Differential evolution optimization of intertwining logistic map-DNA based image encryption technique

Abstract

Differential evolution (DE) is a powerful evolutionary algorithms, widely applied in different fields of science and engineering for solving the problem of optimization. Since image encryption has been viewed as an interesting research topic by many experts and innumerable methods to encrypt images have emerged, currently, the focus is on obtaining optimized images. The paper presents a novel image encryption scheme that uses intertwining logistic map (ILM), DNA encoding and DE optimization. The proposed approach is based on three phases: permutation involving ILM, diffusion engaging DNA and optimization using DE. Parameters like entropy, key sensitivity, secret key space, unified average change in intensity (UACI), correlation coefficient —vertical, horizontal and diagonal, and number of pixel change rate have been evaluated to test the efficiency of the proposed method. The paper also compares this performance with that of the genetic algorithms (GA), used previously for optimization. The significance of this approach is enhancing entropy, the essential characteristic of randomness, resisting against numerous statistical and differential attacks and generating good experimental results. The main contribution of this paper is to present the efficiency of DE in image optimization and exhibit how DE is better than GA.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. 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

    Google Scholar 

  2. Adleman LM (1994) Molecular computation of solutions to combinatorial problems. Science 266(5187):1021–1024

    Google Scholar 

  3. Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurc Chaos 6(8):2129–2151

    MathSciNet  MATH  Google Scholar 

  4. Bisht A, Jaroli P, Dua M, Dua S (2018) Symmetric multiple image encryption using multiple new one-dimensional chaotic functions and two-dimensional cat map. In: IEEE international conference on inventive research in computing applications (ICIRCA). Coimbatore, pp 676–682

  5. Bisht A, Dua M, Dua S (2019a) A novel approach to encrypt multiple images using multiple chaotic maps and chaotic discrete fractional random transform. J Ambient Intell Hum Comput 10(9):3519–3531

    Google Scholar 

  6. Bisht A, Dua M, Dua S, Jaroli P (2019) A color image encryption technique based on bit-level permutation and alternate logistic maps. J Intell Syst

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

    MathSciNet  MATH  Google Scholar 

  8. Chen J, Zhou J, Wong K (2011) A modified chaos-based joint compression and encryption scheme. IEEE Trans Circuits Syst II Express Briefs 58(2):110–114

    Google Scholar 

  9. Chen Y-Y, Hsia C-H, Jhong S-Y, Lin H-J (2018) Data hiding method for AMBTC compressed images. J Ambient Intell Hum Comput 208:1–9

    Google Scholar 

  10. 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

    Google Scholar 

  11. Enayatifar R, Sadaei HJ, Abdullah AH, Lee M, Isnin IF (2015) A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata. Opt Lasers Eng 71:33–41

    Google Scholar 

  12. Enayatifar R, Abdullah AH, Isnin IF, Altameem A, Lee M (2017) Image encryption using a synchronous permutation-diffusion technique. Opt Lasers Eng 90:146–154

    Google Scholar 

  13. Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurc Chaos 8(6):1259–1284

    MathSciNet  MATH  Google Scholar 

  14. Gómez J, Dasgupta D, González F (2003) Using adaptive operators in genetic search. In: Genetic and evolutionary computation conference, 2724, pp 1580–1581

  15. Guesmi R, Farah M, Kachouri A, Samet M (2016) A novel chaos-based image encryption using DNA sequence operation and secure hash algorithm SHA-2. Nonlinear Dyn 83(3):1123–1136

    MathSciNet  MATH  Google Scholar 

  16. Head T, Rozenberg G, Bladergroen R, Breek C, Lommerse P, Spaink H (2000) Computing with DNA by operating on plasmids. Biosystems 57(2):87–93

    Google Scholar 

  17. Ilonen J, Kamarainen J-K, Lampinen J (2003) Differential evolution training algorithm for feed-forward neural networks. Neural Process Lett 17(1):93–105

    Google Scholar 

  18. Jaroli P, Dua AB, Dua S (2018) A color image encryption using four dimensional differential equations and arnold chaotic map. In: IEEE international conference on inventive research in computing applications (ICIRCA). Coimbatore, pp 869–876

  19. Joshi R, Sanderson A (1999) Minimal representation multisensor fusion using differential evolution. IEEE Trans Syst Man Cybern Part A Syst Hum 29(1):63–76

    Google Scholar 

  20. Julstrom BA (1995) What have you done for me lately? Adapting operator probabilities in a steady-state genetic algorithm. In: 6th international conference on genetic algorithm (ICGA). CINII, pp 81–87

  21. Khade PN, Narnaware PM (2012) 3D chaotic functions for image encryption. IJCSI Int J Comput Sci Issues 9(3):1–6

    Google Scholar 

  22. Khan JS, Rehman AU, 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 (CIACS), pp 16–21

  23. Khan FA, Ahmed J, Khan JS, Ahmad JC, Khan MA (2017) A novel image encryption based on Lorenz equation, Gingerbreadman chaotic map and S8 permutation. J Intell Fuzzy Syst 33(6):3753–3765

    Google Scholar 

  24. Kumar M, Kumar S, Budhiraja R, Das MK, Singh S (2016) Intertwining logistic map and cellular automata based color image encryption model. In: IEEE international conference on computational techniques in information and communication technologies (ICCTICT). New Delhi, pp 618–623

  25. Li S, Chen G, Cheung A, Bhargava B, Lo K (2007) On the design of perceptual mpeg-video encryption algorithms. IEEE Trans Circ Syst Video Technol 17(2):214–223

    Google Scholar 

  26. Liu H, Wang X (2010) Color image encryption based on one-time keys and robust chaotic maps. Comput Math Appl 59(10):3320–3327

    MathSciNet  MATH  Google Scholar 

  27. Liu H, Wang X (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284(16–17):3895–3903

    Google Scholar 

  28. Liu H, Wang X, Kadir A (2012a) Image encryption using DNA complementary rule and chaotic maps. Appl Soft Comput 12(5):1457–1466

    Google Scholar 

  29. Liu L, Zhang Q, Wei X (2012b) A RGB image encryption algorithm based on DNA encoding and chaos map. Comput Electr Eng 38(5):1240–1248

    Google Scholar 

  30. Masuda N, Jakimoski G, Aihara K, Kocarev L (2006) Chaotic block ciphers: from theory to practical algorithms. IEEE Trans Circuits Syst I Regul Pap 53(6):1341–1352

    MathSciNet  MATH  Google Scholar 

  31. Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett:2837

  32. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Google Scholar 

  33. Rhouma R, Safya B (2008) Cryptanalysis of a new image encryption algorithm based on hyper-chaos. Phys Lett A 372(38):5973–5978

    MATH  Google Scholar 

  34. Sneha PS, Sankar S, Kumar AS (2019) A chaotic colour image encryption scheme combining Walsh-Hadamard transform and Arnold-Tent maps. J Ambient Intell Hum Comput 2019:1–20

    Google Scholar 

  35. Solak E, Çokal C (2011) Algebraic break of image ciphers based on discretized chaotic map lattices. Inf Sci 181(1):227–233

    MathSciNet  Google Scholar 

  36. Solak E, Çokal C, Yildiz OT, Biyikoglu T (2010) Cryptanalysis of fridrich’s chaotic image encryption. Int J Bifurc Chaos 20(5):1405–1413

    MathSciNet  MATH  Google Scholar 

  37. Storn R (1995) Differrential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report, International Computer Science Institute 11

  38. Storn R (1996) On the usage of differential evolution for function optimization. In: Proceedings of North American fuzzy information processing, pp 519–523

  39. Suneja K, Dua S, Dua M (2019) A review of chaos based image encryption. In: IEEE 3rd international conference on computing methodologies and communication (ICCMC). Erode, pp 693–698

  40. Suri S, Vijay R (2017) A bi-objective genetic algorithm optimization of chaos-DNA based hybrid approach. J Intell Syst 28(2):333–346

    Google Scholar 

  41. Suri S, Vijay R (2019) A synchronous intertwining logistic map-DNA approach for color image encryption. J Ambient Intell Hum Comput 10(6):2277–2290

    Google Scholar 

  42. Tuson A, Ross P (1998) Adapting operator settings in genetic algorithms. Evol Comput 6(2):161–184

    Google Scholar 

  43. Wang l, Luan D (2013) A novel image encryption algorithm using chaos and reversible cellular automata. Commun Nonlinear Sci Numer Simul 18(11):3075–3085

    MathSciNet  MATH  Google Scholar 

  44. Wang X, Xu D (2014) Image encryption using genetic operators and intertwining logistic map. Nonlinear Dyn 78(4):2975–2984

    MathSciNet  Google Scholar 

  45. Wang X-Y, Yang L, Liu R, Kadir A (2010) A chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn 62(3):615–621

    MathSciNet  MATH  Google Scholar 

  46. Wang X, Teng L, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92(4):1101–1108

    MathSciNet  Google Scholar 

  47. Wang X, Liu L, Zhang Y (2015a) A novel chaotic block image encryption algorithm based on dynamic random growth technique. Opt Lasers Eng 66:10–18

    Google Scholar 

  48. Wang X-Y, Gu S-X, Zhang Y-Q (2015b) Novel image encryption algorithm based on cycle shift and chaotic system. Opt Lasers Eng 68:126–134

    Google Scholar 

  49. Wang X-Y, Zhang Y-Q, Bao X-M (2015c) A novel chaotic image encryption scheme using DNA sequence operations. Opt Lasers Eng 73:53–61

    Google Scholar 

  50. Wang X, Feng L, Zhao H (2019) Fast image encryption algorithm based on parallel computing system. Inf Sci 486:340–358

    Google Scholar 

  51. Xiao G, Lu M, Lai XQ (2006) New field of cryptography: DNA cryptography. Chin Sci Bull 51(12):1413–1420

    MathSciNet  MATH  Google Scholar 

  52. Zhang Y (2015) Cryptanalysis of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik 126(2):223–229

    Google Scholar 

  53. Zhang Y, Fu LH (2012) Research on DNA cryptography. In: Sen J (ed) Applied cryptography and network security. Rijeka, Intechopen, pp 357–376

    Google Scholar 

  54. Zhang Y-Q, Wang X-Y (2014) A symmetric image encryption algorithm based on mixed linear–nonlinear coupled map lattice. Inf Sci 273:329–351

    Google Scholar 

  55. Zhang Y-Q, Wang X-Y (2015) A new image encryption algorithm based on non-adjacent coupled map lattices. Appl Soft Comput 26:10–20

    Google Scholar 

  56. Zhang Q, Guo L, Wei X (2010a) Image encryption using DNA addition combining with chaotic maps. Math Comput Model 52(11–12):2028–2035

    MathSciNet  MATH  Google Scholar 

  57. Zhang Q, Wang Q, Wei X (2010b) A novel image encryption scheme based on dna coding and multi-chaotic maps. Adv Sci Lett 3(4):447–451

    Google Scholar 

  58. Zhang Y, Li C, Li Q, Zhang D, Shu S (2012) Breaking a chaotic image encryption algorithm based on perceptron model. Nonlinear Dyn 69(3):1091–1096

    MathSciNet  MATH  Google Scholar 

  59. Zhang Q, Guo L, Wei X (2013) A novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik Int J Light Electron Opt 124(18):3596–3600

    Google Scholar 

  60. Zhang Y-Q, Wang X-Y, Liu J, Chi Z-L (2016) An image encryption scheme based on the MLNCML system using DNA sequences. Opt Lasers Eng 82:95–103

    Google Scholar 

  61. Zheng X, Xu J, Li W (2009) Parallel DNA arithmetic operation based on n-moduli set. Appl Math Comput 212(1):177–184

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Mohit Dua.

Ethics declarations

Conflict of interest

All the authors declare that the submitted manuscript and the authors do not 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

Verify currency and authenticity via CrossMark

Cite this article

Dua, M., Wesanekar, A., Gupta, V. et al. Differential evolution optimization of intertwining logistic map-DNA based image encryption technique. J Ambient Intell Human Comput 11, 3771–3786 (2020). https://doi.org/10.1007/s12652-019-01580-z

Download citation

Keywords

  • ILM
  • DE
  • DNA
  • Image encryption