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A novel exponent–sine–cosine chaos map-based multiple-image encryption technique

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Abstract

This paper proposes a multiple-image encryption (MIE) approach that uses a novel exponent–sine–cosine (ESC) chaotic map along with the dynamic permutation and DNA-based diffusion. In the first phase of the proposed approach, the three components of a color image (‘R’, ‘G’, ‘B’) for all given images are split, cross-shuffled, and combined randomly to create three big images. These resultant three images are permuted using dynamic permutation during the second phase. In the third phase, the permutated image is diffused using the DNA-based diffusion process. Both permutation and diffusion phases use the novel proposed ESC chaotic map. The proposed ESC chaotic map has been analyzed using Shannon entropy, Lyapunov exponent, and bifurcation diagram. The results show that the ESC map is chaotic in the range of 1.5–10. In addition, the proposed MIE algorithm has been evaluated using various standard metrics such as number of pixel change rate (NPCR), unified average change intensity (UACI), entropy, brute force attack, key sensitivity, and bit corrected ratio (BCR). The results show that the value of the NPCR, UACI, and entropy lies close to 99.59, 32.9, and 7.9995, respectively. Therefore, it is validated that the proposed algorithm provides a good encryption mechanism.

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References

  1. Daemen, J., Rijmen, V.: Reijndael: The advanced encryption standard. Dr. Dobb’s J. Softw. Tools Prof. Program 26(3), 137–139 (2001)

    Google Scholar 

  2. Basu, S.: International data encryption algorithm (IDEA)—a typical illustration. J. Glob. Res. Comput. Sci. 2(7), 116–118 (2011)

    Google Scholar 

  3. Bentoutou, Y., Bensikaddour, E.H., Taleb, N., Bounoua, N.: An improved image encryption algorithm for satellite applications. Adv. Sp. Res. 66(1), 176–192 (2020). https://doi.org/10.1016/j.asr.2019.09.027

    Article  Google Scholar 

  4. Dua, M., Wesanekar, A., Gupta, V., Bhola, M., Dua, S.: Differential evolution optimization of intertwining logistic map-DNA based image encryption technique. J. Ambient. Intell. Humaniz. Comput. 11(9), 3771–3786 (2020). https://doi.org/10.1007/s12652-019-01580-z

    Article  Google Scholar 

  5. Kumar, A., Dua, M.: A GRU and chaos-based novel image encryption approach for transport images. Multimed. Tools Appl. (2022). https://doi.org/10.1007/s11042-022-13902-z

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Hua, Z., Yi, S., Zhou, Y.: Medical image encryption using high-speed scrambling and pixel adaptive diffusion. Signal Process. 144, 134–144 (2018). https://doi.org/10.1016/j.sigpro.2017.10.004

    Article  Google Scholar 

  8. Zhou, N., Jiang, H., Gong, L., Xie, X.: Double-image compression and encryption algorithm based on co-sparse representation and random pixel exchanging. Opt. Lasers Eng. 110, 72–79 (2018). https://doi.org/10.1016/j.optlaseng.2018.05.014

    Article  Google Scholar 

  9. Bisht, A., Dua, M., Dua, S.: A novel approach to encrypt multiple images using multiple chaotic maps and chaotic discrete fractional random transform. J. Ambient. Intell. Humaniz. Comput. 10(9), 3519–3531 (2019). https://doi.org/10.1007/s12652-018-1072-0

    Article  Google Scholar 

  10. Bisht, A., Dua, M., Dua, S., Jaroli, P.: A color image encryption technique based on bit-level permutation and alternate logistic maps. J. Intell. Syst. 29(1), 1246–1260 (2020). https://doi.org/10.1515/jisys-2018-0365

    Article  Google Scholar 

  11. Dua, M., Wesanekar, A., Gupta, V., Bhola, M., Dua, S.: Color image encryption using synchronous CML-DNA and weighted bi-objective genetic algorithm. In: ACM International Conference Proceeding Series, pp. 121–125. (2019). https://doi.org/10.1145/3361758.3361780

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

    Article  Google Scholar 

  13. Guesmi, R., Farah, M.A.B.: A new efficient medical image cipher based on hybrid chaotic map and DNA code. Multimed. Tools Appl. 80(2), 1925–1944 (2021). https://doi.org/10.1007/s11042-020-09672-1

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. Talhaoui, M.Z., Wang, X., Talhaoui, A.: A new one-dimensional chaotic map and its application in a novel permutation-less image encryption scheme. Vis. Comput. 37(7), 1757–1768 (2021). https://doi.org/10.1007/s00371-020-01936-z

    Article  Google Scholar 

  16. Liu, L., Jiang, D., Wang, X., Rong, X., Zhang, R.: 2D Logistic-Adjusted-Chebyshev map for visual color image encryption. J. Inf. Secur. Appl. 60, 102854 (2021). https://doi.org/10.1016/j.jisa.2021.102854

    Article  Google Scholar 

  17. Wang, X., Xu, D.: Image encryption using genetic operators and intertwining logistic map. Nonlinear Dyn. 78(4), 2975–2984 (2014). https://doi.org/10.1007/s11071-014-1639-z

    Article  MathSciNet  Google Scholar 

  18. Gupta, M.D., Chauhan, R.K.: Secure image encryption scheme using 4D-hyperchaotic systems based reconfigurable pseudo-random number generator and S-Box. Integration 81, 137–159 (2021). https://doi.org/10.1016/j.vlsi.2021.07.002

    Article  Google Scholar 

  19. Jaroli, P., Bisht, A., Dua, M., Dua, S.: A color image encryption using four dimensional differential equations and arnold chaotic map. In: Proceedings of the International Conference on Inventive Research in Computing Applications, ICIRCA 2018, pp. 869–876. (2018). https://doi.org/10.1109/ICIRCA.2018.8597310

  20. Gao, X., Mou, J., Banerjee, S., Cao, Y., Xiong, L., Chen, X.: An effective multiple-image encryption algorithm based on 3D cube and hyperchaotic map. J. King Saud Univ. Comput. Inf. Sci. 34(4), 1535–1551 (2022). https://doi.org/10.1016/j.jksuci.2022.01.017

    Article  Google Scholar 

  21. Patro, K.A.K., Acharya, B.: An efficient dual-layer cross-coupled chaotic map security-based multi-image encryption system. Nonlinear Dyn. 104(3), 2759–2805 (2021). https://doi.org/10.1007/s11071-021-06409-z

    Article  Google Scholar 

  22. Tang, Z., Song, J., Zhang, X., Sun, R.: Multiple-image encryption with bit-plane decomposition and chaotic maps. Opt. Lasers Eng. 80, 1–11 (2016). https://doi.org/10.1016/j.optlaseng.2015.12.004

    Article  Google Scholar 

  23. Zhang, L., Zhang, X.: Multiple-image encryption algorithm based on bit planes and chaos. Multimed. Tools Appl. 79(29–30), 20753–20771 (2020). https://doi.org/10.1007/s11042-020-08835-4

    Article  Google Scholar 

  24. Sahasrabuddhe, A., Laiphrakpam, D.S.: Multiple images encryption based on 3D scrambling and hyper-chaotic system. Inf. Sci. 550, 252–267 (2021). https://doi.org/10.1016/j.ins.2020.10.031

    Article  MathSciNet  Google Scholar 

  25. Li, Y., Zhang, F., Li, Y., Tao, R.: Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform. Opt. Lasers Eng. 72, 18–25 (2015). https://doi.org/10.1016/j.optlaseng.2015.03.027

    Article  Google Scholar 

  26. Gao, X., Mou, J., Xiong, L., Sha, Y., Yan, H., Cao, Y.: A fast and efficient multiple images encryption based on single-channel encryption and chaotic system. Nonlinear Dyn. 108(1), 613–636 (2022). https://doi.org/10.1007/s11071-021-07192-7

    Article  Google Scholar 

  27. Hu, K.Y., Wu, C., Wang, Y., Wang, J., Wang, Q.H.: An asymmetric multi-image cryptosystem based on cylindrical diffraction and phase truncation. Opt. Commun. 449, 100–109 (2019). https://doi.org/10.1016/j.optcom.2019.05.041

    Article  Google Scholar 

  28. Patro, K.A.K., Acharya, B.: A novel multi-dimensional multiple image encryption technique. Multimed. Tools Appl. 79(19–20), 12959–12994 (2020). https://doi.org/10.1007/s11042-019-08470-8

    Article  Google Scholar 

  29. Wang, X., Liu, C., Jiang, D.: A novel triple-image encryption and hiding algorithm based on chaos, compressive sensing and 3D DCT. Inf. Sci. 574, 505–527 (2021). https://doi.org/10.1016/j.ins.2021.06.032

    Article  MathSciNet  Google Scholar 

  30. Hoang, T.M.: A novel design of multiple image encryption using perturbed chaotic map. Multimed. Tools Appl. 81(18), 26535–26589 (2022). https://doi.org/10.1007/s11042-022-12139-0

    Article  Google Scholar 

  31. Dua, M., Kumar, A.: Multiple image encryption approach using non linear chaotic map and cosine transformation. Int. J. Inf. Technol. 14(3), 1627–1641 (2022)

    Google Scholar 

  32. Zhang, L., Wang, Y., Zhang, D.: Research on multiple-image encryption mechanism based on Radon transform and ghost imaging. Opt. Commun. 504, 127494 (2022). https://doi.org/10.1016/j.optcom.2021.127494

    Article  Google Scholar 

  33. Zhang, X., Zhang, L.: Multiple-image encryption algorithm based on chaos and gene fusion. Multimed. Tools Appl. 81(14), 20021–20042 (2022). https://doi.org/10.1007/s11042-022-12554-3

    Article  Google Scholar 

  34. Kocarev, L., Lian, S.: Chaos-Based Cryptography: Theory, Algorithms and Applications, vol. 354. Springer, Berlin (2011)

    Book  Google Scholar 

  35. Hua, Z., Zhou, Y., Huang, H.: Cosine-transform-based chaotic system for image encryption. Inf. Sci. 480, 403–419 (2019). https://doi.org/10.1016/j.ins.2018.12.048

    Article  Google Scholar 

  36. Young, L.-S.: Mathematical theory of Lyapunov exponents. J. Phys. A Math. Theor. 46(25), 254001 (2013)

    Article  MathSciNet  Google Scholar 

  37. Mondal, B., Singh, J.P.: A lightweight image encryption scheme based on chaos and diffusion circuit. Multimed. Tools Appl. 81(24), 34547–34571 (2022). https://doi.org/10.1007/s11042-021-11657-7

    Article  Google Scholar 

  38. Mondal, B.: A secure steganographic scheme based on chaotic map and DNA computing BT—micro-electronics and telecommunication engineering. In: Sharma, D.K., Balas, V.E., Le Son, H., Sharma, R., Cengiz, K. (eds.) Micro-Electronics and Telecommunication Engineering: Proceedings of 3rd ICMETE 2019, pp. 545–554. Springer, Singapore (2020)

  39. Dua, M., Kumar, A., Garg, A., Garg, V.: Multiple image encryption approach using non linear chaotic map and cosine transformation. Int. J. Inf. Technol. 14(3), 1627–1641 (2022). https://doi.org/10.1007/s41870-022-00885-1

    Article  Google Scholar 

  40. Benaissi, S., Chikouche, N., Hamza, R.: A novel image encryption algorithm based on hybrid chaotic maps using a key image. Optik 272, 170316 (2023). https://doi.org/10.1016/j.ijleo.2022.170316

    Article  Google Scholar 

  41. Kumar, A., Dua, M.: Novel pseudo random key & cosine transformed chaotic maps based satellite image encryption. Multimed. Tools Appl. 80(18), 27785–27805 (2021). https://doi.org/10.1007/s11042-021-10970-5

    Article  Google Scholar 

  42. Tiwari, D., Mondal, B., Singh, S.K., Koundal, D.: Lightweight encryption for privacy protection of data transmission in cyber physical systems. Cluster Comput. (2022). https://doi.org/10.1007/s10586-022-03790-1

    Article  Google Scholar 

  43. Suman, R.R., Mondal, B., Singh, S.K., Mandal, T.: A secure color image encryption scheme based on chaos. In: Machine Vision and Augmented Intelligence—Theory and Applications: Select Proceedings of MAI 2021, pp. 365–375 (2021)

  44. Pankaj, S., Dua, M.: A novel ToCC map and two-level scrambling-based medical image encryption technique. Netw. Model. Anal. Heal. Inform. Bioinforma. 10(1), 48 (2021). https://doi.org/10.1007/s13721-021-00324-4

    Article  Google Scholar 

  45. Dua, M., Suthar, A., Garg, A., Garg, V.: An ILM-cosine transform-based improved approach to image encryption. Complex Intell. Syst. 7(1), 327–343 (2021). https://doi.org/10.1007/s40747-020-00201-z

    Article  Google Scholar 

  46. Ye, H.-S., Zhou, N.-R., Gong, L.-H.: Multi-image compression-encryption scheme based on quaternion discrete fractional Hartley transform and improved pixel adaptive diffusion. Signal Process. 175, 107652 (2020). https://doi.org/10.1016/j.sigpro.2020.107652

    Article  Google Scholar 

  47. Wang, X., Wang, Y.: Multiple medical image encryption algorithm based on scrambling of region of interest and diffusion of odd-even interleaved points. Expert Syst. Appl. 213, 118924 (2023). https://doi.org/10.1016/j.eswa.2022.118924

    Article  Google Scholar 

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Kumar, A., Dua, M. A novel exponent–sine–cosine chaos map-based multiple-image encryption technique. Multimedia Systems 30, 141 (2024). https://doi.org/10.1007/s00530-024-01334-8

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