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A color image encryption and hiding algorithm based on hyperchaotic system and discrete cosine transform

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Abstract

Some existing image encryption schemes based on chaotic systems have various security defects, such as non-uniform distribution of the chaotic system's phase trajectory, narrow chaotic range, and the encryption algorithm easily to be cracked, etc. To solve these problems, a new color image encryption and hiding algorithm is proposed in this paper. Firstly, a two-dimensional cross-coupled chaotic model (2D-CCCM) is designed, which can generate a variety of hyperchaotic maps. Performance analysis demonstrates that they exhibit more complex chaotic behavior and a wider range of chaotic distribution than existing chaotic systems, and all of them enter the hyper-chaotic state when the system parameters are in the range of [1, ∞). Further, based on this chaotic system, a new color image encryption algorithm is proposed. The algorithm applies the cyclic shift operation and the improved out-inside shuffling algorithm to simultaneously scramble and diffuse the R, G, and B planes of the color image. Finally, two-dimensional discrete cosine transform is employed to embed the ciphertext image into the visually meaningful carrier image to further improve the security of the encryption algorithm. The main contributions of this study are twofold: firstly, the 2D-CCCM is proposed, and the generated chaotic system overcomes the drawbacks of existing chaotic systems; secondly, simulation analysis and security evaluation demonstrate that the proposed color image encryption and hiding algorithm has better encryption performance and higher security than several advanced image encryption algorithms.

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References

  1. Toughi, S., Fathi, M.H., Sekhavat, Y.A.: An image encryption scheme based on elliptic curve pseudo random and advanced encryption system. Signal Process. 141, 217–227 (2017)

    Google Scholar 

  2. Coppersmith, D.: The data encryption standard (DES) and its strength against attacks. IBM J. Res. Dev. 38(3), 243–250 (1994)

    MATH  Google Scholar 

  3. Qiu, H., Xu, X., Jiang, Z., Sun, K., Xiao, C.: A color image encryption algorithm based on hyperchaotic map and Rubik’s Cube scrambling. Nonlinear Dyn. 108, 4459–4470 (2022)

    Google Scholar 

  4. Xin, J., Hu, H., Zheng, J.: 3D variable-structure chaotic system and its application in color image encryption with new Rubik’s Cube-like permutation. Nonlinear Dyn. 111(8), 7859–7882 (2023)

    Google Scholar 

  5. Sun, F., Lv, Z.: A secure image encryption based on spatial surface chaotic system and AES algorithm. Multimed. Tools. Appl. 81(3), 3959–3979 (2021)

    Google Scholar 

  6. Niyat, A.Y., Moattar, M.H., Torshiz, M.N.: Color image encryption based on hybrid hyper-chaotic system and cellular automata. Opt Lasers Eng 90, 225–237 (2017)

    Google Scholar 

  7. Wang, X., Liu, C., Jiang, D.: An efficient double-image encryption and hiding algorithm using a newly designed chaotic system and parallel compressive sensing. Inf. Sci. 610, 300–325 (2022)

    Google Scholar 

  8. Yildirim, M.: Optical color image encryption scheme with a novel DNA encoding algorithm based on a chaotic circuit. Chaos Solitons Fractals 155, 111631 (2022)

    MathSciNet  Google Scholar 

  9. Huang, X., Dong, Y., Zhu, H., Ye, G.: Visually asymmetric image encryption algorithm based on SHA-3 and compressive sensing by embedding encrypted image. Alex. Eng. J. 61(10), 7637–7647 (2022)

    Google Scholar 

  10. Gao, X.: Image encryption algorithm based on 2D hyperchaotic map. Opt Laser Technol 142, 107252 (2021)

    Google Scholar 

  11. Hua, Z., Zhu, Z., Yi, S., Zhang, Z., Huang, H.: Cross-plane colour image encryption using a two-dimensional logistic tent modular map. Inf. Sci. 546, 1063–1083 (2021)

    MathSciNet  Google Scholar 

  12. Teng, L., Wang, X., Yang, F., Xian, Y.: Color image encryption based on cross 2D hyperchaotic map using combined cycle shift scrambling and selecting diffusion. Nonlinear Dyn. 105(2), 1859–1876 (2021)

    Google Scholar 

  13. Wang, X., Leng, Z.: A Dynamic Image Encryption Algorithm Based on Improved Ant Colony Walking Path Thought. Sens. Imaging 23(1), 2050060 (2022)

    Google Scholar 

  14. Xu, C., Sun, J., Wang, C.: An Image Encryption Algorithm Based on Random Walk and Hyperchaotic Systems. Int J Bifurcat Chaos 30(04), 2050060 (2020)

    MathSciNet  Google Scholar 

  15. Dong, W., Li, Q., Tang, Y.: Image encryption-then-transmission combining random sub-block scrambling and loop DNA algorithm in an optical chaotic system. Chaos Solitons Fractals 153, 111539 (2021)

    MathSciNet  Google Scholar 

  16. Dong, Y., Huang, X., Ye, G., Tan, Z.: Visually Meaningful Image Encryption Scheme Based on DWT and Schur Decomposition. Secur. Commun. Netw. 2021, 1–16 (2021)

    Google Scholar 

  17. Ghaffari, A.: Image compression-encryption method based on two-dimensional sparse recovery and chaotic system. Sci Rep 11(1), 369 (2021)

    MathSciNet  Google Scholar 

  18. He, Y., Zhang, Y.-Q., Wang, X.-Y.: A new image encryption algorithm based on two-dimensional spatiotemporal chaotic system. Neural. Comput. Appl. 32(1), 247–260 (2018)

    Google Scholar 

  19. Huang, H., Yang, S., Ye, R.: Efficient symmetric image encryption by using a novel 2D chaotic system. IET Image Process 14(6), 1157–1163 (2020)

    Google Scholar 

  20. Hua, Z., Zhu, Z., Chen, Y., Li, Y.: Color image encryption using orthogonal Latin squares and a new 2D chaotic system. Nonlinear Dyn. 104(4), 4505–4522 (2021)

    Google Scholar 

  21. Kumar, K., Roy, S., Rawat, U., Malhotra, S.: IEHC: An efficient image encryption technique using hybrid chaotic map. Chaos Solitons Fractals 158, 111994 (2022)

    MATH  Google Scholar 

  22. Li, M., Wang, M., Fan, H., An, K., Liu, G.: A novel plaintext-related chaotic image encryption scheme with no additional plaintext information. Chaos Solitons Fractals 158, 111989 (2022)

    MathSciNet  Google Scholar 

  23. Liu, W., Sun, K., Zhu, C.: A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84, 26–36 (2016)

    Google Scholar 

  24. Liu, X., Tong, X., Wang, Z., Zhang, M.: Uniform non-degeneracy discrete chaotic system and its application in image encryption. Nonlinear Dyn. 108(1), 653–682 (2022)

    Google Scholar 

  25. Nan, S.-X., Feng, X.-F., Wu, Y.-F., Zhang, H.: Remote sensing image compression and encryption based on block compressive sensing and 2D-LCCCM. Nonlinear Dyn. 108(3), 2705–2729 (2022)

    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)

    Google Scholar 

  27. Wang, X., Chen, X.: An image encryption algorithm based on dynamic row scrambling and Zigzag transformation. Chaos Solitons Fractals 147, 110962 (2021)

    MathSciNet  MATH  Google Scholar 

  28. Naskar, P.K., Bhattacharyya, S., Mahatab, K.C., Dhal, K.G., Chaudhuri, A.: An efficient block-level image encryption scheme based on multi-chaotic maps with DNA encoding. Nonlinear Dyn. 105(4), 3673–3698 (2021)

    Google Scholar 

  29. Peng, H.-h., Xu, X.-m., Yang, B.-c., Yin, L.-z.: Implication of Two-Coupled Differential Van der Pol Duffing Oscillator in Weak Signal Detection. J. Phys. Soc. Jpn. 85(4), 044005 (2016)

  30. Sahasrabuddhe, A., Laiphrakpam, D.S.: Multiple images encryption based on 3D scrambling and hyper-chaotic system. Inf. Sci. 550, 252–267 (2021)

    MathSciNet  MATH  Google Scholar 

  31. Teng, L., Wang, X., Xian, Y.: Image encryption algorithm based on a 2D-CLSS hyperchaotic map using simultaneous permutation and diffusion. Inf. Sci. 605, 71–85 (2022)

    Google Scholar 

  32. Bao, L., Zhou, Y.: Image encryption: Generating visually meaningful encrypted images. Inf. Sci. 324, 197–207 (2015)

    MathSciNet  MATH  Google Scholar 

  33. Yu, S.-S., Zhou, N.-R., Gong, L.-H., Nie, Z.: Optical image encryption algorithm based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system. Opt Lasers Eng 124, 105816 (2020)

    Google Scholar 

  34. Zhang, Y., Xie, H., Sun, J., Zhang, H.: An efficient multi-level encryption scheme for stereoscopic medical images based on coupled chaotic system and Otsu threshold segmentation. Comput. Biol. Med. 146, 105542 (2022)

    Google Scholar 

  35. Zhou, W., Wang, X., Wang, M., Li, D.: A new combination chaotic system and its application in a new Bit-level image encryption scheme. Opt Lasers Eng 149, 106782 (2022)

    Google Scholar 

  36. Zhu, L., Jiang, D., Ni, J., Wang, X., Rong, X., Ahmad, M.: A visually secure image encryption scheme using adaptive-thresholding sparsification compression sensing model and newly-designed memristive chaotic map. Inf. Sci. 607, 1001–1022 (2022)

    Google Scholar 

  37. Wu, Y.: Image encryption using the two-dimensional logistic chaotic map. J Electron Imaging 21(1), 013014 (2012)

    Google Scholar 

  38. Hua, Z., Zhou, Y., Pun, C.-M., Chen, C.L.P.: 2D Sine Logistic modulation map for image encryption. Inf. Sci. 297, 80–94 (2015)

    Google Scholar 

  39. Rong, K., Bao, H., Li, H., Hua, Z., Bao, B.: Memristive Hénon map with hidden Neimark-Sacker bifurcations. Nonlinear Dyn. 108(4), 4459–4470 (2022)

    Google Scholar 

  40. Luo, J., Xu, X., Ding, Y., Yuan, Y., Yang, B., Sun, K., et al.: Application of a memristor-based oscillator to weak signal detection. Eur. Phys. J. Plus 133(6), 239 (2018)

    Google Scholar 

  41. ul Haq, T., Shah, T.: 4D mixed chaotic system and its application to RGB image encryption using substitution-diffusion. J Inf Secur Appl 61, 102931 (2021)

  42. Wang, X., Guan, N.: 2D sine-logistic-tent-coupling map for image encryption. J. Ambient. Intell. Humaniz. Comput, 1–21 (2022)

  43. Wang, X., Guan, N., Yang, J.: Image encryption algorithm with random scrambling based on one-dimensional logistic self-embedding chaotic map. Chaos Solitons Fractals 150, 111117 (2021)

    MathSciNet  Google Scholar 

  44. Xian, Y., Wang, X.: Fractal sorting matrix and its application on chaotic image encryption. Inf. Sci. 547, 1154–1169 (2021)

    MathSciNet  MATH  Google Scholar 

  45. Xu, J., Mou, J., Xiong, L., Li, P., Hao, J.: A flexible image encryption algorithm based on 3D CTBCS and DNA computing. Multimed. Tools. Appl. 80(17), 25711–25740 (2021)

    Google Scholar 

  46. Yang, Z., Cao, Y., Ji, Y., Liu, Z., Chen, H.: Securing color image by using bit-level modified integer nonlinear coupled chaos model in Fresnel diffraction domains. Opt Lasers Eng 152, 106969 (2022)

    Google Scholar 

  47. Xu, S., Wang, X., Ye, X.: A new fractional-order chaos system of Hopfield neural network and its application in image encryption. Chaos Solitons Fractals 157, 111889 (2022)

    MathSciNet  MATH  Google Scholar 

  48. Ye, G., Jiao, K., Huang, X.: Quantum logistic image encryption algorithm based on SHA-3 and RSA. Nonlinear Dyn. 104(3), 2807–2827 (2021)

    Google Scholar 

  49. 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)

    Google Scholar 

  50. Ahmad, I., Shin, S.: A novel hybrid image encryption–compression scheme by combining chaos theory and number theory. Signal Process-Image Commun. 98, 116418 (2021)

    Google Scholar 

  51. Chai, X., Bi, J., Gan, Z., Liu, X., Zhang, Y., Chen, Y.: Color image compression and encryption scheme based on compressive sensing and double random encryption strategy. Signal Process. 176, 107684 (2020)

    Google Scholar 

  52. Chai, X., Gan, Z., Chen, Y., Zhang, Y.: A visually secure image encryption scheme based on compressive sensing. Signal Process. 134, 35–51 (2017)

    Google Scholar 

  53. Chai, X., Wu, H., Gan, Z., Zhang, Y., Chen, Y., Nixon, K.W.: An efficient visually meaningful image compression and encryption scheme based on compressive sensing and dynamic LSB embedding. Opt Lasers Eng 124, 105837 (2020)

    Google Scholar 

  54. Huang, X., Dong, Y., Ye, G., Shi, Y.: Meaningful image encryption algorithm based on compressive sensing and integer wavelet transform. Front. Comput. Sci. 17(3), 173804 (2022)

    Google Scholar 

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Funding

The work was supported by the National Natural Science Foundation of China (Grant Nos.61927803, 61071025, 61502538, and 61501525) and the Natural Science Foundation of Hunan Province of China (Grant No. 2015JJ3157).

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Authors and Affiliations

  1. School of Physics and Electronics, Central South University, Changsha, 410012, China

    Xiao Wang, Xuemei Xu, Kehui Sun, Mingjun Li & Jun Wen

  2. School of Automation, Central South University, Changsha, 410083, China

    Zhaohui Jiang

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  1. Xiao Wang
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Correspondence to Xuemei Xu.

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Wang, X., Xu, X., Sun, K. et al. A color image encryption and hiding algorithm based on hyperchaotic system and discrete cosine transform. Nonlinear Dyn 111, 14513–14536 (2023). https://doi.org/10.1007/s11071-023-08538-z

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