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Mathematics
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Chaos Based Computer Security and Functions
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Chaos Based Computer Security and Functions

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 August 2021) | Viewed by 7531

Special Issue Editor

Prof. Dr. Borislav Stoyanov

E-Mail Website
Guest Editor
Department of Computer Informatics, Faculty of Mathematics and Informatics, Konstantin Preslavsky University of Shumen, 9712 Shumen, Bulgaria
Interests: chaos-based cryptography; image encryption; steganographic schemes; pseudorandom generators
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the last few decades, there has been a fast progress in chaos theory. Chaotic systems have been wide-learned and used in diverse fields by mathematicians, computer scientists, engineers, and physicists. 

Chaotic systems possess sensitive dependence to initial conditions, topological transitivity, and dense periodic orbits. Based on these important properties, recent developments include studying chaotic behavior, applying chaos theory to security, and designing a new family of functions that generate chaos. 

This Special Issue is devoted to high-quality mathematical papers in the area of chaos-based computer security and chaos-based systems, algorithms, and functions. 

Topics may include but are not limited to the following:

  • Integration of chaos in computer security schemes
  • Chaos-based cryptography and cryptanalysis
  • New family of functions that generate chaos
  • Chaotic functions in biology, medicine, and chemistry
  • Chaos based algorithms
  • Chaos in computational and applied mathematics 

Prof. Dr. Borislav Stoyanov
Guest Editor

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

  • Chaos
  • Chaotic systems
  • Chaotic synchronization
  • Chaotic cryptography schemes
  • Pseudorandom generators

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Published Papers (3 papers)

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Research

16 pages, 18461 KiB  
Article
Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map
by Lazaros Moysis, Karthikeyan Rajagopal, Aleksandra V. Tutueva, Christos Volos, Beteley Teka and Denis N. Butusov
Mathematics 2021, 9(15), 1821; https://doi.org/10.3390/math9151821 - 2 Aug 2021
Cited by 13 | Viewed by 2330
Abstract
This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of [...] Read more.
This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves. Full article
(This article belongs to the Special Issue Chaos Based Computer Security and Functions)
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22 pages, 2679 KiB  
Article
An Extended Chaotic Map-Based Authentication and Key Agreement Scheme for Multi-Server Environment
by Yicheng Yu, Oliver Taylor, Rui Li and Baiho Sunagawa
Mathematics 2021, 9(8), 798; https://doi.org/10.3390/math9080798 - 7 Apr 2021
Cited by 9 | Viewed by 2194
Abstract
With the increasing number of users and the emergence of different types of network services, a multi-server architecture has emerged in recent years. In order to ensure the secure communication of Internet participants in an open network environment, the authentication and key agreement [...] Read more.
With the increasing number of users and the emergence of different types of network services, a multi-server architecture has emerged in recent years. In order to ensure the secure communication of Internet participants in an open network environment, the authentication and key agreement protocol for multi-server architectures were proposed in the past. In 2018, Chatterjee et al. put forward a lightweight three-factor authentication and key agreement protocol for a multi-server environment, and they claimed that all known security features with satisfactory performance could be realized in their protocol. However, it is found that their scheme is vulnerable to user impersonation attacks and cannot achieve user un-traceability and three-factor security through our cryptanalysis. In order to solve these shortcomings, we propose a new lightweight and anonymous three-factor authentication scheme for the multi-server environment in this article. Furthermore, the proposed protocol is proved to be AKE secure theoretically, and we use BAN-logic to prove that our protocol realizes mutual authentication between communication participants. Finally, we show that our proposed scheme is practical and efficient through the comparison of security features and performance. Full article
(This article belongs to the Special Issue Chaos Based Computer Security and Functions)
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17 pages, 3044 KiB  
Article
Dynamics of Rössler Prototype-4 System: Analytical and Numerical Investigation
by Svetoslav G. Nikolov and Vassil M. Vassilev
Mathematics 2021, 9(4), 352; https://doi.org/10.3390/math9040352 - 10 Feb 2021
Cited by 2 | Viewed by 2121
Abstract
In this paper, the dynamics of a 3D autonomous dissipative nonlinear system of ODEs-Rössler prototype-4 system, was investigated. Using Lyapunov-Andronov theory, we obtain a new analytical formula for the first Lyapunov’s (focal) value at the boundary of stability of the corresponding equilibrium state. [...] Read more.
In this paper, the dynamics of a 3D autonomous dissipative nonlinear system of ODEs-Rössler prototype-4 system, was investigated. Using Lyapunov-Andronov theory, we obtain a new analytical formula for the first Lyapunov’s (focal) value at the boundary of stability of the corresponding equilibrium state. On the other hand, the global analysis reveals that the system may exhibit the phenomena of Shilnikov chaos. Further, it is shown via analytical calculations that the considered system can be presented in the form of a linear oscillator with one nonlinear automatic regulator. Finally, it is found that for some new combinations of parameters, the system demonstrates chaotic behavior and transition from chaos to regular behavior is realized through inverse period-doubling bifurcations. Full article
(This article belongs to the Special Issue Chaos Based Computer Security and Functions)
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