Skip to main content
Log in

A Pareto-optimal evolutionary approach of image encryption using coupled map lattice and DNA

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Evolutionary algorithms are generally a suitable approach for optimization problems, having more than one conflicting objectives. For many complicated engineering optimization problems, multi-objective formulations are treated as realistic models. The paper presents and implements a Pareto-optimal image encryption algorithm that uses coupled map lattice (CML) chaos function and deoxyribonucleic acid (DNA) combination to encrypt an image. The discussed work uses multi-objective genetic algorithm (MOGA) to get the optimized results. The proposed two-step algorithm uses pseudo-random number generators, the chaotic method CML and DNA to create an initial population of DNA masks in its initial stage. The MOGA is applied in the second stage to obtain the best mask for encrypting the given plain image. The focus is on the generation of Pareto fronts by using the Pareto generation method of multi-objective optimization. The paper evaluates the performance of the implemented work using standard metrics like key sensitivity, secret key space, number of pixel change rate, unified average changed intensity, entropy, histogram and correlation coefficient. It also discusses the impact of using a genetic algorithm that uses more than one fitness function as the objective for encrypting images.

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

Access this article

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

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Guesmi R et al (2016) A novel chaos-based image encryption using DNA sequence operation and Secure Hash Algorithm SHA-2. Nonlinear Dyn 83(3):1123–1136

    Article  MathSciNet  MATH  Google Scholar 

  2. Abdullah AH, Enayatifar R, Lee M (2012) A hybrid genetic algorithm and chaotic function model for image encryption. AEU-Int J Electron Commun 66(10):806–816

    Article  Google Scholar 

  3. Guan Z-H, Huang F, Guan W (2005) Chaos-based image encryption algorithm. Phys Lett A 346(1):153–157

    Article  MATH  Google Scholar 

  4. Gao T, Chen Z (2008) A new image encryption algorithm based on hyper-chaos. Phys Lett A 372(4):394–400

    Article  MATH  Google Scholar 

  5. Chai X, Chen Y, Broyde L (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213

    Article  Google Scholar 

  6. Ye G, Huang X (2017) An efficient symmetric image encryption algorithm based on an intertwining logistic map. Neurocomputing 251:45–53

    Article  Google Scholar 

  7. Cheddad A et al (2010) A hash-based image encryption algorithm. Opt Commun 283(6):879–893

    Article  Google Scholar 

  8. Hao Z et al (2017) Application of coupled map lattice with parameter q in image encryption. Opt Lasers Eng 88:65–74

    Article  Google Scholar 

  9. Hraoui S et al. (2013) Benchmarking aes and chaos based logistic map for image encryption. In: Computer systems and applications (AICCSA), 2013 ACS international conference on. IEEE

  10. He J, Li Z, Qian H (2010) Cryptography based on spatiotemporal chaos system and multiple maps. JSW 5(4):421–428

    Article  Google Scholar 

  11. Zhang Q, Xue X, Wei X (2012) A novel image encryption algorithm based on DNA subsequence operation. Sci World J 2012:286741. https://doi.org/10.1100/2012/286741

    Article  Google Scholar 

  12. Wei X et al (2012) A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J Syst Softw 85(2):290–299

    Article  Google Scholar 

  13. Liu J, et al (2008) A cryptosystem based on multiple chaotic maps. In: Information processing (ISIP), 2008 international symposiums on. IEEE

  14. Lian S (2009) Efficient image or video encryption based on spatiotemporal chaos system. Chaos Solitons Fract 40(5):2509–2519

    Article  MATH  Google Scholar 

  15. Hermassi H, Rhouma R, Belghith S (2009) A modified hyperchaos based image cryptosystem. In: Systems, signals and devices, 2009. SSD’09. 6th international multi-conference on. IEEE

  16. Honge R et al (2007) A chaotic algorithm of image encryption based on dispersion sampling. In: Electronic measurement and instruments. ICEMI’07. 8th International conference on. IEEE

  17. Hong-e R et al (2007) Block sampling algorithm of image encryption based on chaotic scrambling. In: Computational intelligence and security workshops, 2007. CISW 2007. International conference on. IEEE

  18. Adleman LM (1994) Molecular computation of solutions to combinatorial problems. Nature 369:40

    Google Scholar 

  19. Xie T, Liu Y, Tang J (2014) Breaking a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Opt-Int J Light Electron Opt 125(24):7166–7169

    Article  Google Scholar 

  20. Zhang Q, Guo L, Wei X (2010) Image encryption using DNA addition combining with chaotic maps. Math Comput Model 52(11):2028–2035

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang X, Zhang H, Bao X (2016) Color image encryption scheme using CML and DNA sequence operations. Biosystems 144:18–26

    Article  Google Scholar 

  22. Enayatifar R, Abdullah AH, Lee M (2013) A weighted discrete imperialist competitive algorithm (WDICA) combined with chaotic map for image encryption. Opt Lasers Eng 51(9):1066–1077

    Article  Google Scholar 

  23. Suri S, Vijay R (2017) A Bi-objective genetic algorithm optimization of chaos-DNA based hybrid approach. J Intell Syst. Retrieved 23 Aug 2017, from https://doi.org/10.1515/jisys-2017-0069

  24. Enayatifar R, Abdullah AH, Isnin IF (2014) Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence. Opt Lasers Eng 56:83–93

    Article  Google Scholar 

  25. Ngatchou P, Zarei A, El-Sharkawi A (2005) Pareto multi objective optimization. In: Intelligent systems application to power systems, 2005. Proceedings of the 13th international conference on. IEEE

  26. Kaneko K (1992) Overview of coupled map lattices. Chaos: Interdiscip J Nonlinear Sci 2(3):279–282

    Article  MathSciNet  MATH  Google Scholar 

  27. Kaneko Kunihiko (1989) Spatiotemporal chaos in one-and two-dimensional coupled map lattices. Physica D 37(1-3):60–82

    Article  MathSciNet  Google Scholar 

  28. Ge X et al (2011) Cryptanalysis of a spatiotemporal chaotic image/video cryptosystem and its improved version. Phys Lett A 375(5):908–913

    Article  MATH  Google Scholar 

  29. Xing-Yuan W, Xue-Mei B (2013) A novel image block cryptosystem based on a spatiotemporal chaotic system and a chaotic neural network. Chin Phys B 22(5):050508

    Article  Google Scholar 

  30. Xing-Yuan W, Lin-Tao L (2013) Cryptanalysis and improvement of a digital image encryption method with chaotic map lattices. Chin Phys B 22(5):050503

    Article  Google Scholar 

  31. Li P et al (2006) A multiple pseudorandom-bit generator based on a spatiotemporal chaotic map. Phys Lett A 349(6):467–473

    Article  Google Scholar 

  32. Pareek NK, Patidar V, Sud KK (2006) Image encryption using chaotic logistic map. Image Vis Comput 24(9):926–934

    Article  Google Scholar 

  33. Gao H et al (2006) A new chaotic algorithm for image encryption. Chaos Solitons Fract 29(2):393–399

    Article  MATH  Google Scholar 

  34. Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurc Chaos 8(06):1259–1284

    Article  MathSciNet  MATH  Google Scholar 

  35. Akhshani A et al (2010) A novel scheme for image encryption based on 2D piecewise chaotic maps. Opt Commun 283(17):3259–3266

    Article  Google Scholar 

  36. Liu H, Wang X (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284(16):3895–3903

    Article  Google Scholar 

  37. Chen G, Mao Y, Chui CK (2004) A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fract 21(3):749–761

    Article  MathSciNet  MATH  Google Scholar 

  38. Song C-Y, Qiao Y-L, Zhang X-Z (2013) An image encryption scheme based on new spatiotemporal chaos. Opt-Int J Light Electron Opt 124(18):3329–3334

    Article  Google Scholar 

  39. Ahadpour S, Sadra Y (2012) A chaos-based image encryption scheme using chaotic coupled map lattices. arXiv preprint arXiv:1211.0090

  40. Wu X (2013) A novel chaos-based image encryption scheme using coupled map lattices. In: Fuzzy systems and knowledge discovery (FSKD), 2013 10th international conference on. IEEE

  41. Wang S et al (2004) Periodicity of chaotic trajectories in realizations of finite computer precisions and its implication in chaos communications. Int J Mod Phys B 18(17–19):2617–2622

    Article  Google Scholar 

  42. Kocarev L (2001) Chaos-based cryptography: a brief overview. IEEE Circuits Syst Mag 1(3):6–21

    Article  Google Scholar 

  43. Li C et al (2009) Cryptanalysis of an image encryption scheme based on a compound chaotic sequence. Image Vis Comput 27(8):1035–1039

    Article  Google Scholar 

  44. Rhouma R, Solak E, Belghith S (2010) Cryptanalysis of a new substitution–diffusion based image cipher. Commun Nonlinear Sci Numer Simul 15(7):1887–1892

    Article  MathSciNet  MATH  Google Scholar 

  45. Yoon E-J et al (2011) Cryptanalysis of an enhanced spatiotemporal chaotic image/video cryptosystem. EURASIP J Adv Signal Process 1:461563

    Article  Google Scholar 

  46. Wang Y et al (2011) A new chaos-based fast image encryption algorithm. Appl Soft Comput 11(1):514–522

    Article  Google Scholar 

  47. Ming Z, Shudong S (1999) Theory of genetic algorithm and its application. National Defense Industry Publishing Company, Beijing, pp 125–127

    Google Scholar 

  48. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271

    Article  Google Scholar 

  49. Konak A, Coit DW, Smith AE (2006) Multi-objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91(9):992–1007

    Article  Google Scholar 

  50. Fonseca CM, Fleming PJ (1993) Genetic algorithms for multiobjective optimization: formulationdiscussion and generalization. Icga 93(July):416–423

    Google Scholar 

  51. Murillo-Escobar MA et al (2017) A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn 87(1):407–425

    Article  MathSciNet  Google Scholar 

  52. Murillo-Escobar MA et al (2015) A RGB image encryption algorithm based on total plain image characteristics and chaos. Sig Process 109:119–131

    Article  Google Scholar 

  53. Murillo-Escobar MA, et al (2014) A novel symmetric text encryption algorithm based on logistic map. In: Proceedings of the international conference on communications, signal processing and computers (ICNC’14)

  54. Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurc Chaos 16(08):2129–2151

    Article  MathSciNet  MATH  Google Scholar 

  55. Fu C et al (2011) A novel chaos-based bit-level permutation scheme for digital image encryption. Opt Commun 284(23):5415–5423

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ritu Vijay.

Ethics declarations

Conflict of interest

The authors declare that they have any conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suri, S., Vijay, R. A Pareto-optimal evolutionary approach of image encryption using coupled map lattice and DNA. Neural Comput & Applic 32, 11859–11873 (2020). https://doi.org/10.1007/s00521-019-04668-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-019-04668-x

Keywords