Next Article in Journal
Security and Accuracy of Fingerprint-Based Biometrics: A Review
Previous Article in Journal
An Approach toward a Q-Neutrosophic Soft Set and Its Application in Decision Making
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Symmetry 2019, 11(2), 140;

A Novel Method to Identify Initial Values of Chaotic Maps in Cybersecurity

Department of Electrical Engineering, HITEC University, Taxila 47080, Pakistan
Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
Author to whom correspondence should be addressed.
Received: 11 November 2018 / Revised: 10 January 2019 / Accepted: 15 January 2019 / Published: 27 January 2019
Full-Text   |   PDF [2632 KB, uploaded 30 January 2019]   |  


Chaos theory has applications in several disciplines and is focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaotic dynamics are the impromptu behavior displayed by some nonlinear dynamical frameworks and have been used as a source of diffusion in cybersecurity for more than two decades. With the addition of chaos, the overall strength of communication security systems can be increased, as seen in recent proposals. However, there is a major drawback of using chaos in communication security systems. Chaotic communication security systems rely on private keys, which are the initial values and parameters of chaotic systems. This paper shows that these chaotic communication security systems can be broken by identifying those initial values through the statistical analysis of standard deviation and variance. The proposed analyses are done on the chaotic sequences of Lorenz chaotic system and Logistic chaotic map and show that the initial values and parameters, which serve as security keys, can be retrieved and broken in short computer times. Furthermore, the proposed model of identifying the initial values can also be applied on other chaotic maps as well. View Full-Text
Keywords: Chaos; cryptography; standard deviation; Lorenz system; Logistic map Chaos; cryptography; standard deviation; Lorenz system; Logistic map

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Anees, A.; Hussain, I. A Novel Method to Identify Initial Values of Chaotic Maps in Cybersecurity. Symmetry 2019, 11, 140.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top