Advertisement

Plaintext related image hybrid encryption scheme using algebraic interpolation and generalized chaotic map

  • Xikun LiangEmail author
  • Xiao Tan
  • Limin Tao
Article
  • 10 Downloads

Abstract

In this paper, a plaintext related image hybrid encryption scheme is proposed based on Lagrange interpolation, generalized Henon map and nonlinear operations of matrices. The proposed scheme consists of three parts. In the first part, a generalized chaotic map is constructed on the basis of Henon map. Using the novel map, a chaotic sequence is built. And then, both the chaotic sequence and the plaintext pixels are used to implement the first nonlinear operation for generating the first cipher matrix associated with the plaintext. By performing an exclusive XOR operation between the original pixels matrix and the first cipher matrix, the diffusion encryption is carried out. In the second part, Lagrange interpolation is used to create the second cipher matrix related to the diffused image; the second nonlinear transformation is developed between the diffused image and the second cipher matrix; and sequence rearrangement is adopted to scramble the diffused image. In the third part, the third nonlinear transformation of matrices based on point operation and rounding operation is implemented on the scrambled image to complete the image encryption. Accordingly, the decryption process is executed by the inverse operations in the opposite order. The proposed algorithm has some distinctive features: a variety of nonlinear tools such as nonlinear polynomial interpolation, nonlinear chaotic map, and nonlinear operations were involved in the scheme. The cryptosystem is designed with the plaintext to enhance the algorithm security. Due to the combination of multiple nonlinear methods and random factors, the scheme is one time pad, which can withstand multiple types of attacks. The algorithm has a clear structure and a simple calculation, so it is easy to program. In addition, encryption simulation and performance analysis are carried out. The feasibility and effectiveness of the algorithm are verified by the simulated results. The security of the algorithm are proved by the objective indicators such as the running time, key space, statistical properties, key sensitivity, and differential analysis, etc.

Keywords

Non-linear methods Lagrange interpolation Chaotic map Plaintext related Image encryption 

Notes

Acknowledgments

Without institutional funding, the authors carry out the research on image encryption solely due to personal interest. The authors express their sincere gratitude to those who have provided information and suggestions for this work.

Compliance with ethical standards

Ethical statements

We solemnly declare that all authors are well aware of the academic ethics of the journal of Nonlinear Dynamics and are committed to unconditionally complying with these norms.

We certify that this manuscript is original and has not been published and will not be submitted elsewhere for publication while being considered by the journal of Multimedia Tools and Applications. And the study is not split up into several parts to increase the quantity of submissions and submitted to various journals or to one journal over time. No data have been fabricated or manipulated (including images) to support our conclusions. No data, text, or theories by others are presented as if they were our own.

The submission has been received explicitly from all co-authors. And authors whose names appear on the submission have contributed sufficiently to the scientific work and therefore share collective responsibility and accountability for the results.

The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors. Informed consent was obtained from all individual participants included in the study.

References

  1. 1.
    101_ObjectCategories, The Caltech 101 dataset[DB/OL] (2019) http://www.vision.caltech.edu/Image_Datasets/Caltech101/Caltech101.html#Download
  2. 2.
    Akif OZ (2012) Image encryption technique using Lagrange interpolation. Ibn Al-Haitham Journal for Pure and Applied Science 25(1):478–493Google Scholar
  3. 3.
    Amalarethinam DIG, Geetha JS (2015) Image encryption and decryption in public key cryptography based on MR. IEEE international conference on computing and communications technologies, Cairo, Egypt. SpringerGoogle Scholar
  4. 4.
    Chai X, Chen Y, Broyde L (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213CrossRefGoogle Scholar
  5. 5.
    Chen YC, Ye RS (2017) A novel image encryption algorithm based on improved standard mapping. Computer Science and Application 7(8):753–773CrossRefGoogle Scholar
  6. 6.
    Cheng P, Yang H, Wei P, Zhang W (2015) A fast image encryption algorithm based on chaotic and lookup table. Nonlinear Dynamics 79(3):2121–2131CrossRefGoogle Scholar
  7. 7.
    CIFAR-10 Matlab version, The CIFAR-10 dataset[DB/OL] (2019) http://www.cs.toronto.edu/~kriz/cifar.html
  8. 8.
    Contour Detection and Image Segmentation Resources[DB/OL] (2018) https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/resources.html
  9. 9.
    Fu C, Chen J, Zou H et al (2017) A selective compression -encryption of images based on SPIHT coding and Chirikov standard map. Signal Process 131:514–526CrossRefGoogle Scholar
  10. 10.
    Ganesan K, Murali K (2014) Image encryption using eight dimensional chaotic cat map. The European Physical Journal Special Topics 223(8):1611–1622CrossRefGoogle Scholar
  11. 11.
    Guo FM, Tu L (2015) Application of chaos theory in cryptography[M]. Beijing Institute of Technology Press, BeijingGoogle Scholar
  12. 12.
    Jin X, Yin S, Liu N, Li X, Zhao G, Ge S (2018) Color image encryption in non-RGB color spaces. Mult Tools Appl (MTAP) 77(12):15851–15873CrossRefGoogle Scholar
  13. 13.
    Kanso A, Ghebleh M (2012) A novel image encryption algorithm based on a 3D chaotic map. Commun Nonlinear Sci Numer Simul 17:2943–2959MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kanso A, Ghebleh M (2015) An efficient and robust image encryption scheme for medical applications. Commun Nonlinear Sci Numer Simul 24(1–3):98–116MathSciNetCrossRefGoogle Scholar
  15. 15.
    Liu CL (2017) Image processing with Matlab[M]. Tsinghua university press, BeijingGoogle Scholar
  16. 16.
    Liu Q, Li P, Zhang M, Sui Y, Yang H (2015) A novel image encryption algorithm based on chaos maps with Markov properties. Commun Nonlinear Sci Numer Simul 20(2):506–515CrossRefGoogle Scholar
  17. 17.
    Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26–36CrossRefGoogle Scholar
  18. 18.
    Miller JE, Moursund DG, Duris CS (2011) Elementary theory and application of numerical analysis [M]. Dover Publications, New YorkGoogle Scholar
  19. 19.
    Norouzi B, Seyedzadeh SM, Mirzakuchaki S et al (2014) A novel image encryption based on hash function with only two-round diffusion process. Multimedia Systems 20(1):45–64CrossRefGoogle Scholar
  20. 20.
    Prasad M, Sudha KL (2011) Chaos image encryption using pixel shuffling[M]. In: Wyld C et al (eds) CCSEA, CS &IT 02, pp 169–179Google Scholar
  21. 21.
    Ritwik MG, Krishna D, Sahoo A (2017) Cryptanalysis of image encryption using traditional encryption techniques. Image Vis Comput 23(5):89–97Google Scholar
  22. 22.
    Shamir A (1979) How to share secret [J]. Commun ACM 24(11):612–613MathSciNetCrossRefGoogle Scholar
  23. 23.
    Sun XH (2013) Image encryption algorithms and practices with implentations in C#[M]. Science Press, BeijingGoogle Scholar
  24. 24.
    Wang X, Xu D (2015) A novel image encryption scheme using chaos and Langton's ant cellular automaton. Nonlinear Dynamics 79(4):2449–2456MathSciNetCrossRefGoogle Scholar
  25. 25.
    Wei XP, Guo L, Zhang Q et al (2012) A novel gray image encryption algorithm based on DNA sequence operation and hyper-chaotic system[J]. J Syst Softw 85(2):290–299CrossRefGoogle Scholar
  26. 26.
    Xu L, Guo X, Li Z et al (2017) A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion. Opt Lasers Eng 91:41–52CrossRefGoogle Scholar
  27. 27.
    Zhang Y (2014) Plaintext related image encryption scheme using chaotic map. TELKOMNIKA 12(1):635–643Google Scholar
  28. 28.
    Zhang Y (2014) A chaotic system based image encryption algorithm using plaintext-related confusion. TELKOMNIKA 12(11):7952–7962Google Scholar
  29. 29.
    Zhang Y (2016) Chaotic digital image cryptosystem[M]. Tsinghua university press, BeijingGoogle Scholar
  30. 30.
    Zhang W, Wong KW, Yu H et al (2013) An image encryption scheme using reverse 2-dimensinal chaotic map and dependant diffusion. Commun Nonlinear Sci Numer Simul 18:2066–2080MathSciNetCrossRefGoogle Scholar
  31. 31.
    Zhang LY, Hu X, Liu Y et al (2014) A chaotic image encryption scheme owning temp-value feedback. Commun Nonlinear Sci Numer Simul 19(10):3653–3659MathSciNetCrossRefGoogle Scholar
  32. 32.
    Zhen P, Zhao G, Min L, Jin X (2016) Chaos-based image encryption scheme combining DNA coding and entropy. Multimed Tools Appl (MTAP) 75(11):6303–6319CrossRefGoogle Scholar
  33. 33.
    Zhu ZL, Zhang W, Wong KW et al (2011) A chaos-based symmetric image encryption scheme using a bit-level permutation[J]. Inf Sci 181:1171–1186CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information Science and EngineeringHangzhou Normal UniversityHangzhouChina
  2. 2.Hangzhou Institute of Service EngineeringHangzhou Normal UniversityHangzhouChina

Personalised recommendations