Skip to main content
SpringerLink
Log in

Cryptanalysis and Improvement of an Image Encryption Scheme Using Fourier Series

  • 3DR Express
  • Published:
3D Research

Abstract

This paper proposes cryptanalysis of an image encryption scheme reported in (Khan, J Vib Control 21(16):3450–3455, 2015). The encryption scheme synthesized nonlinear substitution-box using Fourier series to accomplish encryption of color images. Security investigation unveils that the scheme has inherent flaws which can be exploited by an attacker to reveal the plain-image information. We show that the encryption scheme is breakable under chosen-plaintext attack without owning secret key. The simulation analyses bring to notice that Khan’s scheme is insecure for encryption of images during secure communication. Besides, an improved image encryption scheme is proposed which is backed up by better statistical results and performance.

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
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Furht, B., & Kirovski, D. (2006). Multimedia encryption and authentication techniques and applications. Boca Raton: CRC Press.

    Book  Google Scholar 

  2. Gonçalves, D. D. O., & Costa, D. G. (2015). A survey of image security in wireless sensor networks. Journal of Imaging, 1(1), 4–30.

    Article  Google Scholar 

  3. Ye, G. (2010). Image scrambling encryption algorithm of pixel bit based on chaos map. Pattern Recognition Letters, 31(5), 347–354.

    Article  Google Scholar 

  4. Huang, C. K., & Nien, H. H. (2009). Multi chaotic systems based pixel shuffle for image encryption. Optics Communications, 282(11), 2123–2127.

    Article  Google Scholar 

  5. Huang, C. K., Liao, C. W., Hsu, S. L., & Jeng, Y. C. (2013). Implementation of gray image encryption with pixel shuffling and gray-level encryption by single chaotic system. Telecommunication Systems, 52(2), 563–571.

    Google Scholar 

  6. Shyu, S. J. (2007). Image encryption by random grids. Pattern Recognition, 40(3), 1014–1031.

    Article  MATH  Google Scholar 

  7. Ahmad, M., & Ahmad, T. (2014). Securing multimedia colour imagery using multiple high dimensional chaos-based hybrid keys. International Journal of Communication Networks and Distributed Systems, 12(1), 113–128.

    Article  MathSciNet  Google Scholar 

  8. Xu, Y., Wang, H., Li, Y., & Pei, B. (2014). Image encryption based on synchronization of fractional chaotic systems. Communications in Nonlinear Science and Numerical Simulation, 19(10), 3735–3744.

    Article  MathSciNet  Google Scholar 

  9. Rhouma, R., Meherzi, S., & Belghith, S. (2009). OCML-based colour image encryption. Chaos, Solitons and Fractals, 40(1), 309–318.

    Article  MATH  Google Scholar 

  10. Patidar, V., Pareek, N. K., Purohit, G., & Sud, K. K. (2011). A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption. Optics Communications, 284(19), 4331–4339.

    Article  Google Scholar 

  11. Chen, J. X., Zhu, Z. L., Fu, C., & Yu, H. (2014). A fast image encryption scheme with a novel pixel swapping-based confusion approach. Nonlinear Dynamics, 77(4), 1191–1207.

    Article  Google Scholar 

  12. Xu, L., Gou, X., Li, Z., & Li, J. (2017). A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion. Optics and Lasers in Engineering, 91, 41–52.

    Article  Google Scholar 

  13. Khan, J. S., ur Rehman, A., Ahmad, J., & Habib, Z. (2015). A new chaos-based secure image encryption scheme using multiple substitution boxes. In Conference on Information Assurance and Cyber Security, (pp. 16–21), IEEE.

  14. Shah, T., & Qureshi, A. (2016). Encrypting grayscale images using S-boxes chosen by logistic map. International Journal of Computer Science and Information Security, 14(4), 440.

    Google Scholar 

  15. Gondal, M. A., & Hussain, I. (2015). An image encryption scheme based on nonlinear chaotic algorithm and substitution box transformation. Applied Mathematics and Information Sciences, 9(6), 2991.

    Google Scholar 

  16. Hussain, I. (2016). Optical image encryption based on S-box transformation and fractional Hartley transform. Journal of Vibration and Control, 22(4), 1143–1146.

    Article  MathSciNet  Google Scholar 

  17. Hermassi, H., Rhouma, R., & Belghith, S. (2012). Security analysis of image cryptosystems only or partially based on a chaotic permutation. Journal of Systems and Software, 85(9), 2133–2144.

    Article  Google Scholar 

  18. Jakimoski, G., & Subbalakshmi, K. P. (2008). Cryptanalysis of some multimedia encryption schemes. IEEE Transactions on Multimedia, 10(3), 330–338.

    Article  Google Scholar 

  19. Dooley, J. F. (2013). A brief history of cryptology and cryptographic algorithms. Springer.

  20. Al-Kadit, I. A. (1992). Origins of cryptology: The Arab contributions. Cryptologia, 16(2), 97–126.

    Article  MathSciNet  MATH  Google Scholar 

  21. Biryukov, A., Daemen, J., Lucks, S., & Vaudenay, S. (2017). Topics and Research Directions for Symmetric Cryptography. In Proceedings of Early Symmetric Crypto workshop, (pp. 1–4). University of Luxembourg.

  22. Scopus: https://www.scopus.com. Accessed 19 Aug 2017.

  23. Schneier, B. (1996). Applied Cryptography: Protocols Algorithms and Source Code in C. New York: Wiley.

    MATH  Google Scholar 

  24. Khan, M. (2015). A novel image encryption using Fourier series. Journal of Vibration and Control, 21(16), 3450–3455.

    Article  MathSciNet  Google Scholar 

  25. Fourier Series: http://mathworld.wolfram.com/FourierSeries.html. Accessed 21 Aug 2017.

  26. Folland, G. B. (1992). Fourier Analysis and Its Applications. Pacific Grove: Brooks/Cole.

    MATH  Google Scholar 

  27. Military Cryptanalysis Part I- National Security Agency: http://www.nsa.gov/public_info/_files/military_cryptanalysis/mil_crypt_I.pdf. Accessed 7 Aug 2017.

  28. Kerckhoffs’s principle: http://crypto-it.net/eng/theory/kerckhoffs.html. Accessed 26 July 2017.

  29. Parvin, Z., Seyedarabi, H., & Shamsi, M. (2016). A new secure and sensitive image encryption scheme based on new substitution with chaotic function. Multimedia Tools and Applications, 75(17), 10631–10648.

    Article  Google Scholar 

  30. Chen, Z., Lu, J., Yang, P., & Luo, X. (2017). Recognizing substitution steganography of spatial domain based on the characteristics of pixels correlation. International Journal of Digital Crime and Forensics, 9(4), 48–61.

    Article  Google Scholar 

  31. Liu, H., & Wang, X. (2011). Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Optics Communications, 284(16), 3895–3903.

    Article  Google Scholar 

  32. Anees, A., Siddiqui, A. M., & Ahmed, F. (2014). Chaotic substitution for highly autocorrelated data in encryption algorithm. Communications in Nonlinear Science and Numerical Simulation, 19(9), 3106–3118.

    Article  MathSciNet  Google Scholar 

  33. Khan, F. A., Ahmed, J., Khan, J. S., Ahmad, J., & Khan, M. A. (2017). A novel image encryption based on Lorenz equation, Gingerbreadman chaotic map and S 8 permutation. Journal of Intelligent and Fuzzy Systems, 33(6), 1–13. (preprint).

    Google Scholar 

  34. Wu, Y., Zhou, Y., Saveriades, G., Agaian, S., Noonan, J. P., & Natarajan, P. (2013). Local Shannon entropy measure with statistical tests for image randomness. Information Sciences, 222, 323–342.

    Article  MathSciNet  MATH  Google Scholar 

  35. Chen, J., Zhu, Z. L., Zhang, L. B., Zhang, Y., & Yang, B. Q. (2018). Exploiting self-adaptive permutation–diffusion and DNA random encoding for secure and efficient image encryption. Signal Processing, 142, 340–353.

    Article  Google Scholar 

  36. Wu, Y., Noonan, J. P., & Agaian, S. (2011). NPCR and UACI randomness tests for image encryption. Cyber journals: Multidisciplinary journals in science and technology, Journal of Selected Areas in Telecommunications, April Edition, 31–38.

  37. Fouda, J. A. E., Effa, J. Y., & Ali, M. (2014). Highly secured chaotic block cipher for fast image encryption. Applied Soft Computing, 25, 435–444.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Jamia Millia Islamia, New Delhi, 110025, India

    Musheer Ahmad & M. N. Doja

  2. Department of Computer Engineering, Aligarh Muslim University, Aligarh, 202002, India

    M. M. Sufyan Beg

Authors
  1. Musheer Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. N. Doja
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. M. Sufyan Beg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Musheer Ahmad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmad, M., Doja, M.N. & Beg, M.M.S. Cryptanalysis and Improvement of an Image Encryption Scheme Using Fourier Series. 3D Res 8, 40 (2017). https://doi.org/10.1007/s13319-017-0150-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13319-017-0150-y

Keywords

Search

Navigation