Mathematics

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20 pages, 11976 KiB

Open AccessArticle

Synchronization of Chaotic Extremum-Coded Random Number Generators and Its Application to Segmented Image Encryption

by Shunsuke Araki, Ji-Han Wu and Jun-Juh Yan

Mathematics 2024, 12(19), 2983; https://doi.org/10.3390/math12192983 - 25 Sep 2024

Viewed by 558

This paper proposes a highly secure image encryption technique based on chaotic synchronization. Firstly, through the design of a synchronization controller, we ensure that the master–slave chaotic extremum-coded random number generators (ECRNGs) embedded in separated transmitters and receivers are fully synchronized to provide [...] Read more.

This paper proposes a highly secure image encryption technique based on chaotic synchronization. Firstly, through the design of a synchronization controller, we ensure that the master–slave chaotic extremum-coded random number generators (ECRNGs) embedded in separated transmitters and receivers are fully synchronized to provide synchronized dynamic random sequences for image encryption applications. Next, combining these synchronized chaotic sequences with the AES encryption algorithm, we propose an image segmentation and multi-encryption method to enhance the security of encrypted images and realize a secure image transmission system. Notably, in the design of the synchronization controller, the transient time before complete synchronization between the master and slave ECRNGs is effectively controlled by specifying the eigenvalues of the matrix in the synchronization error dynamics. Research results in this paper also show that complete synchronization of ECRNGs can be achieved within a single sampling time, which significantly contributes to the time efficiency of the image transmission system. As for the image encryption technique, we propose the method of image segmentation and use the synchronized dynamic random sequences generated by the ECRNGs to produce the keys and initialization vectors (IVs) required for AES-CBC image encryption, greatly enhancing the security of the encrypted images. To highlight the contribution of the proposed segmented image encryption, statistical analyses are conducted on the encrypted images, including histogram analysis (HA), information entropy (IE), correlation coefficient analysis (CCA), number of pixels change rate (NPCR), and unified average changing intensity (UACI), and compared with existing literature. The comparative results fully demonstrate that the proposed encryption method significantly enhances image encryption performance. Finally, under the network transmission control protocol (TCP), the synchronization of ECRNGs, dynamic keys, and IVs is implemented as well as segmented image encryption and transmission, and a highly secure image transmission system is realized to validate the practicality and feasibility of our design. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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17 pages, 690 KiB

Open AccessArticle

A Privacy-Preserving Electromagnetic-Spectrum-Sharing Trading Scheme Based on ABE and Blockchain

by Xing Pu, Ruixian Wang and Xin Lu

Mathematics 2024, 12(18), 2908; https://doi.org/10.3390/math12182908 - 18 Sep 2024

Viewed by 614

Abstract

The electromagnetic spectrum is a limited resource. With the widespread application of the electromagnetic spectrum in various fields, the contradiction between the demand for the electromagnetic spectrum and electromagnetic spectrum resources has become increasingly prominent. Spectrum sharing is an effective way to improve [...] Read more.

The electromagnetic spectrum is a limited resource. With the widespread application of the electromagnetic spectrum in various fields, the contradiction between the demand for the electromagnetic spectrum and electromagnetic spectrum resources has become increasingly prominent. Spectrum sharing is an effective way to improve the utilization of the electromagnetic spectrum. However, there are many challenges in existing distributed electromagnetic spectrum trading based on blockchain technology. Since a blockchain does not provide privacy protection, the risk of privacy leakage during the trading process makes electromagnetic spectrum owners unwilling to share. In addition, a blockchain only guarantees integrity, and the imperfect trading dispute resolution mechanism causes electromagnetic spectrum owners to be afraid to share. Therefore, we propose a privacy-preserving electromagnetic-spectrum-sharing trading scheme based on blockchain and ABE. The scheme not only designs an ABE fine-grained access control model in ciphertext form but also constructs a re-encryption algorithm that supports trading arbitration to achieve privacy protection for electromagnetic spectrum trading. Finally, we experimentally evaluated the efficiency of the proposed electromagnetic spectrum trading scheme. The experimental results show that the electromagnetic spectrum trading scheme we propose was highly efficient. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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20 pages, 1756 KiB

Open AccessArticle

Quantum Attacks on MIBS Block Cipher Based on Bernstein–Vazirani Algorithm

by Huiqin Xie, Zhangmei Zhao, Ke Wang, Yanjun Li and Hongcai Xin

Mathematics 2024, 12(17), 2678; https://doi.org/10.3390/math12172678 - 28 Aug 2024

Viewed by 813

Abstract

Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing [...] Read more.

Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing Grover’s algorithm and Bernstein–Vazirani algorithm. We first construct linear-structure functions based on the 5-round MIBS cipher according to the characteristics of the linear transformations, and then we obtain a quantum distinguisher of the 5-round MIBS cipher by applying Bernstein–Vazirani algorithm to the constructed functions. Finally, utilizing this distinguisher and Grover’s algorithm, we realize a 7-round key-recovery attack on the MIBS cipher, and then we expand the attack to more rounds of MIBS based on a similar idea. The quantum attack on the 7-round MIBS requires 156 qubits and has a time complexity of

2^{10.5}

. An 8-round attack requires 179 qubits and has a time complexity of

2^{22}

. Compared with existing quantum attacks, our attacks have better time complexity when attacking the same number of rounds. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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26 pages, 1279 KiB

Open AccessArticle

Quantum Automated Tools for Finding Impossible Differentials

by Huiqin Xie, Qiqing Xia, Ke Wang, Yanjun Li and Li Yang

Mathematics 2024, 12(16), 2598; https://doi.org/10.3390/math12162598 - 22 Aug 2024

Viewed by 650

Abstract

Due to the superiority of quantum computing, traditional cryptography is facing a severe threat. This makes the security evaluation of cryptographic systems in quantum attack models both significant and urgent. For symmetric ciphers, the security analysis heavily relies on cryptanalysis tools. Thus, exploring [...] Read more.

Due to the superiority of quantum computing, traditional cryptography is facing a severe threat. This makes the security evaluation of cryptographic systems in quantum attack models both significant and urgent. For symmetric ciphers, the security analysis heavily relies on cryptanalysis tools. Thus, exploring the use of quantum algorithms in traditional cryptanalysis tools has garnered considerable attention. In this study, we utilize quantum algorithms to improve impossible differential attacks and design two quantum automated tools to search for impossible differentials. The proposed quantum algorithms exploit the idea of miss-in-the-middle and the properties of truncated differentials. We rigorously prove their validity and calculate the quantum resources required for their implementation. Compared to the existing classical automated cryptanalysis, the proposed quantum tools have the advantage of accurately characterizing S-boxes while only requiring polynomial complexity, and can take into consideration the impact of the key schedules in a single-key model. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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24 pages, 6335 KiB

Open AccessArticle

A Dynamic Behavior Verification Method for Composite Smart Contracts Based on Model Checking

by Jun Jin, Wenhao Zhan, Haisheng Li, Yi Ding and Jie Li

Mathematics 2024, 12(15), 2431; https://doi.org/10.3390/math12152431 - 5 Aug 2024

Viewed by 732

Abstract

A composite smart contract can execute smart contracts that may belong to other owners or companies through external calls, bringing more security challenges to blockchain applications. Traditional static verification methods are inadequate for analyzing the dynamic execution of these contracts, resulting in misjudgment [...] Read more.

A composite smart contract can execute smart contracts that may belong to other owners or companies through external calls, bringing more security challenges to blockchain applications. Traditional static verification methods are inadequate for analyzing the dynamic execution of these contracts, resulting in misjudgment and omission issues. Therefore, this paper proposes a model checking approach based on dynamic behavior that verifies the security and business logic of composite smart contracts. Utilizing automata, the method models contracts, users, attackers, and extracts properties, focusing on six types of common security vulnerabilities. A thorough case study and experimental evaluation demonstrate the method’s efficiency in identifying vulnerabilities and ensuring alignment with business requirements. The UPPAAL tool is employed for comprehensive verification, proving its effectiveness in enhancing smart contract security. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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15 pages, 2670 KiB

Open AccessArticle

Research on Smart Contract Verification and Generation Method Based on BPMN

by Jun Jin, Le Yan, Yidan Zou, Jie Li and Zhen Yu

Mathematics 2024, 12(14), 2158; https://doi.org/10.3390/math12142158 - 10 Jul 2024

Viewed by 1078

Abstract

The post-deployment challenges in developing and upgrading blockchain smart contracts necessitate a high level of accuracy in their development and business logic. However, current methodologies for verifying the business logic of smart contracts frequently fail to address their alignment with end-user business requirements. [...] Read more.

The post-deployment challenges in developing and upgrading blockchain smart contracts necessitate a high level of accuracy in their development and business logic. However, current methodologies for verifying the business logic of smart contracts frequently fail to address their alignment with end-user business requirements. This paper introduces a two-step language transformation process to bridge this gap. Initially, we establish a transformation rule from the Business Process Model and Notation (BPMN) to Prolog, enabling the translation of business processes into a Prolog representation. This step not only validates the business process logic but also ensures it meets user specifications. Subsequently, we introduce a transformation rule from the BPMN to Go, which facilitates the transformation of the BPMN model, once validated, into a Go language smart contract. To enhance usability, we have engineered a dedicated tool that streamlines this transformation process. We present a case study involving a banking loan process to exemplify the utility of our tool in creating BPMN diagrams, conducting requirement and syntax validations, and effecting the transformation to Go smart contracts. The case study and empirical results suggest that our methodology and the accompanying tool mitigate the complexities inherent in smart contract development. They also ensure the fidelity of business logic to user demands, thereby promoting the broader adoption of blockchain smart contract technology. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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17 pages, 1358 KiB

Open AccessArticle

Adaptive Parallel Scheduling Scheme for Smart Contract

by Wenjin Yang, Meng Ao, Jing Sun, Guoan Wang, Yongxuan Li, Chunhai Li and Zhuguang Shao

Mathematics 2024, 12(9), 1347; https://doi.org/10.3390/math12091347 - 29 Apr 2024

Cited by 1 | Viewed by 1108

Abstract

With the increasing demand for decentralized systems and the widespread usage of blockchain, low throughput and high latency have become the biggest stumbling blocks in the development of blockchain systems. This problem seriously hinders the expansion of blockchain and its application in production. [...] Read more.

With the increasing demand for decentralized systems and the widespread usage of blockchain, low throughput and high latency have become the biggest stumbling blocks in the development of blockchain systems. This problem seriously hinders the expansion of blockchain and its application in production. Most existing smart contract scheduling solutions use static feature analysis to prevent contract conflicts during parallel execution. However, the conflicts between transactions are complex; static feature analysis is not accurate enough. In this paper, we first build the dependency between smart contracts by analyzing the features. After numerous experiments, we propose a conflict model to adjust the relationship between threads and conflict to achieve high throughput and low latency. Based on these works, we propose adaptive parallel scheduling for smart contracts on the blockchain. Our adaptive parallel scheduling can distinguish conflicts between smart contracts and dynamically adjust the execution strategy of smart contracts based on the conflict factors we define. We implement our scheme on ChainMaker, one of the most popular open-source permissioned blockchains, and build experiments to verify our solution. Regarding latency, our solution demonstrates remarkable efficiency compared with the fully parallel scheme, particularly in high-conflict transaction scenarios, where our solution achieves latency levels just one-twentieth of the fully parallel scheme. Regarding throughput, our solution significantly outperforms the fully parallel scheme, achieving 30 times higher throughput in high-conflict transaction scenarios. These results highlight the superior performance and effectiveness of our solution in addressing latency and throughput challenges, particularly in environments with high transaction conflicts. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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14 pages, 631 KiB

Open AccessArticle

BNS: A Detection System to Find Nodes in the Bitcoin Network

by Ruiguang Li, Liehuang Zhu, Chao Li, Fudong Wu and Dawei Xu

Mathematics 2023, 11(24), 4885; https://doi.org/10.3390/math11244885 - 6 Dec 2023

Viewed by 1777

Abstract

Bitcoin was launched over a decade ago and has made an increasing impact on the world’s financial order, which has attracted the attention of researchers all over the world. The Bitcoin system runs on a dynamic P2P network, containing tens of thousands of [...] Read more.

Bitcoin was launched over a decade ago and has made an increasing impact on the world’s financial order, which has attracted the attention of researchers all over the world. The Bitcoin system runs on a dynamic P2P network, containing tens of thousands of nodes, including reachable nodes and unreachable nodes. In this article, a detection system, BNS (Bitcoin Network Sniffer), which could collect as many Bitcoin nodes as possible is proposed. For reachable nodes, the authors designed an algorithm, BRF (Bitcoin Reachable-Nodes Finding), based on node activity evaluation which reduces the nodes to be detected and greatly shortens the detection time. For unreachable nodes, the authors trained a decision tree model, BUF (Bitcoin Unreachable-Nodes Finding), to identify unreachable nodes based on attribute features from a large number of node addresses. Experiments showed that BNS discovered an average of 1093 more reachable nodes (6.4%) and 662 more unreachable nodes (2.3%) than the well-known website “Bitnodes” per day. It showed better performance in total nodes and efficiency. Based on the experimental results, the authors analyzed the real network size, node “churn”, and geographical distribution. Full article

(This article belongs to the Special Issue New Advances in Coding Theory and Cryptography, 2nd Edition)

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