Mathematical Methods and Models in Information Security with Applications

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

Deadline for manuscript submissions: 31 March 2026 | Viewed by 583

Special Issue Editors

1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541002, China
2. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541002, China
3. Center for Applied Mathematics of Guangxi (GUET), Guilin 541002, China
Interests: Interests: fractals and chaos; chaotic system design; memristors; image–audio encryption algorithms; chaotic circuit design
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Guest Editor
School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
Interests: meta learning; artificial intelligence; deep learning

Special Issue Information

Dear Colleagues,

In the rapidly evolving digital world, the importance of information security and machine learning cannot be overstated. Using mathematical models in machine learning within this domain is pivotal in enhancing data protection, ensuring secure communication channels, and thwarting cyber attacks. Mathematical models provide a rigorous framework for analyzing security algorithms, assessing vulnerabilities, and quantifying the degree of security. Moreover, the integration of mathematical models ensures that security systems possess desired properties such as confidentiality, authenticity, and non-repudiation. This Special Issue aims to explore innovative methodologies, fundamental theories, and practical applications that address evolving challenges in security and machine learning, offering new insights into the ways in which mathematical models can be applied to enhance the security and resilience of systems.

The scope of this Special Issue encompasses a wide range of topics related to mathematical models in information security and machine learning. Research areas may include (but are not limited to) the following:

  • Mathematical foundations of machine learning in information security;
  • Security protocols and algorithms based on machine learning with mathematical optimization;
  • Secure multiparty computation incorporating machine learning techniques and mathematical models;
  • Post-quantum cryptography and machine learning with mathematical theories;
  • Cryptanalysis and attacks using machine learning methods supported by mathematical analysis;
  • Privacy-enhancing technologies powered by machine learning and mathematical cryptography;
  • Authentication and anonymity protocols incorporating machine learning and mathematical models;
  • Security and privacy in federated learning, crowdsourcing, and cloud computing using machine learning approaches with mathematical foundations;
  • Security considerations in emerging technologies such as IoT and blockchain enhanced by machine learning and mathematical models.

Dr. Guodong Li
Dr. Maofa Wang
Guest Editors

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Keywords

  • information security
  • machine learning
  • mathematical models
  • security and privacy
  • privacy-enhancing technologies

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Published Papers (2 papers)

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Research

22 pages, 492 KiB  
Article
Identification of a Time-Dependent Source Term in Multi-Term Time–Space Fractional Diffusion Equations
by Yushan Li, Yuxuan Yang and Nanbo Chen
Mathematics 2025, 13(13), 2123; https://doi.org/10.3390/math13132123 (registering DOI) - 28 Jun 2025
Abstract
This paper investigates the inverse problem of identifying a time-dependent source term in multi-term time–space fractional diffusion Equations (TSFDE). First, we rigorously establish the existence and uniqueness of strong solutions for the associated direct problem under homogeneous Dirichlet boundary conditions. A novel implicit [...] Read more.
This paper investigates the inverse problem of identifying a time-dependent source term in multi-term time–space fractional diffusion Equations (TSFDE). First, we rigorously establish the existence and uniqueness of strong solutions for the associated direct problem under homogeneous Dirichlet boundary conditions. A novel implicit finite difference scheme incorporating matrix transfer technique is developed for solving the initial-boundary value problem numerically. Regarding the inverse problem, we prove the solution uniqueness and stability estimates based on interior measurement data. The source identification problem is reformulated as a variational problem using the Tikhonov regularization method, and an approximate solution to the inverse problem is obtained with the aid of the optimal perturbation algorithm. Extensive numerical simulations involving six test cases in both 1D and 2D configurations demonstrate the high effectiveness and satisfactory stability of the proposed methodology. Full article
37 pages, 6550 KiB  
Article
Multiphase Transport Network Optimization: Mathematical Framework Integrating Resilience Quantification and Dynamic Algorithm Coupling
by Linghao Ren, Xinyue Li, Renjie Song, Yuning Wang, Meiyun Gui and Bo Tang
Mathematics 2025, 13(13), 2061; https://doi.org/10.3390/math13132061 - 21 Jun 2025
Viewed by 163
Abstract
This study proposes a multi-dimensional urban transportation network optimization framework (MTNO-RQDC) to address structural failure risks from aging infrastructure and regional connectivity bottlenecks. Through dual-dataset validation using both the Baltimore road network and PeMS07 traffic flow data, we first develop a traffic simulation [...] Read more.
This study proposes a multi-dimensional urban transportation network optimization framework (MTNO-RQDC) to address structural failure risks from aging infrastructure and regional connectivity bottlenecks. Through dual-dataset validation using both the Baltimore road network and PeMS07 traffic flow data, we first develop a traffic simulation model integrating Dijkstra’s algorithm with capacity-constrained allocation strategies for guiding reconstruction planning for the collapsed Francis Scott Key Bridge. Next, we create a dynamic adaptive public transit optimization model using an entropy weight-TOPSIS decision framework coupled with an improved simulated annealing algorithm (ISA-TS), achieving coordinated suburban–urban network optimization while maintaining 92.3% solution stability under simulated node failure conditions. The framework introduces three key innovations: (1) a dual-layer regional division model combining K-means geographical partitioning with spectral clustering functional zoning; (2) fault-tolerant network topology optimization demonstrated through 1000-epoch Monte Carlo failure simulations; (3) cross-dataset transferability validation showing 15.7% performance variance between Baltimore and PeMS07 environments. Experimental results demonstrate a 28.7% reduction in road network traffic variance (from 42,760 to 32,100), 22.4% improvement in public transit path redundancy, and 30.4–44.6% decrease in regional traffic load variance with minimal costs. Hyperparameter analysis reveals two optimal operational modes: rapid cooling (rate = 0.90) achieves 85% improvement within 50 epochs for emergency response, while slow cooling (rate = 0.99) yields 12.7% superior solutions for long-term planning. The framework establishes a new multi-objective paradigm balancing structural resilience, functional connectivity, and computational robustness for sustainable smart city transportation systems. Full article
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