Special Issue "Mathematical Models in Security, Defense, Cyber Security and Cyber Defense"

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

Deadline for manuscript submissions: closed (31 October 2020) | Viewed by 14457

Special Issue Editor

Dr. Angel Martín-del-Rey
E-Mail Website
Guest Editor
Institute of Fundamental Physics and Mathematics, Department of Applied Mathematics, University of Salamanca, 37008 Salamanca, Spain
Interests: cryptography; mathematical modeling; wireless sensor network security
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The role of mathematical modeling in theoretical and applied scientific development is crucial. This discipline covers almost all areas of knowledge, providing models that simulate different phenomena and behaviors of all types. Nowadays, one of the most important problems that our society is facing is to guarantee the security of citizens and infrastructures against intentional or non-intentional threats. This refers not only to physical assets but also to those of logical nature.

The main goal of this Special Issue is to gather high-quality research papers and reviews focused on the design, analysis, and development of mathematical models with applications in the field of security, defense, cyber security, and cyber defense. Specifically, this Special Issue will cover different perspectives on these and related potential topics:

  • Mathematical modeling in security and defense.
  • Mathematical modeling in cyber security and cyber defense.
  • Complex networks analysis in security and defense.
  • Complex network analysis applied to cyber security.
  • Mathematical modeling of biological agents and malware propagation.
  • Mathematical models for critical infrastructure protection.
  • Theoretical and applied cryptography.

Prof. Angel Martin del Rey
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 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

  • Mathematical modeling
  • Complex networks
  • Security and cyber security
  • Defense and cyber defense
  • Cryptography

Published Papers (10 papers)

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Research

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Article
Propagation of the Malware Used in APTs Based on Dynamic Bayesian Networks
Mathematics 2021, 9(23), 3097; https://doi.org/10.3390/math9233097 - 30 Nov 2021
Cited by 1 | Viewed by 500
Abstract
Malware is becoming more and more sophisticated these days. Currently, the aim of some special specimens of malware is not to infect the largest number of devices as possible, but to reach a set of concrete devices (target devices). This type of malware [...] Read more.
Malware is becoming more and more sophisticated these days. Currently, the aim of some special specimens of malware is not to infect the largest number of devices as possible, but to reach a set of concrete devices (target devices). This type of malware is usually employed in association with advanced persistent threat (APT) campaigns. Although the great majority of scientific studies are devoted to the design of efficient algorithms to detect this kind of threat, the knowledge about its propagation is also interesting. In this article, a new stochastic computational model to simulate its propagation is proposed based on Bayesian networks. This model considers two characteristics of the devices: having efficient countermeasures, and the number of infectious devices in the neighborhood. Moreover, it takes into account four states: susceptible devices, damaged devices, infectious devices and recovered devices. In this way, the dynamic of the model is SIDR (susceptible–infectious–damaged–recovered). Contrary to what happens with global models, the proposed model takes into account both the individual characteristics of devices and the contact topology. Furthermore, the dynamics is governed by means of a (practically) unexplored technique in this field: Bayesian networks. Full article
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Article
Perspectives on Adversarial Classification
Mathematics 2020, 8(11), 1957; https://doi.org/10.3390/math8111957 - 05 Nov 2020
Cited by 1 | Viewed by 727
Abstract
Adversarial classification (AC) is a major subfield within the increasingly important domain of adversarial machine learning (AML). So far, most approaches to AC have followed a classical game-theoretic framework. This requires unrealistic common knowledge conditions untenable in the security settings typical of the [...] Read more.
Adversarial classification (AC) is a major subfield within the increasingly important domain of adversarial machine learning (AML). So far, most approaches to AC have followed a classical game-theoretic framework. This requires unrealistic common knowledge conditions untenable in the security settings typical of the AML realm. After reviewing such approaches, we present alternative perspectives on AC based on adversarial risk analysis. Full article
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Article
Privacy Preservation in Edge Consumer Electronics by Combining Anomaly Detection with Dynamic Attribute-Based Re-Encryption
Mathematics 2020, 8(11), 1871; https://doi.org/10.3390/math8111871 - 29 Oct 2020
Cited by 2 | Viewed by 989
Abstract
The expanding utilization of edge consumer electronic (ECE) components and other innovations allows medical devices to communicate with one another to distribute sensitive clinical information. This information is used by health care authorities, specialists and emergency clinics to offer enhanced medication and help. [...] Read more.
The expanding utilization of edge consumer electronic (ECE) components and other innovations allows medical devices to communicate with one another to distribute sensitive clinical information. This information is used by health care authorities, specialists and emergency clinics to offer enhanced medication and help. The security of client data is a major concern, since modification of data by hackers can be life-threatening. Therefore, we have developed a privacy preservation approach to protect the wearable sensor data gathered from wearable medical devices by means of an anomaly detection strategy using artificial intelligence combined with a novel dynamic attribute-based re-encryption (DABRE) method. Anomaly detection is accomplished through a modified artificial neural network (MANN) based on a gray wolf optimization (GWO) technique, where the training speed and classification accuracy are improved. Once the anomaly data are removed, the data are stored in the cloud, secured through the proposed DABRE approach for future use by doctors. Furthermore, in the proposed DABRE method, the biometric attributes, chosen dynamically, are considered for encryption. Moreover, if the user wishes, the data can be modified to be unrecoverable by re-encryption with the true attributes in the cloud. A detailed experimental analysis takes place to verify the superior performance of the proposed method. From the experimental results, it is evident that the proposed GWO–MANN model attained a maximum average detection rate (DR) of 95.818% and an accuracy of 95.092%. In addition, the DABRE method required a minimum average encryption time of 95.63 s and a decryption time of 108.7 s, respectively. Full article
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Article
Secret Sharing, Zero Sum Sets, and Hamming Codes
Mathematics 2020, 8(10), 1644; https://doi.org/10.3390/math8101644 - 23 Sep 2020
Cited by 1 | Viewed by 678
Abstract
A (t,n)-secret sharing scheme is a method of distribution of information among n participants such that any t>1 of them can reconstruct the secret but any t1 cannot. A ramp secret sharing scheme is [...] Read more.
A (t,n)-secret sharing scheme is a method of distribution of information among n participants such that any t>1 of them can reconstruct the secret but any t1 cannot. A ramp secret sharing scheme is a relaxation of that protocol that allows that some (t1)-coalitions could reconstruct the secret. In this work, we explore some ramp secret sharing schemes based on quotients of polynomial rings. The security analysis depends on the distribution of zero-sum sets in abelian groups. We characterize all finite commutative rings for which the sum of all elements is zero, a result of independent interest. When the quotient is a finite field, we are led to study the weight distribution of a coset of shortened Hamming codes. Full article
Article
On the Optimal Control of a Malware Propagation Model
Mathematics 2020, 8(9), 1518; https://doi.org/10.3390/math8091518 - 05 Sep 2020
Cited by 1 | Viewed by 946
Abstract
An important way considered to control malware epidemic processes is to take into account security measures that are associated to the systems of ordinary differential equations that governs the dynamics of such systems. We can observe two types of control measures: the analysis [...] Read more.
An important way considered to control malware epidemic processes is to take into account security measures that are associated to the systems of ordinary differential equations that governs the dynamics of such systems. We can observe two types of control measures: the analysis of the basic reproductive number and the study of control measure functions. The first one is taken at the beginning of the epidemic process and, therefore, we can consider this to be a prevention measure. The second one is taken during the epidemic process. In this work, we use the theory of optimal control that is associated to systems of ordinary equations in order to find a new function to control malware epidemic through time. Specifically, this approach is evaluate on a particular compartmental malware model that considers carrier devices. Full article
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Article
Lanchester Models for Irregular Warfare
Mathematics 2020, 8(5), 737; https://doi.org/10.3390/math8050737 - 07 May 2020
Cited by 3 | Viewed by 1401
Abstract
Military operations research and combat modeling apply mathematical models to analyze a variety of military conflicts and obtain insights about these phenomena. One of the earliest and most important set of models used for combat modeling is the Lanchester equations. Legacy Lanchester equations [...] Read more.
Military operations research and combat modeling apply mathematical models to analyze a variety of military conflicts and obtain insights about these phenomena. One of the earliest and most important set of models used for combat modeling is the Lanchester equations. Legacy Lanchester equations model the mutual attritional dynamics of two opposing military forces and provide some insights regarding the fate of such engagements. In this paper, we review recent developments in Lanchester modeling, focusing on contemporary conflicts in the world. Specifically, we present models that capture irregular warfare, such as insurgencies, highlight the role of target information in such conflicts, and capture multilateral situations where several players are involved in the conflict (such as the current war in Syria). Full article
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Article
FastText-Based Local Feature Visualization Algorithm for Merged Image-Based Malware Classification Framework for Cyber Security and Cyber Defense
Mathematics 2020, 8(3), 460; https://doi.org/10.3390/math8030460 - 24 Mar 2020
Cited by 10 | Viewed by 1805
Abstract
The importance of cybersecurity has recently been increasing. A malware coder writes malware into normal executable files. A computer is more likely to be infected by malware when users have easy access to various executables. Malware is considered as the starting point for [...] Read more.
The importance of cybersecurity has recently been increasing. A malware coder writes malware into normal executable files. A computer is more likely to be infected by malware when users have easy access to various executables. Malware is considered as the starting point for cyber-attacks; thus, the timely detection, classification and blocking of malware are important. Malware visualization is a method for detecting or classifying malware. A global image is visualized through binaries extracted from malware. The overall structure and behavior of malware are considered when global images are utilized. However, the visualization of obfuscated malware is tough, owing to the difficulties encountered when extracting local features. This paper proposes a merged image-based malware classification framework that includes local feature visualization, global image-based local feature visualization, and global and local image merging methods. This study introduces a fastText-based local feature visualization method: First, local features such as opcodes and API function names are extracted from the malware; second, important local features in each malware family are selected via the term frequency inverse document frequency algorithm; third, the fastText model embeds the selected local features; finally, the embedded local features are visualized through a normalization process. Malware classification based on the proposed method using the Microsoft Malware Classification Challenge dataset was experimentally verified. The accuracy of the proposed method was approximately 99.65%, which is 2.18% higher than that of another contemporary global image-based approach. Full article
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Article
A New Individual-Based Model to Simulate Malware Propagation in Wireless Sensor Networks
Mathematics 2020, 8(3), 410; https://doi.org/10.3390/math8030410 - 13 Mar 2020
Cited by 13 | Viewed by 1462
Abstract
Wireless Sensor Networks (WSNs) are a set of sensor devices deployed in a given area that form a network without a pre-established architecture. Recently, malware has increased as a potential vulnerability for the Internet of Things, and consequently for these networks. The spread [...] Read more.
Wireless Sensor Networks (WSNs) are a set of sensor devices deployed in a given area that form a network without a pre-established architecture. Recently, malware has increased as a potential vulnerability for the Internet of Things, and consequently for these networks. The spread of malware on wireless sensor networks has been studied from different perspectives, excluding individual characteristics in most of the models proposed. The primary goal of this work is to introduce an Agent-Based Model for analysing malware propagation on these networks, and its agents, coefficients and transition rules are detailed. Finally, some simulations of the proposed model are included. Full article
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Article
Applying Undesirable Output Model to Security Evaluation of Taiwan
Mathematics 2019, 7(11), 1023; https://doi.org/10.3390/math7111023 - 29 Oct 2019
Cited by 3 | Viewed by 1187
Abstract
The requirements and demand for personal security and public order have increased under great pressure from economic growth and society. This research applied the undesirable output model, which is a mathematical model, to measure the efficiencies of the security department in Taiwan. Further [...] Read more.
The requirements and demand for personal security and public order have increased under great pressure from economic growth and society. This research applied the undesirable output model, which is a mathematical model, to measure the efficiencies of the security department in Taiwan. Further analysis has considered the efficient frontier to classify the efficiency of all 22 counties/cities in Taiwan in 2016, towards a sustainable security environment. The result of this research shown some cities have performed excellent efficiency in the security problem. According to analysis, the efficiency can be improved by decreasing excesses in inputs and bad outputs. This research has evaluated the police departments in Taiwan comprehensively and differentiated the efficiency in safety management of all police departments in Taiwan. Full article
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Review

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Review
Analysis of the Cryptographic Tools for Blockchain and Bitcoin
Mathematics 2020, 8(1), 131; https://doi.org/10.3390/math8010131 - 15 Jan 2020
Cited by 9 | Viewed by 3525
Abstract
Blockchain is one of the most interesting emerging technologies nowadays, with applications ranging from cryptocurrencies to smart contracts. This paper presents a review of the cryptographic tools necessary to understand the fundamentals of this technology and the foundations of its security. Among other [...] Read more.
Blockchain is one of the most interesting emerging technologies nowadays, with applications ranging from cryptocurrencies to smart contracts. This paper presents a review of the cryptographic tools necessary to understand the fundamentals of this technology and the foundations of its security. Among other elements, hash functions, digital signatures, elliptic curves, and Merkle trees are reviewed in the scope of their usage as building blocks of this technology. Full article
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