modular Python (version 3.13.3) framework that automatically synthesizes reversible quantum circuits from S-box specifications and applies a sequence of depth optimization techniques to produce optimized QASM circuits. Our experiments show that ADOQ achieves circuit depths comparable to prior work on 4-qubit S-boxes, and it also supports synthesis for larger S-boxes. Full article
(This article belongs to the Special Issue Recent Advances in Quantum Optimization)
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24 pages, 455 KB  
Review
Post-Quantum Cryptography in Networking Protocols: Challenges, Solutions, and Future Directions
by Sang-Yoon Chang and Qaiser Khan
Cryptography 2026, 10(1), 12; https://doi.org/10.3390/cryptography10010012 - 12 Feb 2026
Cited by 6 | Viewed by 4821
Abstract
Post-quantum cryptography (PQC) provides the essential cryptographic algorithms needed to secure digital networking systems against future adversaries equipped with quantum computing. This paper reviews the PQC research landscape and identifies open challenges and future directions for the critical transition to PQC in digital [...] Read more.
Post-quantum cryptography (PQC) provides the essential cryptographic algorithms needed to secure digital networking systems against future adversaries equipped with quantum computing. This paper reviews the PQC research landscape and identifies open challenges and future directions for the critical transition to PQC in digital networking systems. Building on the NIST standardization process which has hardened the PQC cipher algorithm security, this paper analyzes and describes the recent research on PQC implementations and integrations into scalable and standardized networking systems (Internet, web and cellular networks). We review research on the security, side-channel threats, performances, overheads, and compatibility of PQC ciphers. We also study the research incorporating PQC into the standardized web and cellular networking protocols, ranging from testing the PQC feasibility to proposing protocol solutions and mechanisms to enable PQC. Our study highlights the PQC challenge of large parameter sizes, common across the PQC cipher algorithms, and the research proposing protocol- and system-level mechanisms to address them. Informed by the survey, this paper identifies and highlights the research gaps and future directions to facilitate further research and development for PQC and to secure next-generation digital networking systems. Full article
(This article belongs to the Special Issue Advances in Post-Quantum Cryptography)
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25 pages, 705 KB  
Article
Privacy-Preserving Set Intersection Protocol Based on SM2 Oblivious Transfer
by Zhibo Guan, Hai Huang, Haibo Yao, Qiong Jia, Kai Cheng, Mengmeng Ge, Bin Yu and Chao Ma
Computers 2026, 15(1), 44; https://doi.org/10.3390/computers15010044 - 10 Jan 2026
Viewed by 687
Abstract
Private Set Intersection (PSI) is a fundamental cryptographic primitive in privacy-preserving computation and has been widely applied in federated learning, secure data sharing, and privacy-aware data analytics. However, most existing PSI protocols rely on RSA or standard elliptic curve cryptography, which limits their [...] Read more.
Private Set Intersection (PSI) is a fundamental cryptographic primitive in privacy-preserving computation and has been widely applied in federated learning, secure data sharing, and privacy-aware data analytics. However, most existing PSI protocols rely on RSA or standard elliptic curve cryptography, which limits their applicability in scenarios requiring domestic cryptographic standards and often leads to high computational and communication overhead when processing large-scale datasets. In this paper, we propose a novel PSI protocol based on the Chinese commercial cryptographic standard SM2, referred to as SM2-OT-PSI. The proposed scheme constructs an oblivious transfer-based Oblivious Pseudorandom Function (OPRF) using SM2 public-key cryptography and the SM3 hash function, enabling efficient multi-point OPRF evaluation under the semi-honest adversary model. A formal security analysis demonstrates that the protocol satisfies privacy and correctness guarantees assuming the hardness of the Elliptic Curve Discrete Logarithm Problem. To further improve practical performance, we design a software–hardware co-design architecture that offloads SM2 scalar multiplication and SM3 hashing operations to a domestic reconfigurable cryptographic accelerator (RSP S20G). Experimental results show that, for datasets with up to millions of elements, the presented protocol significantly outperforms several representative PSI schemes in terms of execution time and communication efficiency, especially in medium and high-bandwidth network environments. The proposed SM2-OT-PSI protocol provides a practical and efficient solution for large-scale privacy-preserving set intersection under national cryptographic standards, making it suitable for deployment in real-world secure computing systems. Full article
(This article belongs to the Special Issue Mobile Fog and Edge Computing)
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14 pages, 1305 KB  
Article
Quantum-Enhanced Facial Biometrics: A Hybrid Framework with Post-Quantum Security
by Satinder Singh, Avnish Thakur, Moin Hasan and Guneet Singh Bhatia
Quantum Rep. 2025, 7(4), 64; https://doi.org/10.3390/quantum7040064 - 15 Dec 2025
Viewed by 1575
Abstract
Face recognition systems are widely used for biometric authentication but face two major problems. First, processing high-resolution images and large databases requires extensive computational time. Second, emerging quantum computers threaten to break the encryption methods that protect stored facial templates. Quantum computers will [...] Read more.
Face recognition systems are widely used for biometric authentication but face two major problems. First, processing high-resolution images and large databases requires extensive computational time. Second, emerging quantum computers threaten to break the encryption methods that protect stored facial templates. Quantum computers will soon be able to decrypt current security systems, putting biometric data at permanent risk since facial features cannot be changed like passwords. This paper presents a solution that uses quantum computing to speed up face recognition while adding quantum-resistant security. It applies quantum principal component analysis (QPCA) and the SWAP test to reduce the computational complexity and implement lattice-based cryptography, which quantum computers cannot break. Experimental evaluation demonstrates a significant overall speedup with improved accuracy. The proposed framework achieves a significant improvement in performance, provides 125-bit security against quantum attacks and compresses the data storage requirements significantly. These results demonstrate that quantum-enhanced face recognition can solve both the speed and security challenges facing current biometric systems, making it practical for real-world deployment as quantum technology advances. Full article
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23 pages, 717 KB  
Article
An Adaptive Hybrid Cryptographic Framework for Resource-Constrained IoT Devices
by Manal Jazzaa Alanazi, Renad Atallah Alhoweiti, Gadah Ahmad Alhwaity and Adel R. Alharbi
Electronics 2025, 14(23), 4666; https://doi.org/10.3390/electronics14234666 - 27 Nov 2025
Cited by 3 | Viewed by 1941
Abstract
Recently, the record-level rise in Internet of Things (IoT) devices has produced unparalleled security challenges, particularly for resource-constrained devices operating under limited computational resources, memory, and power. In this context, traditional cryptographic methods not only fail but are also expensive and require extensive [...] Read more.
Recently, the record-level rise in Internet of Things (IoT) devices has produced unparalleled security challenges, particularly for resource-constrained devices operating under limited computational resources, memory, and power. In this context, traditional cryptographic methods not only fail but are also expensive and require extensive resources, given their static nature. In this article, an Adaptive Hybrid Cryptographic Framework (AHCF) is proposed to address the security challenges of resource-constrained IoT devices by adaptively balancing performance and protection levels, which can adaptively adjust cryptographic parameters based on the state of the device at a given time under a specific network environment and security needs. It also effectively balances security level and resource usage and employs low-overhead asymmetric key management with lightweight symmetric cryptography and machine learning-based predictors for the optimal selection of encryption schemes. Experimental testing on multiple IoT platforms has demonstrated its significant benefits, namely 42% less energy consumption, a 38% increase in processor speed, and improved security responsiveness over static deployments. This solution can be applied on boards with as little as 2 KB RAM and 16 KB flash and outperforms existing IoT standards and protocols. Full article
(This article belongs to the Section Computer Science & Engineering)
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30 pages, 2917 KB  
Article
A Post-Quantum Cryptography Enabled Feature-Level Fusion Framework for Privacy-Preserving Multimodal Biometric Recognition
by David Palma and Pier Luca Montessoro
Cryptography 2025, 9(4), 72; https://doi.org/10.3390/cryptography9040072 - 19 Nov 2025
Viewed by 2150
Abstract
As quantum computing continues to advance, it threatens the long-term protection of traditional cryptographic methods, especially in biometric authentication systems where it is important to protect sensitive data. To overcome this challenge, we present a comprehensive, privacy-preserving framework for multimodal biometric authentication that [...] Read more.
As quantum computing continues to advance, it threatens the long-term protection of traditional cryptographic methods, especially in biometric authentication systems where it is important to protect sensitive data. To overcome this challenge, we present a comprehensive, privacy-preserving framework for multimodal biometric authentication that can easily integrate any two binary-encoded modalities through feature-level fusion, ensuring that all sensitive information remains encrypted under a CKKS-based homomorphic encryption scheme resistant to both classical and quantum-enabled attacks. To demonstrate its versatility and effectiveness, we apply this framework to the retinal vascular patterns and palm vein features, which are inherently spoof-resistant and particularly well suited to high-security applications. This method not only ensures the secrecy of the combined biometric sample, but also enables the complete assessment of recognition performance and resilience against adversarial attacks. The results show that our approach provides protection against threats such as data leakage and replay attacks while maintaining high recognition performance and operational efficiency. These findings demonstrate the feasibility of integrating multimodal biometrics with post-quantum cryptography, giving a strong, privacy-oriented authentication solution suitable for mission-critical applications in the post-quantum era. Full article
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47 pages, 3115 KB  
Review
Digital Twin-Driven Cybersecurity for 5G/6G-Enabled Electric Vehicle Charging Infrastructure: A Review
by Ernest Fiko Morgan and Mohd. Hasan Ali
Energies 2025, 18(22), 6048; https://doi.org/10.3390/en18226048 - 19 Nov 2025
Cited by 6 | Viewed by 3151
Abstract
The increasing adoption of electric vehicles (EVs) and the integration of 5G/6G networks are driving the demand for secure, intelligent, and interoperable charging infrastructure within the Internet of Vehicles (IoV) ecosystem. Electric Vehicle Charging Stations (EVCS) face growing cyber–physical threats, including spoofing, data [...] Read more.
The increasing adoption of electric vehicles (EVs) and the integration of 5G/6G networks are driving the demand for secure, intelligent, and interoperable charging infrastructure within the Internet of Vehicles (IoV) ecosystem. Electric Vehicle Charging Stations (EVCS) face growing cyber–physical threats, including spoofing, data injection, and firmware tampering, risking user privacy, grid stability, and EVCS reliability. While artificial intelligence (AI), blockchain, and cryptography have been applied in cybersecurity, comprehensive solutions tailored to EVCS challenges, such as real-time threat mitigation and scalability, are often lacking. This paper addresses these critical cybersecurity gaps by presenting a comprehensive overview of novel strategies for enhancing EVCS security through the Internet of Digital Twins (IoDT) technology. The primary objective is to evaluate advanced frameworks that synergize digital twins with artificial intelligence, blockchain, and quantum-resistant cryptography. Through systematic literature analysis, global threat assessments, and review of international standards, this study identifies key attack vectors and their impacts on EVCS. Key findings demonstrate that digital twin-driven solutions facilitate real-time monitoring, anomaly detection, predictive threat mitigation, and secure system governance. This review offers actionable insights for researchers, industry stakeholders, and policymakers to strengthen the cybersecurity and resilience of next-generation electric mobility infrastructure, addressing challenges like scalability and implementation barriers. Full article
(This article belongs to the Collection "Electric Vehicles" Section: Review Papers)
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20 pages, 10948 KB  
Article
Efficient Parameter Search for Chaotic Dynamical Systems Using Lyapunov-Based Reinforcement Learning
by Gang-Cheng Huang
Symmetry 2025, 17(11), 1832; https://doi.org/10.3390/sym17111832 - 1 Nov 2025
Cited by 2 | Viewed by 1452
Abstract
This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the Hénon map, the Lorenz system, Chua’s circuit, the Lorenz–Haken model, and a custom 5D hyperchaotic design. The largest Lyapunov exponent (LLE) is used [...] Read more.
This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the Hénon map, the Lorenz system, Chua’s circuit, the Lorenz–Haken model, and a custom 5D hyperchaotic design. The largest Lyapunov exponent (LLE) is used as a scalar reward to guide exploration toward regions with high sensitivity to initial conditions. Under matched evaluation budgets, the approach reduces redundant simulations relative to grid scans and accelerates discovery of parameter sets with large positive LLE. Experiments report learning curves, parameter heatmaps, and representative phase portraits that are consistent with Lyapunov-based assessments. Q-learning typically reaches high-reward regions earlier, whereas SARSA shows smoother improvements over iterations. Several evaluated systems possess equation-level symmetry—most notably sign-reversal invariance in the Lorenz system and Chua’s circuit models and a coordinate-wise sign pattern in the Lorenz–Haken equations—which manifests as mirror attractors and paired high-reward regions; one representative is reported for each symmetric pair. Overall, Lyapunov-guided reinforcement learning serves as a practical complement to grid and random search for chaos identification in both discrete maps and continuous flows, and transfers with minimal changes to higher-dimensional settings. The framework provides an efficient method for identifying high-complexity parameters for applications in chaos-based cryptography and for assessing stability boundaries in engineering design. Full article
(This article belongs to the Topic Recent Trends in Nonlinear, Chaotic and Complex Systems)
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