Skip to main content
SpringerLink
Log in

A novel randomized bit-level two-dimensional hyperchaotic image encryption algorithm

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

Abstract

In this paper, we designed a new hyperchaotic two-dimensional map with wide distribution and two large positive Lyapunov exponents. Then, we used it to construct a new randomized bit-level chaotic image encryption algorithm with the proposed hyperchaotic map as the source of randomization for permutation and diffusion. The input image is randomized by appending an extra random row and an additional random column to it. Then, the whole permutation and diffusion process are randomized by relating the parameters of the hyperchaotic mapping dependent on the hash value of the randomized image. In the permutation step, the randomized image is split into binary images, and then each binary image is randomly and independently permuted. Then, the permuted binary images are combined, and diffusion is applied to each pixel. Various security experiments are designed to assess the performance of the proposed encryption algorithm, including entropy analysis, histogram analysis, key-space analysis, the pixel-level and the bit-level correlation analysis, and differential attacks as well as key-sensitivity and randomization analysis. According to these experiments, the proposed algorithm shows an excellent security performance compared to several recent image encryption algorithms. Moreover, the proposed encryption algorithm is robust against data loss and noise attacks. Finally, the running time of the proposed algorithm is smaller compared to several recent algorithms.

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
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Ali TS, Ali R (2020) A novel medical image signcryption scheme using TLTS and Henon chaotic map. IEEE Access 8:71,974–71,992

    Google Scholar 

  2. Blum L, Blum M, Shub M (1986) A simple unpredictable pseudo-random number generator. SIAM J Comput 15(2):364–383

    MathSciNet  MATH  Google Scholar 

  3. Cao C, Sun K, Liu W (2018) A novel bit-level image encryption algorithm based on 2d-LICM hyperchaotic map. Signal Process 143:122–133

    Google Scholar 

  4. 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 

  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  MATH  Google Scholar 

  6. Diab H (2018) An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations. IEEE Access 6:42,227–42,244

    Google Scholar 

  7. Donner A, Rosner B (1980) On inferences concerning a common correlation coefficient. J R Stat Soc Ser C Appl Stat 29(1):69–76

    Google Scholar 

  8. Fan H, Li M, Liu D, An K (2018) Cryptanalysis of a plaintext-related chaotic RGB image encryption scheme using total plain image characteristics. Multimed Tools Appl 77(15):20, 103–20, 127

    Google Scholar 

  9. Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurc Chaos 8(06):1259–1284

    MathSciNet  MATH  Google Scholar 

  10. Gagunashvili N (2010) Chi-square tests for comparing weighted histograms. Nucl Instrum Methods Phys Res B 614(2):287–296

    Google Scholar 

  11. Guo H, Zhang X, Zhao X, Yu H, Zhang L (2020) Quadratic function chaotic system and its application on digital image encryption. IEEE Access 8:55,540–55,549

    Google Scholar 

  12. Gupta K, Silakari S (2012) Novel approach for fast compressed hybrid color image cryptosystem. Adv Eng Softw 49:29–42

    Google Scholar 

  13. Hermassi H, Rhouma R, Belghith S (2013) Improvement of an image encryption algorithm based on hyper-chaos. Telecommun Syst 52(2):539–549

    Google Scholar 

  14. Hu T, Liu Y, Gong LH, Guo SF, Yuan HM (2017) Chaotic image cryptosystem using DNA deletion and DNA insertion. Signal Process 134:234–243

    Google Scholar 

  15. Hua Z, Jin F, Xu B, Huang H (2018) 2D logistic-Sine-coupling map for image encryption. Signal Process 149:148–161

    Google Scholar 

  16. Hua Z, Zhou Y (2016) Image encryption using 2d logistic-adjusted-sine map. Inf Sci 339:237–253

    Google Scholar 

  17. Huang C, Nien H (2009) Multi chaotic systems based pixel shuffle for image encryption. Opt Commun 282(11):2123–2127

    Google Scholar 

  18. Huang L, Cai S, Xiong X, Xiao M (2019) On symmetric color image encryption system with permutation-diffusion simultaneous operation. Opt Lasers Eng 115:7–20

    Google Scholar 

  19. Kadir A, Hamdulla A, Guo WQ (2014) Color image encryption using skew tent map and hyper chaotic system of 6th-order CNN. Optik-Int J Light Electron Opt 125(5):1671–1675

    Google Scholar 

  20. Khan M (2015) A novel image encryption scheme based on multiple chaotic s-boxes. Nonlinear Dyn 82(1-2):527–533

    MathSciNet  Google Scholar 

  21. Kocarev L, Tasev Z (2003) Public-key encryption based on chebyshev maps. In: Circuits and systems, 2003. ISCAS’03. Proceedings of the 2003 international symposium on, vol 3. IEEE, pp III–III

  22. Li S, Chen G, Cheung A, Bhargava B, Lo KT (2007) On the design of perceptual mpeg-video encryption algorithms. IEEE Trans Circ Syst Video Technol 17(2):214–223

    Google Scholar 

  23. Li T, Yan W, Ping L, Fang P (2019) A WSN positioning algorithm based on 3d discrete chaotic mapping. EURASIP J Wirel Commun Netw 2019 (1):126

    Google Scholar 

  24. Li Y, Wang C, Chen H (2017) A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation. Opt Lasers Eng 90:238–246

    Google Scholar 

  25. Li Z, Peng C, Li L, Zhu X (2018) A novel plaintext-related image encryption scheme using hyper-chaotic system. Nonlinear Dyn 94(2):1319–1333

    Google Scholar 

  26. Lindell Y, Katz J (2014) Introduction to modern cryptography. Chapman and Hall/CRC, London

    MATH  Google Scholar 

  27. Liu H, Wang X, Kadir A (2013) Color image encryption using choquet fuzzy integral and hyper chaotic system. Optik-Int J Light Electron Opt 124 (18):3527–3533

    Google Scholar 

  28. Liu H, Wang X, et al. (2012) Image encryption using DNA complementary rule and chaotic maps. Appl Soft Comput 12(5):1457–1466

    Google Scholar 

  29. Liu L, Zhang Z, Chen R (2019) Cryptanalysis and improvement in a plaintext-related image encryption scheme based on hyper chaos. IEEE Access 7:126,450–126,463

    Google Scholar 

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

    Google Scholar 

  31. Liu X, Song Y, Jiang GP (2019) Hierarchical bit-level image encryption based on chaotic map and Feistel network. Int J Bifurc Chaos 29(02):1950,016

    MathSciNet  MATH  Google Scholar 

  32. Luo Y, Zhou R, Liu J, Cao Y, Ding X (2018) A parallel image encryption algorithm based on the piecewise linear chaotic map and hyper-chaotic map. Nonlinear Dyn 93(3):1165–1181

    Google Scholar 

  33. Mao Y, Chen G, Lian S (2004) A novel fast image encryption scheme based on 3D chaotic baker maps. Int J Bifurc Chaos 14(10):3613–3624

    MathSciNet  MATH  Google Scholar 

  34. Mason JC, Handscomb DC (2002) Chebyshev polynomials. Chapman and hall/CRC, London

    MATH  Google Scholar 

  35. Murillo-Escobar M, Cruz-Hernández C., Abundiz-Pérez F., López-Gutiérrez R. M., Del Campo OA (2015) A rgb image encryption algorithm based on total plain image characteristics and chaos. Signal Process 109:119–131

    Google Scholar 

  36. Murillo-Escobar M, Cruz-Hernández C., Abundiz-Pérez F., López-Gutiérrez R. M., Del Campo OA (2015) A RGB image encryption algorithm based on total plain image characteristics and chaos. Signal Process 109:119–131

    Google Scholar 

  37. Norouzi B, Mirzakuchaki S, Seyedzadeh SM, Mosavi MR (2014) A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Multimed Tools Appl 71(3):1469–1497

    Google Scholar 

  38. Pak C, Huang L (2017) A new color image encryption using combination of the 1d chaotic map. Signal Process 138:129–137

    Google Scholar 

  39. Pareschi F, Setti G, Rovatti R (2010) Implementation and testing of high-speed cmos true random number generators based on chaotic systems. IEEE Trans Circ Syst I Reg Papers 57(12):3124–3137

    MathSciNet  Google Scholar 

  40. Rhouma R, Meherzi S, Belghith S (2009) OCML-Based colour image encryption. Chaos Solitons Fract 40(1):309–318

    MATH  Google Scholar 

  41. Rostami MJ, Shahba A, Saryazdi S, Nezamabadi-pour H (2017) A novel parallel image encryption with chaotic windows based on logistic map. Comput Electr Eng 62:384–400

    Google Scholar 

  42. Seyedzadeh SM, Norouzi B, Mosavi MR, Mirzakuchaki S (2015) A novel color image encryption algorithm based on spatial permutation and quantum chaotic map. Nonlinear Dyn 81(1-2):511– 529

    MathSciNet  MATH  Google Scholar 

  43. Shakiba A (2019) A novel randomized one-dimensional chaotic chebyshev mapping for chosen plaintext attack secure image encryption with a novel chaotic breadth first traversal. Multimed Tools Appl

  44. Shakiba A (2019) A randomized CPA-secure asymmetric-key chaotic color image encryption scheme based on the chebyshev mappings and one-time pad. J King Saud Univ Comp Info Sci

  45. Shakiba A (2019) Security analysis for chaotic maps-based mutual authentication and key agreement using smart cards for wireless networks. J Inf Optim Sci 40(3):725–750

    MathSciNet  Google Scholar 

  46. Shakiba A (2020) Generating dynamic S-boxes using 1D Chebyshev chaotic maps. https://doi.org/10.22108/jcs.2020.116547.1023

  47. Shakiba A, Hooshmandasl MR, Meybodi MA (2016) Cryptanalysis of multiplicative coupled cryptosystems based on the chebyshev polynomials. Int J Bifurc Chaos 26(07):1650,112

    MathSciNet  MATH  Google Scholar 

  48. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423

    MathSciNet  MATH  Google Scholar 

  49. Shrivastava G, Kumar P, Gupta B, Bala S, Dey N (2018) Handbook of research on network forensics and analysis techniques IGI global

  50. Shrivastava G, Pandey A, Sharma K (2013) Steganography and its technique: Technical overview. In: Proceedings of the Third International Conference on Trends in Information, Telecommunication and Computing. Springer, pp 615–620

  51. Souyah A, Faraoun KM (2016) An image encryption scheme combining chaos-memory cellular automata and weighted histogram. Nonlinear Dyn 86(1):639–653

    MathSciNet  Google Scholar 

  52. Stallings W (2017) Cryptography and network security: principles and practice. Pearson, Upper Saddle River

    Google Scholar 

  53. Stergiou C, Psannis KE (2017) Recent advances delivered by mobile cloud computing and internet of things for Big data applications: a survey. Int J Netw Manag 27(3):e1930

    Google Scholar 

  54. Stergiou C, Psannis KE, Kim BG, Gupta B (2018) Secure integration of iot and cloud computing. Futur Gener Comput Syst 78:964–975

    Google Scholar 

  55. Stergiou C, Psannis KE, Plageras AP, Ishibashi Y, Kim BG (2018) Algorithms for efficient digital media transmission over IoT and cloud networking. J Multimed Inf Syst 5(1):27–34

    Google Scholar 

  56. Tu G, Liao X, Xiang T (2013) Cryptanalysis of a color image encryption algorithm based on chaos. Optik 124(22):5411–5415

    Google Scholar 

  57. 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 

  58. Wang X, Teng L, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92(4):1101–1108

    MathSciNet  Google Scholar 

  59. Wang X, Wang Q, Zhang Y (2015) A fast image algorithm based on rows and columns switch. Nonlinear Dyn 79(2):1141–1149

    MathSciNet  Google Scholar 

  60. Wei X, Guo L, Zhang Q, Zhang J, Lian S (2012) A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J Syst Softw 85(2):290–299

    Google Scholar 

  61. Wu X, Wang D, Kurths J, Kan H (2016) A novel lossless color image encryption scheme using 2d dwt and 6d hyperchaotic system. Inf Sci 349:137–153

    Google Scholar 

  62. Wu X, Wang K, Wang X, Kan H (2017) Lossless chaotic color image cryptosystem based on DNA encryption and entropy. Nonlinear Dyn 90 (2):855–875

    MathSciNet  MATH  Google Scholar 

  63. Wu Y, Hua Z (2015) Zhou, y.: n-dimensional discrete cat map generation using laplace expansions. IEEE Trans Cybern 46(11):2622–2633

    Google Scholar 

  64. Xu L, Li Z, Li J, Hua W (2016) A novel bit-level image encryption algorithm based on chaotic maps. Opt Lasers Eng 78:17–25

    Google Scholar 

  65. Yang YG, Tian J, Lei H, Zhou Y, Shi WM (2016) Novel quantum image encryption using one-dimensional quantum cellular automata. Inf Sci 345:257–270

    Google Scholar 

  66. Ye G, Pan C, Huang X, Zhao Z, He J (2018) A chaotic image encryption algorithm based on information entropy. Int J Bifurc Chaos 28 (01):1850,010

    MathSciNet  MATH  Google Scholar 

  67. Ye G, Wong KW (2012) An efficient chaotic image encryption algorithm based on a generalized arnold map. Nonlinear Dyn 69(4):2079–2087

    MathSciNet  Google Scholar 

  68. Yin Q, Wang C (2018) A new chaotic image encryption scheme using breadth-first search and dynamic diffusion. Int J Bifurc Chaos 28(04):1850,047

    MathSciNet  Google Scholar 

  69. Zhang Y (2018) The unified image encryption algorithm based on chaos and cubic s-box. Inf Sci 450:361–377

    MathSciNet  MATH  Google Scholar 

  70. Zhang Y, Xiao D (2014) An image encryption scheme based on rotation matrix bit-level permutation and block diffusion. Commun Nonlinear Sci Numer Simul 19(1):74–82

    MATH  Google Scholar 

  71. Zhang Y, Zhang LY, Zhou J, Liu L, Chen F, He X (2016) A review of compressive sensing in information security field. IEEE access 4:2507–2519

    Google Scholar 

  72. Zhang YQ, Wang XY (2014) Analysis and improvement of a chaos-based symmetric image encryption scheme using a bit-level permutation. Nonlinear Dyn 77 (3):687–698

    Google Scholar 

  73. Zhen P, Zhao G, Min L, Jin X (2016) Chaos-based image encryption scheme combining dna coding and entropy. Multimed Tools Appl 75(11):6303–6319

    Google Scholar 

  74. Zhou Y, Hua Z, Pun CM, Chen CP (2015) Cascade chaotic system with applications. IEEE Trans Cybern 45(9):2001–2012

    Google Scholar 

  75. Zhu ZL, Zhang W, Wong KW, Yu H (2011) A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf Sci 181(6):1171–1186

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, 77188-97111, Iran

    Ali Shakiba

Authors
  1. Ali Shakiba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Shakiba.

Ethics declarations

Conflict of interests

The author declares that they have no conflict of interest.

Additional information

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shakiba, A. A novel randomized bit-level two-dimensional hyperchaotic image encryption algorithm. Multimed Tools Appl 79, 32575–32605 (2020). https://doi.org/10.1007/s11042-020-09434-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-09434-z

Keywords

Search

Navigation