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Mathematics
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Scalability, Sustainability and Security: Searching for New Blockchain Solutions
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Scalability, Sustainability and Security: Searching for New Blockchain Solutions

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 15 July 2025 | Viewed by 12092

Special Issue Editors

Dr. Yu Guo

E-Mail Website
Guest Editor
School of Artificial Intelligence, Beijing Normal University, Beijing, China
Interests: cloud computing security; network security; privacy-preserving data processing; blockchain technology
Prof. Dr. Rongfang Bie

E-Mail Website
Guest Editor
School of Artificial Intelligence, Beijing Normal University, Beijing, China
Interests: data mining and knowledge engineering; blockchain technology and educational applications; machine learning methods in biofeedback

Special Issue Information

Dear Colleagues,

We invite you to submit your latest applied research on the field of blockchains to this Special Issue, entitled “Scalability, Sustainability and Security: Searching for New Blockchain Solutions”. The aim of the Special Issue is to expand the applicability of blockchains and commit to the search for scalable, sustainable, and secure blockchain solutions. Any experimental research or empirical study on theoretical developments in blockchains is highly welcome. Additionally, research papers presenting solution methods and/or studying their computational complexity, as well as proposing new algorithms with which to solve blockchain problems in an effective and efficient manner, are also welcome. We are looking forward to receiving innovative approaches that apply, in practical settings, state-of-the art techniques from blockchain technology, protocols, and algorithms based on blockchains, with the aim of offering effective solutions to complex blockchain problems. Such types of papers will address the scalability, sustainability, and security of using blockchain technologies in addition to the enhancement of them by using intelligent methods to treat real-life problems from various disciplines.

Dr. Yu Guo
Prof. Dr. Rongfang Bie
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • theories of blockchain and distributed ledger technology.
  • new blockchain architecture. 
  • distributed consensus and fault tolerance mechanisms. 
  • security, privacy, and trust of blockchains. 
  • applications and services based on blockchains. 
  • protocols and algorithms based on blockchains. 
  • blockchains in the Internet of things (IoT).
  • blockchains in social networking. 
  • blockchains in supply chain management. 
  • blockchains in edge and cloud computing. 
  • blockchains and artificial intelligence. 
  • meta applications of blockchains. 
  • DeFi, NFTs, and GameFi

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Published Papers (7 papers)

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Research

23 pages, 1032 KiB  
Article
Concurrency Conflict Modeling for Asynchronous Processing in Blockchain-Based Transactive Energy Systems
by Fabiola Marcos Solis, Saul Eduardo Pomares Hernandez, José Roberto Pérez Cruz and Lil María Rodríguez Henríquez
Mathematics 2024, 12(24), 3968; https://doi.org/10.3390/math12243968 - 17 Dec 2024
Viewed by 801
Abstract
Blockchain is widely adopted for decentralized transaction management in systems like Transactive Energy (TE). Unfortunately, conventional blockchains with sequential models and restrictive participation rules do not meet energy sector requirements. High volumes of asynchronous-generated transactions impose severe concurrency challenges for blockchain. These difficulties [...] Read more.
Blockchain is widely adopted for decentralized transaction management in systems like Transactive Energy (TE). Unfortunately, conventional blockchains with sequential models and restrictive participation rules do not meet energy sector requirements. High volumes of asynchronous-generated transactions impose severe concurrency challenges for blockchain. These difficulties worsen when participants process blocks concurrently, prompting branching and conflicting versions. This issue is often addressed by discarding blocks and reverting transactions, which is detrimental to TE systems. Preserving validated transactions is crucial to avoid disrupting physical asset exchanges and wasting computational resources. To address these challenges, this paper proposes a new model for identifying transaction discrepancies in conflict blocks while maintaining validated transactions. The model enables collaborative block building by integrating multiple blockchain views, eliminating competition, leader selection, and transaction reversals or discards. Block and transaction generation conflicts are addressed by establishing logical-temporal dependencies and leveraging pairwise interactions to detect them toward accelerating consensus. Hence, the model promotes concurrency to enhance transaction processing and avoid resource waste. Simulations indicate traditional models limit network potential to below 5% as blockchain height increases because of single contributions. Conversely, the proposed model uses multiple nodes’ views to achieve up to 90% of the network’s processing capacity. Full article
(This article belongs to the Special Issue Scalability, Sustainability and Security: Searching for New Blockchain Solutions)
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23 pages, 704 KiB  
Article
Addressing the Cost Optimization Issue for IOTA Based on Lyapunov Optimization Theory
by Yinfeng Chen, Baojun Sun, Yaofei Wang, Zhixin Qiu and Yang Li
Mathematics 2024, 12(21), 3391; https://doi.org/10.3390/math12213391 - 30 Oct 2024
Viewed by 1004
Abstract
IOTA is an emerging decentralized computing paradigm for developing blockchain-based Internet of Things (IoT) applications. It has the advantages of zero transaction fees, incremental scalability, and high-performance transaction rates. Despite its well-understood benefits, IOTA nodes need to withstand considerable resource costs to generate [...] Read more.
IOTA is an emerging decentralized computing paradigm for developing blockchain-based Internet of Things (IoT) applications. It has the advantages of zero transaction fees, incremental scalability, and high-performance transaction rates. Despite its well-understood benefits, IOTA nodes need to withstand considerable resource costs to generate the distributed ledger. The main reason for this is that IOTA abandons the original blockchain reward mechanism and does not charge transaction fees. Therefore, in this paper we address the cost optimization issue for IOTA based on Lyapunov optimization theory. We take the first step in investigating the cost optimization problem of IOTA and exploring a new optimization scheme using Lyapunov optimization theory. Our proposed scheme enables IOTA to minimize the total cost of IOTA nodes through a computational optimization algorithm. Then, an optimized transaction rate control algorithm can be designed based on the large deviation theory to reduce orphan tangles that waste computational costs. In addition, we define and deduce the effective width of the tangle to monitor the total throughput and reduce the time spent on cost optimization to avoid unnecessary waste of resources. Lastly, a comprehensive theoretical analysis and simulation experiments demonstrate that the proposed strategy is both efficient and practical. Full article
(This article belongs to the Special Issue Scalability, Sustainability and Security: Searching for New Blockchain Solutions)
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34 pages, 6961 KiB  
Article
S&SEM: A Secure and Speed-Up Election Mechanism for PoS-Based Blockchain Network
by Sana Naz, Mohsin Javaid Siddiqui and Scott Uk-Jin Lee
Mathematics 2024, 12(20), 3263; https://doi.org/10.3390/math12203263 - 17 Oct 2024
Viewed by 1115
Abstract
To be a stakeholder/validator/token holder is not so difficult in the Proof of Stake (POS)-based blockchain networks; that is why the number of validators is large in these networks. These validators play an essential part in the block creation process in the PoS-based [...] Read more.
To be a stakeholder/validator/token holder is not so difficult in the Proof of Stake (POS)-based blockchain networks; that is why the number of validators is large in these networks. These validators play an essential part in the block creation process in the PoS-based blockchain network. Due to the large validators, the block creation time and communication message broadcasting overhead get increased in the network. Many consensus algorithms use different techniques to reduce the number of validators, such as Delegated Proof of Stake (DPoS) consensus algorithms, which select the set of delegators via stake transactions for the block creation process. In this paper, we propose S&SEM, a secure and speed-up election process to select the ‘z’ number of validators/delegators. The presented election process is based on a traditional voting style with multiple numbers of rounds. The presented election mechanism reduces the possibility of malicious activity in the voting process by introducing a special vote message and a round that checks duplicate votes. We did horizontal scaling in the network to speed up the election process. We designed an improved incentive mechanism for the fairness of the election process. The designed reward and penalty procedure controls the nodes’ behaviors in the network. We simulate the S&SEM, and the result shows that the presented election process is faster and more secure to select delegators than the existing process used by DPOS. Full article
(This article belongs to the Special Issue Scalability, Sustainability and Security: Searching for New Blockchain Solutions)
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40 pages, 8764 KiB  
Article
Sea Shield: A Blockchain Technology Consensus to Improve Proof-of-Stake-Based Consensus Blockchain Safety
by Sana Naz and Scott Uk-Jin Lee
Mathematics 2024, 12(6), 833; https://doi.org/10.3390/math12060833 - 12 Mar 2024
Cited by 5 | Viewed by 1949
Abstract
In a blockchain network, a rule set called consensus mechanism is used to create and finalize a block. In a proof-of-stake (PoS), consensus-based blockchain network, nodes become validators, minters, or stakeholders’ nodes to complete the consensus mechanism. In these networks, when a node [...] Read more.
In a blockchain network, a rule set called consensus mechanism is used to create and finalize a block. In a proof-of-stake (PoS), consensus-based blockchain network, nodes become validators, minters, or stakeholders’ nodes to complete the consensus mechanism. In these networks, when a node becomes a validator node, its details need to be saved because the details of the validators are used in the network for many important decisions, such as selecting block proposers for the consensus process. In this paper, we present Sea Shield, which uses a validator chain to save a node’s information when it becomes a validator or leaves its responsibility as a validator in the PoS-based blockchain network. The validator chain is a blockchain that can run with the main chain of a PoS-based blockchain. The internal features of the validator chain are similar to those of the blockchain. We designed and simulated a consensus mechanism to create and finalize the block for the validator chain with no forks. We present a process by which a node may join or unjoin as a validator in a PoS-based blockchain network to improve the overall security of the main chain-consensus process. Full article
(This article belongs to the Special Issue Scalability, Sustainability and Security: Searching for New Blockchain Solutions)
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18 pages, 9293 KiB  
Article
Data-Driven Consensus Protocol Classification Using Machine Learning
by Marco Marcozzi, Ernestas Filatovas, Linas Stripinis and Remigijus Paulavičius
Mathematics 2024, 12(2), 221; https://doi.org/10.3390/math12020221 - 9 Jan 2024
Cited by 3 | Viewed by 1898
Abstract
The consensus protocol plays a vital role in the performance and security of a specific Distributed Ledger Technology (DLT) solution. Currently, the traditional classification of consensus algorithms relies on subjective criteria, such as protocol families (Proof of Work, Proof of Stake, etc.) or [...] Read more.
The consensus protocol plays a vital role in the performance and security of a specific Distributed Ledger Technology (DLT) solution. Currently, the traditional classification of consensus algorithms relies on subjective criteria, such as protocol families (Proof of Work, Proof of Stake, etc.) or other protocol features. However, such classifications often result in representatives with strongly different characteristics belonging to the same category. To address this challenge, a quantitative data-driven classification methodology that leverages machine learning—specifically, clustering—is introduced here to achieve unbiased grouping of analyzed consensus protocols implemented in various platforms. When different clustering techniques were used on the analyzed DLT dataset, an average consistency of 78% was achieved, while some instances exhibited a match of 100%, and the lowest consistency observed was 55%. Full article
(This article belongs to the Special Issue Scalability, Sustainability and Security: Searching for New Blockchain Solutions)
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17 pages, 1234 KiB  
Article
Addressing the Transaction Validation Issue in IOTA Tangle: A Tip Selection Algorithm Based on Time Division
by Yinfeng Chen, Yaofei Wang, Baojun Sun and Junxin Liu
Mathematics 2023, 11(19), 4116; https://doi.org/10.3390/math11194116 - 28 Sep 2023
Cited by 11 | Viewed by 2565
Abstract
IOTA is a new public chain system specifically designed for the Internet of Things (IoT), which provides strong support for the high concurrency, scalability, and zero handling fees of the IoT. The distributed ledger of IOTA, called the tangle, adopts a Directed Acyclic [...] Read more.
IOTA is a new public chain system specifically designed for the Internet of Things (IoT), which provides strong support for the high concurrency, scalability, and zero handling fees of the IoT. The distributed ledger of IOTA, called the tangle, adopts a Directed Acyclic Graph (DAG) structure. However, compared to the single-chain architecture, the tangle is more complex and highly vulnerable to security threats. The existing transaction verification methods still cannot simultaneously meet the need for accelerating approval speed and improving security to resist illegal transactions, such as lazy tips and permanent tips. In this work, we propose TDTS, a tip-selection algorithm based on time division to improve the efficiency of transaction verification. The main idea of the algorithm is to quickly determine two tips of an incoming transaction that need to be confirmed by sorting tip values in a time slot. It shortens the transaction verification time and reduces the number of lazy tips and permanent tips. A comprehensive theoretical analysis confirmed the effectiveness of our proposed algorithm. Based on 1000 IOTA nodes, the evaluations showed that TDTS can select tips quickly like URTS and resist lazy tips like MCMC. Full article
(This article belongs to the Special Issue Scalability, Sustainability and Security: Searching for New Blockchain Solutions)
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25 pages, 673 KiB  
Article
Enabling High-Quality Machine Learning Model Trading on Blockchain-Based Marketplace
by Chunxiao Li, Haodi Wang, Yu Zhao, Yuxin Xi, Enliang Xu and Shenling Wang
Mathematics 2023, 11(12), 2636; https://doi.org/10.3390/math11122636 - 9 Jun 2023
Cited by 3 | Viewed by 1798
Abstract
Machine learning model sharing markets have emerged as a popular platform for individuals and companies to share and access machine learning models. These markets enable more people to benefit from the field of artificial intelligence and to leverage its advantages on a broader [...] Read more.
Machine learning model sharing markets have emerged as a popular platform for individuals and companies to share and access machine learning models. These markets enable more people to benefit from the field of artificial intelligence and to leverage its advantages on a broader scale. However, these markets face challenges in designing effective incentives for model owners to share their models, and for model users to provide honest feedback on model quality. This paper proposes a novel game theoretic framework for machine learning model sharing markets that addresses these challenges. Our framework includes two main components: a mechanism for incentivizing model owners to share their models, and a mechanism for encouraging the honest evaluation of model quality by the model users. To evaluate the effectiveness of our framework, we conducted experiments and the results demonstrate that our mechanism for incentivizing model owners is effective at encouraging high-quality model sharing, and our reputation system encourages the honest evaluation of model quality. Full article
(This article belongs to the Special Issue Scalability, Sustainability and Security: Searching for New Blockchain Solutions)
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