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Comparative analysis of image encryption based on 1D maps and their integrated chaotic maps

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Abstract

The Maximum Lyapunov Exponent(MLE) measures the sensitivity of a chaotic system to its initial conditions. In chaos theory, systems with positive MLE values are considered chaotic, and larger MLE values generally indicate more robust chaos. A higher MLE suggests a more chaotic and complex behavior, which could be beneficial for encryption as it might provide enhanced security due to increased sensitivity to initial conditions and resistance to attacks. This paper searches for whether a 1D seed chaotic map or a 1D integrated chaotic map is preferred for image encryption. Does the MLE have any role? Firstly, three 1D integrated chaotic maps were designed: Sine-Cubic Integrated Map(SCIM), Tent-Logistic Integrated Map(TLIM), and Sine-Logistic Integrated Map(SLIM). These integrated chaotic maps are designed using the four available seed maps: sine, logistics, cubic, and tent. Thus, we have considered seven 1D chaotic maps to analyse and answer the question. Secondly, image encryption and decryption are performed using the considered seven 1D chaotic maps, one after the other, and the security measures of the encrypted image are analysed using various available tools. The image encryption is performed using block shuffling as diffusion and bit-Xor operation as the confusion process. A comparative analysis is performed using the six quantitative security analysis tools. According to the encryption correlation coefficient value of 0.0017, the Pick Signal-To-Noise Ratio(PSNR) value of 9.204, the Mean Square Error(MSE) value of 7809.1, the Number of Pixel Change Rate(NPCR) value of 95.3903, the Unified Average Change Intensity(UACI) value of 33.3676, and the information entropy value of 7.9635, the sine map is ranked first in security. The comparative analysis result reveals that seed maps give better encrypted image security than integrated chaotic maps. Therefore, integrating 1D chaotic maps is not guaranteed to get a better-secured encrypted image. Further analysis is made to understand if the MLE directly impacts the security of the encrypted process. It is found that the integrated chaotic maps provide a higher MLE. However, in this analysis, we couldn’t observe the direct relationship between the MLE and the security of the encrypted image. This suggests that other factors beyond just MLE contribute to the security of the encryption process.

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References

  1. Zhu Y, Wang C, Sun J, Yu F (2023) A chaotic image encryption method based on the artificial fish swarms algorithm and the DNA coding. Mathematics 11(3):767. https://doi.org/10.3390/math11030767

  2. Yang C, Taralova I, El Assad S, Loiseau JJ (2022) Image encryption based on fractional chaotic pseudo-random number generator and DNA encryption method. Nonlinear Dynamics 109(3):2103–2127. https://doi.org/10.1007/s11071-022-07534-z

    Article  Google Scholar 

  3. Alexan W, Elkandoz M, Mashaly M, Azab E, Aboshousha A (2023) Color image encryption through Chaos and KAA map. IEEE Access 11:11541–11554. https://doi.org/10.1109/ACCESS.2023.3242311

    Article  Google Scholar 

  4. Alexan W, Chen YL, Por LY, Gabr M (2023) Hyperchaotic maps and the single neuron model: a novel framework for chaos-based image encryption. Symmetry 15(5):1–31. https://doi.org/10.3390/sym15051081

    Article  Google Scholar 

  5. Sathiyamurthi P, Ramakrishnan S (2022) Speech encryption using hybrid-hyper chaotic system and binary masking technique. Multimedia Tools and Applications 81. https://doi.org/10.1007/s11042-021-11757-4

  6. Tlelo-Cuautle E, González-Zapata AM, Díaz-Muñoz JD, de la Fraga LG, Cruz-Vega I (2022) Optimization of fractional-order chaotic cellular neural networks by metaheuristics. European Physical Journal: Special Topics 231. https://doi.org/10.1140/epjs/s11734-022-00452-6

  7. Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26–36. https://doi.org/10.1016/j.optlaseng.2016.03.019

    Article  Google Scholar 

  8. Liu H, Kadir A, Ma C, Xu C (2020) Constructing keyed hash algorithm using enhanced chaotic map with varying parameter. Math Probl Eng 2020. https://doi.org/10.1155/2020/4071721

  9. Liu H, Kadir A, Xu C (2020) Cryptanalysis and constructing S-Box based on chaotic map and backtracking. Appl MathComput 376:125153. https://doi.org/10.1016/j.amc.2020.125153

    Article  MathSciNet  Google Scholar 

  10. Vassallo K, Garg L, Prakash V, Ramesh K (2019) Contemporary technologies and methods for cross-platform application development. J Comput Theor Nanosci 16(9):3854–3859

    Article  Google Scholar 

  11. Zahmoul R, Ejbali R, Zaied M (2017) Image encryption based on new Beta chaotic maps. Opt Lasers Eng 96(April):39–49. https://doi.org/10.1016/j.optlaseng.2017.04.009

    Article  Google Scholar 

  12. Ye G, Huang X (2017) An efficient symmetric image encryption algorithm based on an intertwining logistic map. Neurocomput 251:45–53. https://doi.org/10.1016/j.neucom.2017.04.016

    Article  Google Scholar 

  13. Kanso A, Ghebleh M (2012) A novel image encryption algorithm based on a 3D chaotic map. Commun Nonlinear Sci Numer Simul 17(7):2943–2959. https://doi.org/10.1016/j.cnsns.2011.11.030

    Article  MathSciNet  Google Scholar 

  14. Kaur M, Singh D, Kumar V (2022) Improved seven-dimensional (i7D) hyperchaotic map-based image encryption technique. Soft Comput 26(6):2689–2698. https://doi.org/10.1007/s00500-021-06423-8

    Article  Google Scholar 

  15. Almawgani AHM, Alhawari ARH, Hindi AT, Al-Arashi WH, Al-Ashwal AY (2022) Hybrid image steganography method using Lempel Ziv Welch and genetic algorithms for hiding confidential data. Multidim Syst Signal Proc 33(2):561–578. https://doi.org/10.1007/s11045-021-00793-w

    Article  Google Scholar 

  16. Yang B, Liao X (2018) Some properties of the Logistic map over the finite field and its application. Signal Proc 153:231–242. https://doi.org/10.1016/j.sigpro.2018.07.011

    Article  Google Scholar 

  17. Zheng J, Liu LF (2020) Novel image encryption by combining dynamic DNA sequence encryption and the improved 2D logistic sine map. IET Image Process 14(11):2310–2320. https://doi.org/10.1049/iet-ipr.2019.1340

    Article  Google Scholar 

  18. Lan R, He J, Wang S, Gu T, Luo X (2018) Integrated chaotic systems for image encryption. Signal Process 147:133–145. https://doi.org/10.1016/j.sigpro.2018.01.026

    Article  Google Scholar 

  19. Hua Z, Jin F, Xu B, Huang H (2018) 2D Logistic-Sine-coupling map for image encryption. Signal Process 149:148–161. https://doi.org/10.1016/j.sigpro.2018.03.010

    Article  Google Scholar 

  20. Yousif B, Khalifa F, Makram A, Takieldeen A (2020) A novel image encryption/decryption scheme based on integrating multiple chaotic maps. AIP Advances 10:(7). https://doi.org/10.1063/5.0009225

  21. Zhou Y, Bao L, Chen CLP (2014) A new 1D chaotic system for image encryption. Signal Process 97:172–182. https://doi.org/10.1016/j.sigpro.2013.10.034

    Article  Google Scholar 

  22. Saravanan S, Sivabalakrishnan M (2021) A hybrid chaotic map with coefficient improved whale optimization-based parameter tuning for enhanced image encryption. Soft Comput 25(7):5299–5322. https://doi.org/10.1007/s00500-020-05528-w

    Article  Google Scholar 

  23. Munir N, Khan M, Ismail Al Karim Haj A, Hussain I (2022) Cryptanalysis and improvement of novel image encryption technique using hybrid method of discrete dynamical chaotic maps and brownian motion. Multimed Tools Appl 81(5):6571–6584. https://doi.org/10.1007/s11042-021-11810-2

  24. Farah MAB, Farah A, Farah T (2020) An image encryption scheme based on a new hybrid chaotic map and optimized substitution box. Nonlinear Dyn 99(4):3041–3064. https://doi.org/10.1007/s11071-019-05413-8

    Article  Google Scholar 

  25. Alawida M, Samsudin A, Teh JS, Alkhawaldeh RS (2019) A new hybrid digital chaotic system with applications in image encryption. Signal Process 160:45–58. https://doi.org/10.1016/j.sigpro.2019.02.016

    Article  Google Scholar 

  26. Yasser I, Khalifa F, Mohamed MA, Samrah AS (2020) A new image encryption scheme based on hybrid chaotic maps.Complexity 2020(i) (2020). https://doi.org/10.1155/2020/9597619

  27. Khalil N, Sarhan A, Alshewimy MAM (2021) An efficient color/grayscale image encryption scheme based on hybrid chaotic maps. Opt Laser Technol 143(June):107326. https://doi.org/10.1016/j.optlastec.2021.107326

    Article  Google Scholar 

  28. Pak C, Huang L (2017) A new color image encryption using combination of the 1D chaotic map. Signal Process 138:129–137. https://doi.org/10.1016/j.sigpro.2017.03.011

    Article  Google Scholar 

  29. Parvaz R, Zarebnia M (2018) A combination chaotic system and application in color image encryption. Opt Laser Technol 101:30–41. https://doi.org/10.1016/j.optlastec.2017.10.024

    Article  Google Scholar 

  30. Ali TS, Ali R (2022) A novel color image encryption scheme based on a new dynamic compound chaotic map and S-box. Multimed Tools Appl 81(15):20585–20609. https://doi.org/10.1007/s11042-022-12268-6

    Article  Google Scholar 

  31. Li T, Yan W, Chi Z (2022) A new image encryption algorithm based on optimized Lorenz chaotic system. Concurrency and Computation: Practice and Experience 34(13):1–12. https://doi.org/10.1002/cpe.5902

    Article  Google Scholar 

  32. Liu JL, Zhang M, Tong X, Wang Z (2022) Image compression and encryption algorithm based on 2D compressive sensing and hyperchaotic system. Multimed Syst 28(2):595–610. https://doi.org/10.1007/s00530-021-00859-6

    Article  Google Scholar 

  33. Hua Z, Zhou Y, Pun CM, Chen CLP (2015) 2D Sine Logistic modulation map for image encryption. Inf Sci 297:80–94. https://doi.org/10.1016/j.ins.2014.11.018

    Article  Google Scholar 

  34. Yahi A, Bekkouche T, Daachi MEH, Diffellah N (2022) A color image encryption scheme based on 1d cubic map. Optik 249:168290

    Article  Google Scholar 

  35. Herbadji D, Belmeguenai A, Derouiche N, Liu H (2020) Colour image encryption scheme based on enhanced quadratic chaotic map. IET Image Process 14(1):40–52

    Article  Google Scholar 

  36. Mondal B, Behera PK, Gangopadhyay S (2021) A secure image encryption scheme based on a novel 2d sine-cosine cross-chaotic (sc3) map. J Real-Time Image Process 18(1):1–18

    Article  Google Scholar 

  37. Hua Z, Zhu Z, Chen Y, Li Y (2021) Color image encryption using orthogonal Latin squares and a new 2D chaotic system. Nonlinear Dyn 104(4):4505–4522. https://doi.org/10.1007/s11071-021-06472-6

    Article  Google Scholar 

  38. Gebereselassie SA, Roy BK (2022) Secure speech communication based on the combination of chaotic oscillator and logistic map. Multimed Tools Appl 26061–26079. https://doi.org/10.1007/s11042-022-12803-5

  39. Elkamchouchi H, Salama WM, Abouelseoud Y (2020) New video encryption schemes based on chaotic maps. IET Image Process 14(2):397–406. https://doi.org/10.1049/iet-ipr.2018.5250

    Article  Google Scholar 

  40. Mansouri A, Wang X (2021) A novel one-dimensional chaotic map generator and its application in a new index representation-based image encryption scheme. Inf Sci 563:91–110. https://doi.org/10.1016/j.ins.2021.02.022

    Article  MathSciNet  Google Scholar 

  41. Amigó JM, Kocarev L, Szczepanski J (2007) Discrete lyapunov exponent and resistance to differential cryptanalysis. IEEE Transactions on Circuits and Systems II: Express Briefs 54(10):882–886. https://doi.org/10.1109/TCSII.2007.901576

    Article  Google Scholar 

  42. Li M, Lu D, Wen W, Ren H, Zhang Y (2018) Cryptanalyzing a color image encryption scheme based on hybrid hyper-chaotic system and cellular automata. IEEE Access 6:47102–47111. https://doi.org/10.1109/ACCESS.2018.2867111

    Article  Google Scholar 

  43. Al Nahian SA, Hosen Z, Ahmed P (2019) An Elementary Study of Chaotic Behaviors in 1-D Maps. J Appl Math Phys 07(05):1149–1173. https://doi.org/10.4236/jamp.2019.75077

    Article  Google Scholar 

  44. Zhou Y, Hua Z, Pun CM, Philip Chen CL (2015) Cascade chaotic system with applications. IEEE Trans Cybern 45(9):2001–2012. https://doi.org/10.1109/TCYB.2014.2363168

    Article  Google Scholar 

  45. Jakimoski G, Subbalakshmi K (2007) Discrete lyapunov exponent and differential cryptanalysis. IEEE Transactions on Circuits and Systems II: Express Briefs 54(6):499–501

    Google Scholar 

  46. Liu H, Wang X (2010) Color image encryption based on one-time keys and robust chaotic maps. Comput Math Appl 59(10):3320–3327. https://doi.org/10.1016/j.camwa.2010.03.017

    Article  MathSciNet  Google Scholar 

  47. Hanchinamani G, Kulakarni L (2014) Image encryption based on 2-d zaslavskii chaotic map and pseudo hadmard transform. Int J Hybrid Inf Technol 7(4):185–200. https://doi.org/10.14257/ijhit.2014.7.4.16

  48. Thiyagarajan J, Murugan B, Gounder AGN (2019) A chaotic image encryption scheme with complex diffusion matrix for plain image sensitivity. Serbian J Electr Eng 16(2):247–265. https://doi.org/10.2298/SJEE1902247T

    Article  Google Scholar 

  49. Wang X, Xue W, An J (2021) Image encryption algorithm based on LDCML and DNA coding sequence. Multimed Tools Appl 80(1):591–614. https://doi.org/10.1007/s11042-020-09688-7

    Article  Google Scholar 

  50. Zhang G, Liu Q (2011) A novel image encryption method based on total shuffling scheme. Opt Commun 284(12):2775–2780. https://doi.org/10.1016/j.optcom.2011.02.039

    Article  Google Scholar 

  51. Liu H, Liu J, Ma C (2023) Constructing dynamic strong S-Box using 3D chaotic map and application to image encryption. Multimed Tools Appl 82:(16). https://doi.org/10.1007/s11042-022-12069-x

  52. Chen J, Zhu ZL, Zhang LB, Zhang Y, Yang BQ (2018) Exploiting self-adaptive permutation-diffusion and DNA random encoding for secure and efficient image encryption. Signal Process 142:340–353. https://doi.org/10.1016/j.sigpro.2017.07.034

    Article  Google Scholar 

  53. Wu Y, Noonan JP, Agaian S (2011) NPCR and UACI randomness tests for image encryption. Cyberjournals, Com

    Google Scholar 

  54. Shannon CE (1949) Communication theory of secrecy systems. Bell Syst Tech J 28(4):656–715. https://doi.org/10.1002/j.1538-7305.1949.tb00928.x

    Article  MathSciNet  Google Scholar 

  55. Li C, Lin D, Feng B, Lu J, Hao F (2018) Cryptanalysis of a chaotic image encryption algorithm based on information entropy. IEEE Access 6:75834–75842. https://doi.org/10.1109/ACCESS.2018.2883690

    Article  Google Scholar 

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  1. Binoy Krishna Roy contributed equally to this work.

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  1. Electrical Engineering, National Institute of Technology Silchar, Silchar, 788010, Assam, India

    Samuel Amde Gebereselassie & Binoy Krishna Roy

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  1. Samuel Amde Gebereselassie
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Correspondence to Samuel Amde Gebereselassie.

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Gebereselassie, S.A., Roy, B.K. Comparative analysis of image encryption based on 1D maps and their integrated chaotic maps. Multimed Tools Appl (2024). https://doi.org/10.1007/s11042-024-18319-4

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