Skip to main content
SpringerLink
Log in

A fast image encryption algorithm with variable key space

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

The security of images is of great importance given the current development of Internet technology. The existing encryption algorithms have some defects, such as the key space is not large enough and the encryption speed is slow. A fast image encryption algorithm with variable key space is proposed. The algorithm key space is dynamically changeable and the variable key space is associated with the initial condition of Hénon map, making this cryptosystem extremely sensitive to the key. The overall algorithm uses a permutation-diffusion-permutation-diffusion encryption structure. The first permutation process is implemented by cross-sampling and the first diffusion is implemented by modal operation. The second permutation is implemented using the chaotic sequence approach and the second diffusion is implemented using the XOR operation. The designed permutation and diffusion operations are executed with high efficiency, and the two different diffusion operations make the encryption process with nonlinear mapping capability, making the algorithm effective against existing typical differential attack schemes. Experiments show that the algorithm has a dynamically adjustable key space, high efficiency of algorithm encryption, good robustness, and effective resistance to statistical attack analysis and differential attack analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Algorithm 1
Fig. 3
Algorithm 2
Fig. 4
Algorithm 3
Fig. 5
Algorithm 4
Algorithm 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Jain K, Aji A, Krishnan P (2021) Medical image encryption scheme using multiple chaotic maps. Pattern Recogn Lett 152:356–364

    Google Scholar 

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

    Google Scholar 

  3. Idrees B, Zafar S, Rashid T, Gao W (2020) Image encryption algorithm using s-box and dynamic hénon bit level permutation. Multimedia Tools and Applications 79:6135–6162

    Google Scholar 

  4. Ding Y, Tan F, Qin Z, Cao M, Choo K-KR, Qin Z (2021) Deepkeygen: a deep learning-based stream cipher generator for medical image encryption and decryption. IEEE Trans Neural Netw Learn Syst 33(9):4915–4929

    Google Scholar 

  5. 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  Google Scholar 

  6. Sun F, Liu S, Li Z, Lü Z (2008) A novel image encryption scheme based on spatial chaos map. Chaos, Solitons & Fractals 38(3):631–640

    MathSciNet  Google Scholar 

  7. Ogasahara Y, Hori Y, Koike H (2016) Implementation of pseudo linear feedback shift register physical unclonable function on silicon. In: 2016 IEEE international symposium on circuits and systems (ISCAS), pp 758–761. IEEE

  8. Roy M, Chakraborty S, Mali K (2021) A chaotic framework and its application in image encryption. Multimedia Tools and Applications 80:24069–24110

    Google Scholar 

  9. Zhang Y-Q, He Y, Li P, Wang X-Y (2020) A new color image encryption scheme based on 2dnlcml system and genetic operations. Opt Lasers Eng 128:106040

    Google Scholar 

  10. Talhaoui MZ, Wang X, Midoun MA (2021) A new one-dimensional cosine polynomial chaotic map and its use in image encryption. The Visual Computer 37:541–551

    Google Scholar 

  11. Ali TS, Ali R (2020) A new chaos based color image encryption algorithm using permutation substitution and boolean operation. Multimedia Tools and Applications 79(27–28):19853–19873

    Google Scholar 

  12. Zhang X, Wang L, Zhou Z, Niu Y (2019) A chaos-based image encryption technique utilizing hilbert curves and h-fractals. IEEE Access 7:74734–74746

    Google Scholar 

  13. Sneha P, Sankar S, Kumar AS (2020) A chaotic colour image encryption scheme combining walsh-hadamard transform and arnold-tent maps. J Ambient Intell Humanized Comput 11:1289–1308

    Google Scholar 

  14. Li Q, Wang X, Wang X, Ma B, Wang C, Xian Y, Shi Y (2020) A novel grayscale image steganography scheme based on chaos encryption and generative adversarial networks. IEEE Access 8:168166–168176

    Google Scholar 

  15. Pourjabbar Kari A, Habibizad Navin A, Bidgoli AM, Mirnia M (2021) A new image encryption scheme based on hybrid chaotic maps. Multimedia Tools and Applications 80:2753–2772

    Google Scholar 

  16. Chai X, Zheng X, Gan Z, Han D, Chen Y (2018) An image encryption algorithm based on chaotic system and compressive sensing. Signal Process 148:124–144

    Google Scholar 

  17. Fernandez-Carames TM, Fraga-Lamas P (2020) Towards post-quantum blockchain: A review on blockchain cryptography resistant to quantum computing attacks. IEEE Access 8:21091–21116

    Google Scholar 

  18. Zhou NR, Hua TX, Gong LH, Pei DJ, Liao QH (2015) Quantum image encryption based on generalized arnold transform and double random-phase encoding. Quantum Inf Process 14:1193–1213

    MathSciNet  Google Scholar 

  19. Cheng G, Wang C, Xu C (2020) A novel hyper-chaotic image encryption scheme based on quantum genetic algorithm and compressive sensing. Multimedia Tools and Applications 79(39–40):29243–29263

    Google Scholar 

  20. Ye G, Jiao K, Huang X (2021) Quantum logistic image encryption algorithm based on sha-3 and rsa. Nonlinear Dynamics 104:2807–2827

    Google Scholar 

  21. Pareek NK, Patidar V, Sud KK (2006) mage encryption using chaotic logistic map. Image and Vision Computing 24(9):926–934

    Google Scholar 

  22. Wang Y, Wong K-W, Liao X, Chen G (2011) A new chaos-based fast image encryption algorithm. Applied Soft Computing 11(1):514–522

    Google Scholar 

  23. Chai X, Chen Y, Broyde L (2017) novel chaos-based image encryption algorithm using dna sequence operations. Optics Lasers Eng 88:197–213

    Google Scholar 

  24. Zhou M, Wang C (2020) A novel image encryption scheme based on conservative hyperchaotic system and closed-loop diffusion between blocks. Signal Process 171:107484

    Google Scholar 

  25. Xiang H, Liu L (2021) A novel image encryption algorithm based on improved key selection and digital chaotic map. Multimedia Tools and Applications 80:22135–22162

    Google Scholar 

  26. Kaur M, Kumar V (2020) A comprehensive review on image encryption techniques. Archives Comput Methods Eng 27:15–43

    MathSciNet  Google Scholar 

  27. Tsafack N, Kengne J, Abd-El-Atty B, Iliyasu AM, Hirota K, Abd-EL-Latif AA (2020) Design and implementation of a simple dynamical 4-d chaotic circuit with applications in image encryption. Inf Sci 515:191–217

    Google Scholar 

  28. Wu G-C, Deng Z-G, Baleanu D, Zeng D-Q (2019) New variable-order fractional chaotic systems for fast image encryption. Chaos : An Interdisciplinary J Nonlinear Sci 29(8):083103

    MathSciNet  Google Scholar 

  29. Li S, Chen G, Mou X (2005) On the dynamical degradation of digital piecewise linear chaotic maps. Int J Bifurcation Chaos 15(10):3119–3151

    MathSciNet  Google Scholar 

  30. Xu Q, Sun K, Cao C, Zhu C (2019) A fast image encryption algorithm based on compressive sensing and hyperchaotic map. Optics Lasers Eng 121:203–214

    Google Scholar 

  31. Wu J, Xia W, Zhu G, Liu H, Ma L, Xiong J (2021) Image encryption based on adversarial neural cryptography and sha controlled chaos. J Mod Opt 68(8):409–418

    MathSciNet  Google Scholar 

  32. Yu J, Xie W, Zhong Z, Wang H (2022) Image encryption algorithm based on hyperchaotic system and a new dna sequence operation. Chaos, Solitons & Fractals 162:112456

    MathSciNet  Google Scholar 

  33. Meranza-Castillón M, Murillo-Escobar M, López-Gutiérrez R, Cruz-Hernández C (2019) Pseudorandom number generator based on enhanced hénon map and its implementation. AEU-International J Electron Commun 107:239–251

    Google Scholar 

  34. Ibrahim S, Alharbi A (2020) Efficient image encryption scheme using henon map, dynamic s-boxes and elliptic curve cryptography. IEEE Access 8:194289–194302

    Google Scholar 

  35. Ping P, Xu F, Mao Y, Wang Z (2018) Designing permutation-substitution image encryption networks with henon map. Neurocomputing 283:53–63

    Google Scholar 

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

    MathSciNet  Google Scholar 

  37. Tsafack N, Kengne J, Abd-El-Atty B, Iliyasu AM, Hirota K, Abd-EL-Latif AA (2020) Design and implementation of a simple dynamical 4-d chaotic circuit with applications in image encryption. Inf Sci 515:191–217

    Google Scholar 

  38. Wu Y, Noonan JP, Agaian S et al (2011) Npcr and uaci randomness tests for image encryption. Cyber journals: multidisciplinary journals in science and technology. J Selected Areas Telecommun (JSAT) 1(2):31–38

    Google Scholar 

  39. Wu Y, Zhou Y, Saveriades G, Agaian S, Noonan JP, Natarajan P (2013) Local shannon entropy measure with statistical tests for image randomness. Inf Sci 222:323–342

    MathSciNet  Google Scholar 

  40. Rukhin A, Soto J, Nechvatal J, Smid M, Barker E (2001) A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical report, Booz-allen and hamilton inc mclean va

    Google Scholar 

  41. Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings eighth IEEE international conference on computer vision. ICCV 2001, vol 2, pp 416–423

  42. Sun S (2017) Chaotic image encryption scheme using two-by-two deoxyribonucleic acid complementary rules. Opt Eng 56(11):116117–116117

    Google Scholar 

  43. Xie EY, Li C, Yu S, Lü J (2017) On the cryptanalysis of fridrich’s chaotic image encryption scheme. Signal Process 132:150–154

    Google Scholar 

  44. Wang H, Xiao D, Chen X, Huang H (2018) Cryptanalysis and enhancements of image encryption using combination of the 1d chaotic map. Signal Process 144:444–452

    Google Scholar 

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

    Google Scholar 

  46. Chen J, Chen L, Zhou Y (2020) Cryptanalysis of image ciphers with permutation-substitution network and chaos. IEEE Trans Circ Syst Video Technol 31(6):2494–2508

    Google Scholar 

  47. Zheng Y, Jin J (2015) A novel image encryption scheme based on hénon map and compound spatiotemporal chaos. Multimedia Tools and Applications 74:7803–7820

    Google Scholar 

  48. Wang X, Wang Y, Zhu X, Luo C (2020) A novel chaotic algorithm for image encryption utilizing one-time pad based on pixel level and dna level. Optics Lasers Eng 125:105851

    Google Scholar 

  49. Luo Y, Ouyang X, Liu J, Cao L (2019) An image encryption method based on elliptic curve elgamal encryption and chaotic systems. IEEE Access 7:38507–38522

    Google Scholar 

  50. Dhall S, Pal SK, Sharma K (2022) A chaos-based probabilistic block cipher for image encryption. J King Saud University-Comput Inf Sci 34(1):1533–1543

    Google Scholar 

  51. Wang X, Zhu X, Wu X, Zhang Y (2018) Image encryption algorithm based on multiple mixed hash functions and cyclic shift. Optics Lasers Eng 107:370–379

    Google Scholar 

  52. Hua Z, Zhou Y, Huang H (2019) Cosine-transform-based chaotic system for image encryption. Inf Sci 480:403–419

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11672104), the Chair Professor of Lotus Scholars Program in Hunan Province (No. XJT2015408). The authors also would like to thank the support from the scientific research project of Hengyang Normal University (NO.18D24), the Science and Technology Plan Project of Hunan Province (No. 2016TP1020), the General Scientific Research Fund of Hunan Provincial Education Department (No. 18A333,NO. 19A066).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Hengyang Normal University, Hengyang, 421002, Hunan, China

    Sun Xiyu & Chen Zhong

  2. Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang, 421002, Hunan, China

    Chen Zhong

Authors
  1. Sun Xiyu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chen Zhong.

Ethics declarations

Conflicts of interest

The authors declare that they have no known competing fnancial interests or personal relationships that could have appeared to infuence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Chen Zhong contributed equally to this work.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiyu, S., Zhong, C. A fast image encryption algorithm with variable key space. Multimed Tools Appl 83, 35427–35447 (2024). https://doi.org/10.1007/s11042-023-16981-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-16981-8

Keywords

Search

Navigation