Construction of Non-linear Component of Block Cipher by Means of Chaotic Dynamical System and Symmetric Group

  • Adnan JaveedEmail author
  • Tariq Shah
  • Atta Ullah


The interesting features of chaos theory are utilized now a day’s in information security. The simplest chaotic dynamical system is the double pendulum. Here in this article, two double pendulums are used to enhance the chaotic behavior of a dynamical system. This system is sensitive to initial conditions and bears complex and chaotic trajectory. Moreover, being multi dimensional system it endures grander solution space for the generation of large number of S-boxes. Furthermore, a permutation comprising on only two cycles of symmetric group of order 256 is applied to generate integer values for the construction of desired substitution box. The algebraic analysis of suggested S-box emphasis on its application, thereafter, an image is encrypted with the help of this S-box, whose statistical analysis validates its efficacy.


Chaotic dynamical system Symmetric group Substitution box (S-box) Image encryption 


Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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