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A fast visually meaningful image encryption algorithm based on compressive sensing and joint diffusion and scrambling

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Abstract

This paper introduces a novel Fast Visually Meaningful Image Encryption based on Compressive Sensing and Joint Diffusion and Scrambling (FVMIECJ). Our approach leverages several innovative aspects: First, we employ a novel seven-dimensional (7D) hyper-chaotic system to generate the measurement matrix for Compressive Sensing (CS) and the random sequences essential for subsequent encryption operations. Utilizing this 7D hyper-chaotic system enhances the randomness and security of the image encryption process. Second, we propose a novel joint diffusion and scrambling encryption scheme to improve the security performance of the algorithm further. This algorithm combines different cryptographic techniques to provide robust protection against attacks. Finally, we present an efficient visual image encryption framework for high-speed encryption applications. This framework ensures robust security and delivers exceptional encryption speed, making it suitable for scenarios where fast encryption is required. Through simulations and comparative analysis, FVMIECJ demonstrated outstanding performance in terms of security and speed, making it a promising solution for image encryption applications.

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Data Availibility Statement

The USC-SIPI dataset analysed in this paper are available in the USC-SIPI repository, URL: https://sipi.usc.edu/database/database.php?volume=misc. The BossBase 1.01 dataset analysed in this paper are available in the BossBase 1.01 repository, URL: http://dde.binghamton.edu/download/. The source codes of FVMIECJ algorithm are available in the GitHub repository, URL: https://github.com/wushuang42/FVMIECJ.

Abbreviations

CS::

Compressive sensing

FVMIECJ::

Fast Visually Meaningful Image Encryption algorithm based on Compressive sensing and Joint diffusion and scrambling

LSB::

Least Significant Bit

7D::

Seven-dimensional

DNA::

Deoxyribonucleic Acid

VMIE::

Visually Meaningful Image Encryption algorithm

IWT::

Discrete Integer Wavelet Transform

SVD::

Singular Value Decomposition

DCT::

Discrete Cosine Transform

LE::

Lyapunov Exponents

FFT::

Fast Fourier Transform

DWT::

Discrete Wavelet Transform

LL::

Low-Low Component

LH::

Low-High Component

HL::

High-Low Component

HH::

High-High Component

RIP::

Restricted Isometry Property

MP::

Matching pursuit

OMP::

Orthogonal Matching Pursuit

\(\varvec{\textrm{SL}}\) \({_0}\)::

Smoothed \(l_0\) norm

SHA-256::

Secure Hash Algorithm 256-bit

CR::

Compression Ratio

PSNR::

Peak Signal-to-Noise Ratio

MSSIM::

Mean Structural Similarity

MSE::

Mean Square Error

TS::

Threshold

CC::

Correlation Coefficient

References

  1. Li X-W (2015) I-K Lee Modified computational integral imaging-based double image encryption using fractional fourier transform. Opt Lasers Eng 66:112–121

    Google Scholar 

  2. Wang Y, Quan C, Tay CJ (2016) Asymmetric optical image encryption based on an improved amplitude-phase retrieval algorithm. Opt Lasers Eng 78:8–16

    Google Scholar 

  3. Chai X, Gan Z, Yuan K, Chen Y, Liu X (2019) A novel image encryption scheme based on dna sequence operations and chaotic systems. Neural Comput Appl 31(1):219–237

    Google Scholar 

  4. Chen J, Chen L, Zhou Y (2020) Cryptanalysis of a dna-based image encryption scheme. Inf Sci 520:130–141

    MathSciNet  Google Scholar 

  5. Wang X, Li Y (2021) Chaotic image encryption algorithm based on hybrid multi-objective particle swarm optimization and dna sequence. Opt Lasers Eng 137:106393

    Google Scholar 

  6. Abbasi AA, Mazinani M, Hosseini R (2020) Chaotic evolutionary-based image encryption using rna codons and amino acid truth table. Opt Laser Technol 132:106465

    Google Scholar 

  7. Liu L, Lei Y, Wang D (2020) A fast chaotic image encryption scheme with simultaneous permutation-diffusion operation. IEEE Access 8:27361–27374

    Google Scholar 

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

    MathSciNet  Google Scholar 

  9. Wang X, Guan N (2020) A novel chaotic image encryption algorithm based on extended zigzag confusion and rna operation. Opt Laser Technol 131:106366

    Google Scholar 

  10. Wang X, Liu L (2021) Application of chaotic josephus scrambling and rna computing in image encryption. Multimed Tools Appl 80:23337–23358

  11. Zhang D, Chen L, Li T (2021) Hyper-chaotic color image encryption based on transformed zigzag diffusion and rna operation. Entropy 23(3):361

    MathSciNet  Google Scholar 

  12. Zhou N, Yan X, Liang H, Tao X, Li G (2018) Multi-image encryption scheme based on quantum 3d arnold transform and scaled zhongtang chaotic system. Quantum Inf Process 17(12):1–36

  13. Chai X, Gan Z, Yang K, Chen Y, Liu X (2017) An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and dna sequence operations. Signal Process Image Commun 52:6–19

    Google Scholar 

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

    Google Scholar 

  15. Yang Y-G, Guan B-W, Li J, Li D, Zhou Y-H, Shi W-M (2019) Image compression-encryption scheme based on fractional order hyper-chaotic systems combined with 2d compressed sensing and dna encoding. Opt Laser Technol 119:105661

    Google Scholar 

  16. Diab H (2018) An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations. IEEE Access 6:42227–42244

    Google Scholar 

  17. Hu T, Liu Y, Gong L-H, Guo S-F, Yuan H-M (2017) Chaotic image cryptosystem using dna deletion and dna insertion. Signal Process 134:234–243

    Google Scholar 

  18. Hu T, Liu Y, Gong L-H, Ouyang C-J (2017) An image encryption scheme combining chaos with cycle operation for dna sequences. Nonlinear Dyn 87(1):51–66

    Google Scholar 

  19. Li T, Shi J, Zhang D (2021) Color image encryption based on joint permutation and diffusion. J Electron Imaging 30(01):013008

  20. Fang H, Vorobyov SA, Jiang H, Taheri O (2014) Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2d sparse signals. IEEE Trans Signal Process 62(1):196–210

    MathSciNet  Google Scholar 

  21. Zhou N, Jiang H, Gong L, Xie X (2018) Double-image compression and encryption algorithm based on co-sparse representation and random pixel exchanging. Opt Lasers Eng 110:72–79

    Google Scholar 

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

    MathSciNet  Google Scholar 

  23. Kanso A, Ghebleh M (2017) An algorithm for encryption of secret images into meaningful images. Opt Lasers Eng 90:196–208

    Google Scholar 

  24. Wen W, Zhang Y, Fang Y, Fang Z (2018) Image salient regions encryption for generating visually meaningful ciphertext image. Neural Comput Appl 29(3):653–663

    Google Scholar 

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

    Google Scholar 

  26. Huo D, Zhu Z, Wei L, Han C, Zhou X (2021) A visually secure image encryption scheme based on 2d compressive sensing and integer wavelet transform embedding. Opt Commun 492:126976

    Google Scholar 

  27. Zhu L, Song H, Zhang X, Yan M, Zhang T, Wang X, Xu J (2020) A robust meaningful image encryption scheme based on block compressive sensing and svd embedding. Signal Process 175:107629

    Google Scholar 

  28. Jiang D, Liu L, Zhu L, Wang X, Rong X, Chai H (2021) Adaptive embedding: a novel meaningful image encryption scheme based on parallel compressive sensing and slant transform. Signal Process 188:108220

    Google Scholar 

  29. Wang X, Liu C, Jiang D (2021) A novel triple-image encryption and hiding algorithm based on chaos, compressive sensing and 3d dct. Inf Sci 574:505–527

    MathSciNet  Google Scholar 

  30. Wang X, Ren Q, Jiang D (2021) An adjustable visual image cryptosystem based on 6d hyperchaotic system and compressive sensing. Nonlinear Dyn 104(4):4543–4567

    Google Scholar 

  31. Yang Y-G, Wang B-P, Yang Y-L, Zhou Y-H, Shi W-M, Liao X (2023) A visually meaningful image encryption algorithm based on adaptive 2d compressive sensing and chaotic system. Multimed Tools Appl 82:22033–22062

  32. Ye G, Pan C, Dong Y, Shi Y, Huang X (2020) Image encryption and hiding algorithm based on compressive sensing and random numbers insertion. Signal Process 172:107563

    Google Scholar 

  33. Chai X, Wu H, Gan Z, Zhang Y, Chen Y (2020) Hiding cipher-images generated by 2-d compressive sensing with a multi-embedding strategy. Signal Process 171:107525

    Google Scholar 

  34. Ponuma R, Amutha R, Aparna S, Gopal G (2019) Visually meaningful image encryption using data hiding and chaotic compressive sensing. Multimed Tools Appl 78(18):25707–25729

    Google Scholar 

  35. Zhang D, Shafiq M, Wang L, Srivastava G, Yin S (2023) Privacy-preserving remote sensing images recognition based on limited visual cryptography. CAAI Trans Intell Technol 8:1166–1177

  36. Zhang D, Ren L, Shafiq M, Gu Z (2022) A lightweight privacy-preserving system for the security of remote sensing images on iot. Remote Sensing 14(24):6371

    Google Scholar 

  37. Ren L, Zhang D (2022) A privacy-preserving biometric recognition system with visual cryptography. Adv Multimed 1–7:2022

    Google Scholar 

  38. Mukherjee I, Ganguly R (2018) Multiple video clips preservation using folded back audio-visual cryptography scheme. Multimed Tools Appl 77(5):5281–5301

    Google Scholar 

  39. Tripathi J, Saini A, Kishan Nikhil, Shazad (2020) An augmented model for image security: enhanced visual cryptography. Procedia Comput Sci 167:323–333

  40. Al-Obeidi AS, Fawzi Al-Azzawi S, Abdullah Hamad A, Lellis Thivagar M, Meraf Z, Ahmad S (2021) A novel of new 7d hyperchaotic system with self-excited attractors and its hybrid synchronization. Comput Intell Neurosci 2021:3081345

    Google Scholar 

  41. Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306

    MathSciNet  Google Scholar 

  42. Candes EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(12):4203–4215

    MathSciNet  Google Scholar 

  43. Mallat SG, Zhang Z (1993) Matching pursuits with time-frequency dictionaries. IEEE Trans Signal Process 41(12):3397–3415

    Google Scholar 

  44. Needell D, Tropp JA (2009) Cosamp: iterative signal recovery from incomplete and inaccurate samples. Appl Comput Harmon Anal 26(3):301–321

    MathSciNet  Google Scholar 

  45. Mohimani H, Babaie-Zadeh M, Jutten C (2009) A fast approach for overcomplete sparse decomposition based on smoothed \(\ell ^{0}\) norm. IEEE Trans Signal Process 57(1):289–301

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  47. Wen W, Hong Y, Fang Y, Li M, Li M (2020) A visually secure image encryption scheme based on semi-tensor product compressed sensing. Signal Process 173:107580

    Google Scholar 

  48. Li C, Zhang Y, Xie EY (2019) When an attacker meets a cipher-image in 2018: a year in review. J Inf Secur Appl 48:102361

    Google Scholar 

  49. 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

    Google Scholar 

  50. Li C, Lin D, Lu J, Hao F (2018) Cryptanalyzing an image encryption algorithm based on autoblocking and electrocardiography. IEEE Multimedia 25(4):46–56

    Google Scholar 

  51. Zhu L, Jiang D, Ni J, Wang X, Rong X, Ahmad M, Chen Y (2022) A stable meaningful image encryption scheme using the newly-designed 2d discrete fractional-order chaotic map and bayesian compressive sensing. Signal Process 195:108489

    Google Scholar 

  52. Wang X, Liu C, Jiang D (2022) A novel visually meaningful image encryption algorithm based on parallel compressive sensing and adaptive embedding. Expert Syst Appl 209:118426

    Google Scholar 

  53. Wang X, Liu C, Jiang D (2022) Visually meaningful image encryption scheme based on new-designed chaotic map and random scrambling diffusion strategy. Chaos Solitons Fractal 164:112625

    MathSciNet  Google Scholar 

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

    Google Scholar 

  55. Wang H, Xiao D, Li M, Xiang Y, Li X (2019) A visually secure image encryption scheme based on parallel compressive sensing. Signal Process 155:218–232

    Google Scholar 

  56. Gan Z, Sun M, Song Y, Chai X, Jiang D, Long G, He X (2023) Visually meaningful image encryption scheme using multi-parameter fractal theory and block synchronous sorting diffusion. Phys Scr 98(8):085216

    Google Scholar 

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Acknowledgements

This work was supported by the Guanghua Youth Project of Southwestern University of Finance and Economics (Grant no. 220810001002020113).

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Authors and Affiliations

  1. School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Duzhong Zhang, Chao Yan, Yun Duan, Sijian Liang, Jiang Wu & Taiyong Li

  2. Joint Institute of Intelligent Payment, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Duzhong Zhang, Jiang Wu & Taiyong Li

Authors
  1. Duzhong Zhang
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  2. Chao Yan
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  3. Yun Duan
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  4. Sijian Liang
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  5. Jiang Wu
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Contributions

Duzhong Zhang: Conceptualization, Methodology, Software, Writing - original draft. Chao Yan: Software, Validation. Yun Duan: Validation, Writing - review & editing. Sijian Liang: Validation, Writing - review & editing. Jiang Wu: Methodology, Writing - review & editing. Taiyong Li: Conceptualization, Methodology, Writing - review & editing.

Corresponding author

Correspondence to Taiyong Li.

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Appendices

Appendix A

Fig. 11
figure 11

The attractors of 7D hyper-chaotic system

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Fig. 12
figure 12

The flowchart of decryption processes

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Appendix B

Algorithm 1
figure a

Joint diffusion and scrambling encryption.

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Zhang, D., Yan, C., Duan, Y. et al. A fast visually meaningful image encryption algorithm based on compressive sensing and joint diffusion and scrambling. Multimed Tools Appl 83, 70693–70725 (2024). https://doi.org/10.1007/s11042-024-18343-4

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