Skip to main content

Improved ECC-Based Image Encryption with 3D Arnold Cat Map

  • Conference paper
  • First Online:
International Conference on Innovative Computing and Communications

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1387))

Abstract

Maintaining the secrecy and safety of images while sharing digital data online is a huge challenge. Numerous encryption schemes use the Elliptic Curve Cryptography(ECC) to encrypt and decrypt the images as ECC provides higher security with shorter key sizes. The researchers also suggest the use of the popular chaotic maps for added strength of the encryption process. In this paper, a novel encryption scheme for digital images based on ECC and 3D Arnold cat map is proposed. The 3D Arnold cat map scrambles the position of pixels in the image and then transforms the values of pixels. The transformed pixel values are encrypted and decrypted using the Elliptic Curve Analogue ElGamal Encryption Scheme (ECAEES). The proposed model is implemented using Python. We get an average entropy value of 7.9992, NPCR of 99.6%, UACI of 33.3% and PSNR of 27.89. The correlation coefficient values between adjacent pixels of cipher images are minimized. The improved performance proves that the model put forward is more secure and resilient than the existing noteworthy schemes.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhang, X., & Wang, X. (2017). Multiple-image encryption algorithm based on mixed image element and chaos. Computers & Electrical Engineering, 62, 401–413.

    Article  Google Scholar 

  2. Chen, Guanrong, Mao, Yaobin, & Chui, Charles K. (2004). A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos, Solitons & Fractals, 21(3), 749–761.

    Article  MathSciNet  Google Scholar 

  3. Luo, Y., Ouyang, X., Liu, J., & Cao, L. (2019). An image encryption method based on elliptic curve elgamal encryption and chaotic systems. IEEE Access, 7, 38507–38522.

    Article  Google Scholar 

  4. Singh, L. D., & Singh, K. M. (2015). Image encryption using elliptic curve cryptography. Procedia Computer Science, 54, 472–481.

    Article  Google Scholar 

  5. Laiphrakpam, D. S., & Khumanthem, M. S. (2017). Medical image encryption based on improved ElGamal encryption technique. Optik, 147, 88–102.

    Article  Google Scholar 

  6. Ravanna, C. R., & Keshavamurthy, C. (2019). A novel priority based document image encryption with mixed chaotic systems using machine learning approach. Facta Universitatis, Series: Electronics and Energetics, 32(1), 147–177.

    Google Scholar 

  7. Broumandnia, A. (2019). The 3D modular chaotic map to digital color image encryption. Future Generation Computer Systems, 99, 489–499.

    Article  Google Scholar 

  8. Abdelfatah, R. I. (2019). Secure image transmission using chaotic-enhanced elliptic curve cryptography. IEEE Access, 8, 3875–3890.

    Article  Google Scholar 

  9. Niu, Y., Zhou, Z., & Zhang, X. (2020). An image encryption approach based on chaotic maps and genetic operations. Multimedia Tools and Applications, 79(35), 25613–25633.

    Article  Google Scholar 

  10. Koblitz, N. (1987). Elliptic curve cryptosystems. Mathematics of computation, 48(177), 203–209.

    Article  Google Scholar 

  11. Liu, H., Zhu, Z., Jiang, H., & Wang, B. (2008, November). A novel image encryption algorithm based on improved 3D chaotic cat map. In 2008 The 9th International Conference for Young Computer Scientists (pp. 3016-3021). IEEE.

    Google Scholar 

  12. Elliptic Curve Cryptography(ECC) Brainpool Standard Curves and Curve Generation. https://tools.ietf.org/html/rfc5639. Cited 8 Nov,2020

  13. Ye, G. D., Huang, X. L., Zhang, L. Y., & Wang, Z. X. (2017). A self-cited pixel summation based image encryption algorithm. Chinese Physics B, 26(1), 010501.

    Article  Google Scholar 

  14. 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.

    Google Scholar 

  15. Zhang, W., Yu, H., & Zhu, Z. L. (2018). An image encryption scheme using self-adaptive selective permutation and inter-intra-block feedback diffusion. Signal Processing, 151, 130–143.

    Article  Google Scholar 

  16. Paar, Christoff and Pelzi Jan. "Understanding Cryptography a Textbook for Students and Practitioners” . Heidelberg: Springer, 2014.PDF.

    Google Scholar 

  17. Kanso, A., & Ghebleh, M. (2012). A novel image encryption algorithm based on a 3D chaotic map. Communications in Nonlinear Science and Numerical Simulation, 17(7), 2943–2959.

    Article  MathSciNet  Google Scholar 

  18. Soleymani, A., Nordin, M. J., & Sundararajan, E. (2014). A chaotic cryptosystem for images based on Henon and Arnold cat map. The Scientific World Journal, 2014.

    Google Scholar 

  19. Chen, F., Wong, K. W., Liao, X., & Xiang, T. (2012). Period distribution of the generalized discrete Arnold Cat map for \( N= 2^{e} \). IEEE Transactions on information theory, 59(5), 3249–3255.

    Article  Google Scholar 

  20. Toughi, S., Fathi, M. H., & Sekhavat, Y. A. (2017). An image encryption scheme based on elliptic curve pseudo random and advanced encryption system. Signal processing, 141, 217–227.

    Article  Google Scholar 

  21. Kaur, M., & Kumar, V. (2020). A comprehensive review on image encryption techniques. Archives of Computational Methods in Engineering, 27(1), 15–43.

    Article  MathSciNet  Google Scholar 

  22. Hariyanto, E., & Rahim, R. (2016). Arnold’s cat map algorithm in digital image encryption. International Journal of Science and Research (IJSR), 5(10), 1363–1365.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Parida, P., Pradhan, C. (2022). Improved ECC-Based Image Encryption with 3D Arnold Cat Map. In: Khanna, A., Gupta, D., Bhattacharyya, S., Hassanien, A.E., Anand, S., Jaiswal, A. (eds) International Conference on Innovative Computing and Communications. Advances in Intelligent Systems and Computing, vol 1387. Springer, Singapore. https://doi.org/10.1007/978-981-16-2594-7_62

Download citation

Publish with us

Policies and ethics