Skip to main content
SpringerLink
Log in

A Novel Statistical Analysis of Chaotic S-box in Image Encryption

  • 3DR Express
  • Published:
3D Research

Abstract

The S-box is utilized within different block ciphers and the complexity of encryption basically relies on the quality of S-box. The quality of S-box could be measured by breaking down its statistical properties. The S-box is the main non-linear component in different block ciphers fit for creating confusion. Numerous S-boxes have been proposed with comparative algebraic and statistical properties. Thusly, it is off and on again hard to pick S-box for a specific application. The performances of these S-boxes vary and rely on the way of information and their applications. In this paper; we have proposed a novel chaotic S-box by applying affine transformation to study their strengths in order to determine their suitability in image encryption. The proposed chaotic S-box is tested for different criterion such mean squared error, root mean squared error, mean absolute error, peak signal to noise ratio, signal-to-noise ratio, universal image quality index and enhancement error. The results of these analyses are further examined and are used to determine the appropriateness of S-box to image encryption applications.

Graphical Abstract

a–b Lena plain color image, Lena color encrypted image

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Abuelyman, E. S., & Alsehibani, A. A. S. (2008). An optimized implementation of the S-Box using residue of prime numbers. International Journal of Computer Science and Network Security, 8(4), 304–309.

    Google Scholar 

  2. Avcibas, I., Memon, N., & Sankur, B. (2003). Steganalysis using image quality metrics. IEEE Transactions on Image Processing, 12(2), 221–229.

    Article  MathSciNet  Google Scholar 

  3. Alam, G. M., Mat Kiah, M. L., Zaidan, B. B., Zaidan, A. A., & Alanazi, H. O. (2010). Using the features of mosaic image and AES cryptosystem to implement an extremely high rate and high secure data hidden: Analytical study. International Journal of Physical Sciences, 5(21), 3254–3260.

    Google Scholar 

  4. Cui, L., & Cao, Y. (2007). A new S-box structure named affine-power-affine. International Journal of Innovative Computing, Information and Control, 3(3), 45–53.

    Google Scholar 

  5. Chen, S. Y., Lin, W. C., & Chen, C. T. (1991). Split and merge image segmentation based on localized feature analysis and statistical tests. CVGIP: Graphical Models and Image Processing, 53(5), 457–475.

    Google Scholar 

  6. Daemen, J., & Rijmen, V. (1999). AES proposal: Rijndael. AES algorithm submission. http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended.pdf.

  7. Enayatifar, R. (2011). Image encryption via logistic map function and heap tree. International Journal of Physical Sciences, 6(2), 221–228.

    Google Scholar 

  8. Wang, F., Bai, S., Zhu, G., & Song, Z. (2009). An image encryption algorithm based on n-dimension affine transformation. In: ACIS-ICIS (pp. 579–585). IEEE Computer Society.

  9. Bai, S., & Cao, C. (2003). Property of sub-affine transformation and its application. Journal of Computer Aided Design and Computer Graphics, 15(2), 205–208. (in Chinese).

    Google Scholar 

  10. Areed, N. F. F., & Obayya, S. S. A. (2012). Novel design of symmetric photonic bandgap based image encryption system. Progress in Electromagnetics Research C, 30, 225–239.

    Article  Google Scholar 

  11. Grigoryan, A. M., & Grigoryan, M. (2009). Brief notes in advanced DSP: Fourier analysis with MATLAB. CRC Press, 30 Aug 2009.

  12. Gadelmawla, E. S. (2004). A vision system for surface roughness characterization using the gray level co-occurrence matrix. NDT and E International, 37(7), 577–588.

    Article  Google Scholar 

  13. Hussain, I., Shah, T., & Mehmood, H. (2010). A new algorithm to construct secure keys for AES. International Journal of Contemporary Mathematical Sciences, 5(26), 1263–1270.

    MathSciNet  MATH  Google Scholar 

  14. Jing, F., Li, M., Zhang, H., & Zhang, B. (2003). Unsupervised image segmentation using local homogeneity analysis. Proceedings of ISCAS, 2, 456–459.

    Google Scholar 

  15. Lui, J., Wai, B., Cheng, X., & Wang, X. (2005). An AES S-box to increase complexity and cryptgraphic analysis. International Conference on Information Networking and Applications, 1, 724–728.

    Google Scholar 

  16. Prasadh, K., Ramar, K., & Gnanajeyaraman, R. (2009). Public key cryptosystems based on chaotic Chebyshev polynomials. International Journal of Physical Sciences, 1(7), 122–128.

    Google Scholar 

  17. Shi, X. Y., Xiao, H., You, X. C., & Lam, K. Y. (2002). A method for obtaining cryptographically strong 8 × 8 S-boxes. International Conference on Information Networking and Applications, 2(3), 14–20.

    Google Scholar 

  18. Zhang, L., Liao, X., & Wang, X. (2005). An image encryption approach based on chaotic maps. Chaos, Solitons and Fractals, 24, 759–765.

    Article  MathSciNet  MATH  Google Scholar 

  19. Khan, M., Shah, T., Mahmood, H., & Gondal, M. A. (2013). An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dynamics, 71, 493–504.

    Article  MathSciNet  Google Scholar 

  20. Khan, M., Shah, T., & Gondal, M. A. (2013). An efficient technique for the construction of substitution box with chaotic partial differential equation. Nonlinear Dynamics, 73, 1795–1801.

    Article  MathSciNet  Google Scholar 

  21. Khan, M., Shah, T., Mahmood, H., Gondal, M. A., & Hussain, I. (2012). A novel technique for constructions of S-Boxes based on chaotic Lorenz systems. Nonlinear Dynamics, 70, 2303–2311.

    Article  MathSciNet  Google Scholar 

  22. Khan, M., & Shah, T. (2013). A construction of novel chaos base nonlinear component of block cipher. Nonlinear Dynamics. doi:10.1007/s11071-013-1132-0.

  23. Khan, M., & Shah, T. (2013). An efficient construction of substitution box with fractional chaotic system. Signal, Image and Video Processing. doi:10.1007/s11760-013-0577-4.

  24. Hussain, I., Azam, N. A., & Shah, T. (2014). Stego optical encryption based on chaotic S-box transformation. Optics and Laser Technology, 61, 50–56.

    Article  Google Scholar 

  25. Hussain, I., Shah, T., & Mahmood, H. (2013). A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Computer and Applications, 22, 1085–1093.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Majid Khan & Tariq Shah

Authors
  1. Majid Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tariq Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Majid Khan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, M., Shah, T. A Novel Statistical Analysis of Chaotic S-box in Image Encryption. 3D Res 5, 16 (2014). https://doi.org/10.1007/s13319-014-0016-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13319-014-0016-5

Keywords

Search

Navigation