A Novel Hybrid Secure Image Encryption Based on Julia Set of Fractals and 3D Lorenz Chaotic Map

Fawad Masood, Ahmad Jawad, Syed Shah, Sajjad Shaukat Jamal , Iqtadar Hussain

Research output: Contribution to journalArticlepeer-review

103 Citations (Scopus)
230 Downloads (Pure)


Chaos-based encryption schemes have attracted many researchers around the world in the digital image security domain. Digital images can be secured using existing chaotic maps, multiple chaotic maps, and several other hybrid dynamic systems that enhance the non-linearity of digital images. The combined property of confusion and diffusion was introduced by Claude Shannon which can be employed for digital image security. In this paper, we proposed a novel system that is computationally less expensive and provided a higher level of security. The system is based on a shuffing process with fractals key along with three-dimensional Lorenz chaotic map. The shuffing process added the confusion property and the pixels of the standard image is shuffed. Three-dimensional Lorenz chaotic map is used for a diffusion process which distorted all pixels of the image. In the statistical security test, means square error (MSE) evaluated error value was greater than the average value of 10000 for all standard images. The value of peak signal to noise (PSNR) was 7.69(dB) for the test image. Moreover, the calculated correlation coefficient values for each direction of the encrypted images was less than zero with a number of pixel change rate (NPCR) higher than 99%. During the security test, the entropy values were more than 7.9 for each grey channel which is almost equal to the ideal value of 8 for an 8-bit system. Numerous security tests and low computational complexity tests validate the security, robustness, and real-time implementation of the presented scheme.

Original languageEnglish
Article number274
Number of pages28
Issue number3
Publication statusPublished - 28 Feb 2020
Externally publishedYes

Bibliographical note

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.


  • Chaotic maps
  • Confusion
  • Diffusion
  • Fractals
  • Hybrid dynamical system
  • Lorenz chaotic maps
  • Non-linearity
  • Shuffling

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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