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26 pages, 911 KB  
Article
Logarithmic-Size Post-Quantum Linkable Ring Signatures Based on Aggregation Operations
by Minghui Zheng, Shicheng Huang, Deju Kong, Xing Fu, Qiancheng Yao and Wenyi Hou
Entropy 2026, 28(1), 130; https://doi.org/10.3390/e28010130 - 22 Jan 2026
Viewed by 107
Abstract
Linkable ring signatures are a type of ring signature scheme that can protect the anonymity of signers while allowing the public to verify whether the same signer has signed the same message multiple times. This functionality makes linkable ring signatures suitable for applications [...] Read more.
Linkable ring signatures are a type of ring signature scheme that can protect the anonymity of signers while allowing the public to verify whether the same signer has signed the same message multiple times. This functionality makes linkable ring signatures suitable for applications such as cryptocurrencies and anonymous voting systems, achieving the dual goals of identity privacy protection and misuse prevention. However, existing post-quantum linkable ring signature schemes often suffer from issues such as excessive linear data growth the adoption of post-quantum signature algorithms, and high circuit complexity resulting from the use of post-quantum zero-knowledge proof protocols. To address these issues, a logarithmic-size post-quantum linkable ring signature scheme based on aggregation operations is proposed. The scheme constructs a Merkle tree from ring members’ public keys via a hash algorithm to achieve logarithmic-scale signing and verification operations. Moreover, it introduces, for the first time, a post-quantum aggregate signature scheme to replace post-quantum zero-knowledge proof protocols, thereby effectively avoiding the construction of complex circuits. Scheme analysis confirms that the proposed scheme meets the correctness requirements of linkable ring signatures. In terms of security, the scheme satisfies the anonymity, unforgeability, and linkability requirements of linkable ring signatures. Moreover, the aggregation process does not leak information about the signing members, ensuring strong privacy protection. Experimental results demonstrate that, when the ring size scales to 1024 members, our scheme outperforms the existing Dilithium-based logarithmic post-quantum ring signature scheme, with nearly 98.25% lower signing time, 98.90% lower verification time, and 99.81% smaller signature size. Full article
(This article belongs to the Special Issue Quantum Information Security)
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19 pages, 1207 KB  
Article
An Auditable and Trusted Lottery System in the Cloud
by Gwan-Hwan Hwang, Tao-Ku Chang and Yi-Syuan Lu
Appl. Sci. 2026, 16(2), 741; https://doi.org/10.3390/app16020741 - 11 Jan 2026
Viewed by 354
Abstract
Public blockchains offer transparency and tamper resistance, but implementing national-scale lotteries directly on-chain is impractical because each bet would require a separate transaction, incurring substantial gas costs and facing throughput limitations. This paper presents an auditable lottery architecture designed to address these scalability [...] Read more.
Public blockchains offer transparency and tamper resistance, but implementing national-scale lotteries directly on-chain is impractical because each bet would require a separate transaction, incurring substantial gas costs and facing throughput limitations. This paper presents an auditable lottery architecture designed to address these scalability challenges and eliminate the reliance on trusted third parties. The proposed approach decouples high-volume bet recording from on-chain enforcement. Bets are recorded off-chain in a transaction-positioned Merkle tree (TP-Merkle tree), while the service provider commits only the per-round root hash and summary metadata to an Ethereum smart contract. Each player receives a signed receipt and a compact Merkle proof (Slice), enabling independent inclusion checks and third-party audits. A programmable appeal mechanism allows any participant to submit receipts and cryptographic evidence to the contract; if misbehavior is proven, compensation is executed automatically from a pre-deposited margin. A proof-of-concept implementation demonstrates the system’s feasibility, and extensive experiments evaluate collision behavior, storage overhead, proof size, and gas consumption, demonstrating that the proposed design can support national-scale betting volumes (tens of millions of bets per round) while occupying only a small fraction of on-chain resources. Full article
(This article belongs to the Special Issue Advanced Blockchain Technology and Its Applications)
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29 pages, 3775 KB  
Article
Blockchain-Based Batch Authentication and Symmetric Group Key Agreement in MEC Environments
by Yun Deng, Jing Zhang, Jin Liu and Jinyong Li
Symmetry 2025, 17(12), 2160; https://doi.org/10.3390/sym17122160 - 15 Dec 2025
Viewed by 362
Abstract
To address the high computational and communication overheads and the limited edge security found in many existing batch verification methods for Mobile Edge Computing (MEC), this paper presents a blockchain-based batch authentication and symmetric group key agreement protocol. A core feature of this [...] Read more.
To address the high computational and communication overheads and the limited edge security found in many existing batch verification methods for Mobile Edge Computing (MEC), this paper presents a blockchain-based batch authentication and symmetric group key agreement protocol. A core feature of this protocol is the establishment of a shared symmetric key among all authenticated participants. This symmetry in key distribution is fundamental for enabling secure and efficient broadcast or multicast communication within the MEC group. The protocol introduces a chameleon hash function built on elliptic curves, allowing smart mobile devices (SMDs) to generate lightweight signatures. The edge server (ES) then performs efficient large-scale batch authentication using an aggregate signature technique. Considering the need for secure and independent communication between SMDs and ES, the protocol further establishes a one-to-one session key agreement mechanism and uses a Merkle tree to verify session key correctness. Formal verification with ProVerif2.05 tool confirms the protocol’s security and multiple protection properties. Experimental results show that, compared with the CPPBA, ECCAS, and LBVP schemes, the protocol improves computational efficiency of batch authentication by 0.94%, 67.20%, and 49.53%, respectively. For group key agreement, the protocol achieves a 35.26% improvement in computational efficiency over existing schemes. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Embedded Systems)
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19 pages, 4716 KB  
Article
Evaluation of Priority Queues in the Priority Flood Algorithm for Hydrological Modelling
by Lejun Ma, Yue Yuan, Huan Wang, Huihui Liu and Qiuling Wu
Water 2025, 17(22), 3202; https://doi.org/10.3390/w17223202 - 9 Nov 2025
Cited by 1 | Viewed by 875
Abstract
The Priority-Flood algorithm, widely recognized for its computational efficiency in hydrological analysis, serves as the fundamental method for depression identification in DEMs, and the efficiency of the Priority-Flood algorithm hinges largely on the core component—priority queue implementation. Existing studies have focused predominantly on [...] Read more.
The Priority-Flood algorithm, widely recognized for its computational efficiency in hydrological analysis, serves as the fundamental method for depression identification in DEMs, and the efficiency of the Priority-Flood algorithm hinges largely on the core component—priority queue implementation. Existing studies have focused predominantly on reducing the amount of data processed by queues, with few systematic reports on concrete queue implementations and corresponding performance analyses. In this study, six priority queues in the Priority-Flood algorithm are compared: a mini-heap (Heap), an AVL tree, a red-black tree (RBTree), a pairing heap (PairingHeap), a skip list (SkipList), and the Hash Heap (HHeap) structure proposed herein. Using multiscale DEM datasets as benchmarks, the results show that HHeap consistently outperforms the other structures across all scales, with particular advantages in ultralarge queues and in scenarios with high data duplication, rendering it the most effective choice for priority queues. The pairing heap approach typically ranks second in terms of overall runtime, whereas the AVL tree exhibits stable performance across scales; min-heap shows pronounced weaknesses under large-scale data conditions. This study provides empirical evidence to guide efficient priority queue selection and implementation and offers a viable technical pathway for ultralarge-scale terrain analysis. Future work will explore integrating HHeap with learning-based sorting and parallelization to further enhance processing performance and robustness in massive DEM contexts. Full article
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36 pages, 2906 KB  
Review
Data Organisation for Efficient Pattern Retrieval: Indexing, Storage, and Access Structures
by Paraskevas Koukaras and Christos Tjortjis
Big Data Cogn. Comput. 2025, 9(10), 258; https://doi.org/10.3390/bdcc9100258 - 13 Oct 2025
Cited by 1 | Viewed by 2183
Abstract
The increasing scale and complexity of data mining outputs, such as frequent itemsets, association rules, sequences, and subgraphs have made efficient pattern retrieval a critical, yet underexplored challenge. This review addresses the organisation, indexing, and access strategies, which enable scalable and responsive retrieval [...] Read more.
The increasing scale and complexity of data mining outputs, such as frequent itemsets, association rules, sequences, and subgraphs have made efficient pattern retrieval a critical, yet underexplored challenge. This review addresses the organisation, indexing, and access strategies, which enable scalable and responsive retrieval of structured patterns. We examine the underlying types of data and pattern outputs, common retrieval operations, and the variety of query types encountered in practice. Key indexing structures are surveyed, including prefix trees, inverted indices, hash-based approaches, and bitmap-based methods, each suited to different pattern representations and workloads. Storage designs are discussed with attention to metadata annotation, format choices, and redundancy mitigation. Query optimisation strategies are reviewed, emphasising index-aware traversal, caching, and ranking mechanisms. This paper also explores scalability through parallel, distributed, and streaming architectures, and surveys current systems and tools, which integrate mining and retrieval capabilities. Finally, we outline pressing challenges and emerging directions, such as supporting real-time and uncertainty-aware retrieval, and enabling semantic, cross-domain pattern access. Additional frontiers include privacy-preserving indexing and secure query execution, along with integration of repositories into machine learning pipelines for hybrid symbolic–statistical workflows. We further highlight the need for dynamic repositories, probabilistic semantics, and community benchmarks to ensure that progress is measurable and reproducible across domains. This review provides a comprehensive foundation for designing next-generation pattern retrieval systems, which are scalable, flexible, and tightly integrated into analytic workflows. The analysis and roadmap offered are relevant across application areas including finance, healthcare, cybersecurity, and retail, where robust and interpretable retrieval is essential. Full article
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36 pages, 2113 KB  
Article
Self-Sovereign Identities and Content Provenance: VeriTrust—A Blockchain-Based Framework for Fake News Detection
by Maruf Farhan, Usman Butt, Rejwan Bin Sulaiman and Mansour Alraja
Future Internet 2025, 17(10), 448; https://doi.org/10.3390/fi17100448 - 30 Sep 2025
Cited by 2 | Viewed by 4159
Abstract
The widespread circulation of digital misinformation exposes a critical shortcoming in prevailing detection strategies, namely, the absence of robust mechanisms to confirm the origin and authenticity of online content. This study addresses this by introducing VeriTrust, a conceptual and provenance-centric framework designed to [...] Read more.
The widespread circulation of digital misinformation exposes a critical shortcoming in prevailing detection strategies, namely, the absence of robust mechanisms to confirm the origin and authenticity of online content. This study addresses this by introducing VeriTrust, a conceptual and provenance-centric framework designed to establish content-level trust by integrating Self-Sovereign Identity (SSI), blockchain-based anchoring, and AI-assisted decentralized verification. The proposed system is designed to operate through three key components: (1) issuing Decentralized Identifiers (DIDs) and Verifiable Credentials (VCs) through Hyperledger Aries and Indy; (2) anchoring cryptographic hashes of content metadata to an Ethereum-compatible blockchain using Merkle trees and smart contracts; and (3) enabling a community-led verification model enhanced by federated learning with future extensibility toward zero-knowledge proof techniques. Theoretical projections, derived from established performance benchmarks, suggest the framework offers low latency and high scalability for content anchoring and minimal on-chain transaction fees. It also prioritizes user privacy by ensuring no on-chain exposure of personal data. VeriTrust redefines misinformation mitigation by shifting from reactive content-based classification to proactive provenance-based verification, forming a verifiable link between digital content and its creator. VeriTrust, while currently at the conceptual and theoretical validation stage, holds promise for enhancing transparency, accountability, and resilience against misinformation attacks across journalism, academia, and online platforms. Full article
(This article belongs to the Special Issue AI and Blockchain: Synergies, Challenges, and Innovations)
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26 pages, 872 KB  
Article
The Untapped Potential of Ascon Hash Functions: Benchmarking, Hardware Profiling, and Application Insights for Secure IoT and Blockchain Systems
by Meera Gladis Kurian and Yuhua Chen
Sensors 2025, 25(19), 5936; https://doi.org/10.3390/s25195936 - 23 Sep 2025
Viewed by 1708
Abstract
Hash functions are fundamental components in both cryptographic and non-cryptographic systems, supporting secure authentication, data integrity, fingerprinting, and indexing. While the Ascon family, selected by the National Institute of Standards and Technology (NIST) in 2023 for lightweight cryptography, has been extensively evaluated in [...] Read more.
Hash functions are fundamental components in both cryptographic and non-cryptographic systems, supporting secure authentication, data integrity, fingerprinting, and indexing. While the Ascon family, selected by the National Institute of Standards and Technology (NIST) in 2023 for lightweight cryptography, has been extensively evaluated in its authenticated encryption mode, its hashing and extendable-output variants, namely Ascon-Hash256, Ascon-XOF128, and Ascon-CXOF128, have not received the same level of empirical attention. This paper presents a structured benchmarking study of these hash variants using both the SMHasher framework and custom Python-based simulation environments. SMHasher is used to evaluate statistical and structural robustness under constrained, patterned, and low-entropy input conditions, while Python-based experiments assess application-specific performance in Bloom filter-based replay detection at the network edge, Merkle tree aggregation for blockchain transaction integrity, lightweight device fingerprinting for IoT identity management, and tamper-evident logging for distributed ledgers. We compare the performance of Ascon hashes with widely used cryptographic functions such as SHA3 and BLAKE2s, as well as high-speed non-cryptographic hashes including MurmurHash3 and xxHash. We assess avalanche behavior, diffusion consistency, output bias, and keyset sensitivity while also examining Ascon-XOF’s variable-length output capabilities relative to SHAKE for applications such as domain-separated hashing and lightweight key derivation. Experimental results indicate that Ascon hash functions offer strong diffusion, low statistical bias, and competitive performance across both cryptographic and application-specific domains. These properties make them well suited for deployment in resource-constrained systems, including Internet of Things (IoT) devices, blockchain indexing frameworks, and probabilistic authentication architectures. This study provides the first comprehensive empirical evaluation of Ascon hashing modes and offers new insights into their potential as lightweight, structurally resilient alternatives to established hash functions. Full article
(This article belongs to the Special Issue Blockchain-Based Solutions to Secure IoT)
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31 pages, 2138 KB  
Article
A Sustainability Assessment of a Blockchain-Secured Solar Energy Logger for Edge IoT Environments
by Javad Vasheghani Farahani and Horst Treiblmaier
Sustainability 2025, 17(17), 8063; https://doi.org/10.3390/su17178063 - 7 Sep 2025
Viewed by 2246
Abstract
In this paper, we design, implement, and empirically evaluate a tamper-evident, blockchain-secured solar energy logging system for resource-constrained edge Internet of Things (IoT) devices. Using a Merkle tree batching approach in conjunction with threshold-triggered blockchain anchoring, the system combines high-frequency local logging with [...] Read more.
In this paper, we design, implement, and empirically evaluate a tamper-evident, blockchain-secured solar energy logging system for resource-constrained edge Internet of Things (IoT) devices. Using a Merkle tree batching approach in conjunction with threshold-triggered blockchain anchoring, the system combines high-frequency local logging with energy-efficient, cryptographically verifiable submissions to the Ethereum Sepolia testnet, a public Proof-of-Stake (PoS) blockchain. The logger captured and hashed cryptographic chains on a minute-by-minute basis during a continuous 135 h deployment on a Raspberry Pi equipped with an INA219 sensor. Thanks to effective retrial and daily rollover mechanisms, it committed 130 verified Merkle batches to the blockchain without any data loss or unverifiable records, even during internet outages. The system offers robust end-to-end auditability and tamper resistance with low operational and carbon overhead, which was tested with comparative benchmarking against other blockchain logging models and conventional local and cloud-based loggers. The findings illustrate the technical and sustainability feasibility of digital audit trails based on blockchain technology for distributed solar energy systems. These audit trails facilitate scalable environmental, social, and governance (ESG) reporting, automated renewable energy certification, and transparent carbon accounting. Full article
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26 pages, 5349 KB  
Article
Smart Forest Modeling Behavioral for a Greener Future: An AI Text-by-Voice Blockchain Approach with Citizen Involvement in Sustainable Forestry Functionality
by Dimitrios Varveris, Vasiliki Basdekidou, Chrysanthi Basdekidou and Panteleimon Xofis
FinTech 2025, 4(3), 47; https://doi.org/10.3390/fintech4030047 - 1 Sep 2025
Viewed by 1301
Abstract
This paper introduces a novel approach to tree modeling architecture integrated with blockchain technology, aimed at enhancing landscape spatial planning and forest monitoring systems. The primary objective is to develop a low-cost, automated tree CAD modeling methodology combined with blockchain functionalities to support [...] Read more.
This paper introduces a novel approach to tree modeling architecture integrated with blockchain technology, aimed at enhancing landscape spatial planning and forest monitoring systems. The primary objective is to develop a low-cost, automated tree CAD modeling methodology combined with blockchain functionalities to support smart forest projects and collaborative design processes. The proposed method utilizes a parametric tree CAD model consisting of four 2D tree-frames with a 45° division angle, enriched with recorded tree-leaves’ texture and color. An “AI Text-by-Voice CAD Programming” technique is employed to create tangible tree-model NFT tokens, forming the basis of a thematic “Internet-of-Trees” blockchain. The main results demonstrate the effectiveness of the blockchain/Merkle hash tree in tracking tree geometry growth and texture changes through parametric transactions, enabling decentralized design, data validation, and planning intelligence. Comparative analysis highlights the advantages in cost, time efficiency, and flexibility over traditional 3D modeling techniques, while providing acceptable accuracy for metaverse projects in smart forests and landscape architecture. Core contributions include the integration of AI-based user voice interaction with blockchain and behavioral data for distributed and collaborative tree modeling, the introduction of a scalable and secure “Merkle hash tree” for smart forest monitoring, and the facilitation of fintech adoption in environmental projects. This framework offers significant potential for advancing metaverse-based landscape architecture, smart forest surveillance, sustainable urban planning, and the improvement of citizen involvement in sustainable forestry paving the way for a greener future. Full article
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16 pages, 955 KB  
Article
Minimizing Redundant Hash and Witness Operations in Merkle Hash Trees
by DaeYoub Kim
Appl. Sci. 2025, 15(17), 9611; https://doi.org/10.3390/app15179611 - 31 Aug 2025
Viewed by 998
Abstract
Reusing cached data is a widely adopted technique for improving network and system performance. Future Internet architectures such as Named Data Networking (NDN) leverage intermediate nodes—such as proxy servers and routers—to cache and deliver data, reducing latency and alleviating load on original data [...] Read more.
Reusing cached data is a widely adopted technique for improving network and system performance. Future Internet architectures such as Named Data Networking (NDN) leverage intermediate nodes—such as proxy servers and routers—to cache and deliver data, reducing latency and alleviating load on original data sources. However, a fundamental challenge of this approach is the lack of trust in intermediate nodes, as users cannot reliably identify and verify them. To address this issue, many systems adopt data-oriented verification rather than sender authentication, using Merkle Hash Trees (MHTs) to enable users to verify both the integrity and authenticity of received data. Despite its advantages, MHT-based authentication incurs significant redundancy: identical hash values are often recomputed, and witness data are repeatedly transmitted for each segment. These redundancies lead to increased computational and communication overhead, particularly in large-scale data publishing scenarios. This paper proposes a novel scheme to reduce such inefficiencies by enabling the reuse of previously verified node values, especially transmitted witnesses. The proposed scheme improves both computational and transmission efficiency by eliminating redundant computation arising from repeated calculation of identical node values. To achieve this, it stores and reuses received witness values. As a result, when verifying 2n segments (n > 8), the proposed method achieves more than an 80% reduction in total hash operations compared to the standard MHT. Moreover, our method preserves the security guarantees of the MHT while significantly optimizing its performance in terms of both computation and transmission costs. Full article
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17 pages, 362 KB  
Article
An Efficient Distributed Identity Selective Disclosure Algorithm
by Guanzheng Wang and Guoyan Zhang
Appl. Sci. 2025, 15(16), 8834; https://doi.org/10.3390/app15168834 - 11 Aug 2025
Cited by 1 | Viewed by 2000
Abstract
Distributed digital identity is an emerging identity management technology aimed at achieving comprehensive interconnectivity between digital objects. However, there is still the problem of privacy leakage in distributed identities, and selective disclosure technology partially solves the privacy issue in distributed identities. Most of [...] Read more.
Distributed digital identity is an emerging identity management technology aimed at achieving comprehensive interconnectivity between digital objects. However, there is still the problem of privacy leakage in distributed identities, and selective disclosure technology partially solves the privacy issue in distributed identities. Most of the existing selective disclosure algorithms use anonymous credentials or hash functions. Anonymous credential schemes offer high security and meet the requirements of unforgeability and unlinkability, but their exponential operations result in low efficiency. The scheme based on hash functions, although more efficient, is susceptible to man-in-the-middle attacks. This article proposes an efficient selective disclosure scheme based on hash functions and implicit certificates. The attribute values are treated as leaf nodes of the Merkle tree, and the root node is placed in a verifiable credential. According to the implicit certificate algorithm process, a key pair that can use the credential is generated. During the attribute disclosure process, the user autonomously selects the attribute value to be presented and generates a verification path from the attribute to the root node. The verifier checks the Merkle tree verification path. All operations are completed within 10 ms while meeting the unforgeability requirements and resisting man-in-the-middle attacks. This article also utilizes the ZK-SNARK algorithm to hide the validation path of the Merkle tree, enhancing the security of the path during the disclosure process. The experimental results show that the selective disclosure algorithm performs well in both performance and privacy protection, with an efficiency 80% faster than that of existing schemes. This enhances the proposed scheme’s potential and value in the field of identity management; it also holds broad application prospects in fields such as the Internet of Things, finance, and others. Full article
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12 pages, 3315 KB  
Article
NeRF-RE: An Improved Neural Radiance Field Model Based on Object Removal and Efficient Reconstruction
by Ziyang Li, Yongjian Huai, Qingkuo Meng and Shiquan Dong
Information 2025, 16(8), 654; https://doi.org/10.3390/info16080654 - 31 Jul 2025
Viewed by 2915
Abstract
High-quality green gardens can markedly enhance the quality of life and mental well-being of their users. However, health and lifestyle constraints make it difficult for people to enjoy urban gardens, and traditional methods struggle to offer the high-fidelity experiences they need. This study [...] Read more.
High-quality green gardens can markedly enhance the quality of life and mental well-being of their users. However, health and lifestyle constraints make it difficult for people to enjoy urban gardens, and traditional methods struggle to offer the high-fidelity experiences they need. This study introduces a 3D scene reconstruction and rendering strategy based on implicit neural representation through the efficient and removable neural radiation fields model (NeRF-RE). Leveraging neural radiance fields (NeRF), the model incorporates a multi-resolution hash grid and proposal network to improve training efficiency and modeling accuracy, while integrating a segment-anything model to safeguard public privacy. Take the crabapple tree, extensively utilized in urban garden design across temperate regions of the Northern Hemisphere. A dataset comprising 660 images of crabapple trees exhibiting three distinct geometric forms is collected to assess the NeRF-RE model’s performance. The results demonstrated that the ‘harvest gold’ crabapple scene had the highest reconstruction accuracy, with PSNR, LPIPS and SSIM of 24.80 dB, 0.34 and 0.74, respectively. Compared to the Mip-NeRF 360 model, the NeRF-RE model not only showed an up to 21-fold increase in training efficiency for three types of crabapple trees, but also exhibited a less pronounced impact of dataset size on reconstruction accuracy. This study reconstructs real scenes with high fidelity using virtual reality technology. It not only facilitates people’s personal enjoyment of the beauty of natural gardens at home, but also makes certain contributions to the publicity and promotion of urban landscapes. Full article
(This article belongs to the Special Issue Extended Reality and Its Applications)
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26 pages, 831 KB  
Article
An Efficient and Fair Map-Data-Sharing Mechanism for Vehicular Networks
by Kuan Fan, Qingdong Liu, Chuchu Liu, Ning Lu and Wenbo Shi
Electronics 2025, 14(12), 2437; https://doi.org/10.3390/electronics14122437 - 15 Jun 2025
Viewed by 821
Abstract
With the rapid advancement in artificial intelligence, autonomous driving has emerged as a prominent research frontier. Autonomous vehicles rely on high-precision high-definition map data, necessitating timely map updates by map companies to accurately reflect road conditions. This paper proposes an efficient and fair [...] Read more.
With the rapid advancement in artificial intelligence, autonomous driving has emerged as a prominent research frontier. Autonomous vehicles rely on high-precision high-definition map data, necessitating timely map updates by map companies to accurately reflect road conditions. This paper proposes an efficient and fair map-data-sharing mechanism for vehicular networks. To encourage vehicles to share data, we introduce a reputation unit to resolve the cold-start issue for new vehicles, effectively distinguishing legitimate new vehicles from malicious attackers. Considering both the budget constraints of map companies and heterogeneous data collection capabilities of vehicles, we design a fair incentive mechanism based on the proposed reputation unit and a reverse auction algorithm, achieving an optimal balance between data quality and procurement costs. Furthermore, the scheme has been developed to facilitate mutual authentication between vehicles and Roadside Unit(RSU), thereby ensuring the security of shared data. In order to address the issue of redundant authentication in overlapping RSU coverage areas, we construct a Merkle hash tree structure using a set of anonymous certificates, enabling single-round identity verification to enhance authentication efficiency. A security analysis demonstrates the robustness of the scheme, while performance evaluations and the experimental results validate its effectiveness and practicality. Full article
(This article belongs to the Special Issue Cryptography and Computer Security)
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20 pages, 312 KB  
Article
An Analysis of Existing Hash-Based Post-Quantum Signature Schemes
by Cristina Maria Pacurar, Razvan Bocu and Maksim Iavich
Symmetry 2025, 17(6), 919; https://doi.org/10.3390/sym17060919 - 10 Jun 2025
Cited by 1 | Viewed by 4114
Abstract
The rapid development of quantum computing poses challenges to the foundations of traditional cryptography. The threats are significant in terms of both asymmetric cryptography (which exposes schemes like RSA and ECC to efficient attacks) and symmetric cryptography, where key sizes must be increased [...] Read more.
The rapid development of quantum computing poses challenges to the foundations of traditional cryptography. The threats are significant in terms of both asymmetric cryptography (which exposes schemes like RSA and ECC to efficient attacks) and symmetric cryptography, where key sizes must be increased to mitigate these threats. In this paper, we review the evolution of hash-based digital signatures, from early one-time signatures to modern stateless schemes, with an emphasis on their security properties, efficiency, and practical constraints. Moreover, we propose a simple comparative metric that reflects structural symmetry across key parameters such as key size, signature size, and computational cost, enabling a visual clustering of the schemes. We give particular attention to recent developments such as Verkle trees, which preserve symmetric design principles while improving scalability and proof compactness. The study highlights ongoing tradeoffs between stateful and stateless designs and argues for the continued relevance of symmetric cryptographic constructions in building secure, efficient post-quantum systems. Full article
(This article belongs to the Section Computer)
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23 pages, 651 KB  
Article
Post-Quantum Digital Signature: Verkle-Based HORST
by Maksim Iavich, Tamari Kuchukhidze and Razvan Bocu
J. Cybersecur. Priv. 2025, 5(2), 28; https://doi.org/10.3390/jcp5020028 - 22 May 2025
Cited by 2 | Viewed by 2230 | Correction
Abstract
The security of commonly used cryptographic systems like RSA and ECC might be threatened by the future development of quantum computing. Verkle-based HORST decreases the size of signatures by 75% (from 12.8 KB to 3.2 KB) and enables O(1)-sized proofs by replacing Merkle [...] Read more.
The security of commonly used cryptographic systems like RSA and ECC might be threatened by the future development of quantum computing. Verkle-based HORST decreases the size of signatures by 75% (from 12.8 KB to 3.2 KB) and enables O(1)-sized proofs by replacing Merkle trees with Verkle trees. Because verification shifts from O(log t) to constant time, it is ideal for blockchain and IoT applications that require short signatures and fast validation. In order to increase efficiency, this study introduces Verkle-based HORST, a hash-based signature method that uses Verkle trees. Our primary contributions are the following: a formal security analysis proving maintained protection levels under standard assumptions; a thorough performance evaluation demonstrating significant improvements in signature size and verification complexity in comparison to conventional Merkle tree approaches; and a novel signature construction employing polynomial commitments to achieve compact proofs. The proposed approach has a lot of benefits for real-world implementation, especially when dealing with situations that call for a large number of signatures or settings with limited resources. We offer comprehensive implementation instructions and parameter choices to promote uptake while preserving hash-based cryptography’s quantum-resistant security features. Our findings suggest that this method is a good fit for post-quantum cryptography systems’ standardization. Full article
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