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A new image encryption scheme based on hybrid chaotic maps

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Abstract

In this paper, a novel grayscale image cryptosystem based on hybrid chaotic maps is proposed. The scheme employs both confusion phase to scramble the location of pixels and diffusion phase for changing the content of pixels in consecutive manner. In this scheme, Arnold’s cat map is introduced to perform confusion operation and the principle of diffusion is achieved by using the proper selection of combined Sine map, Logistic map, and Tent map. Furthermore, exclusive OR (XOR), exchange, and transform operations are used to enhance the efficiency of diffusion phase. Accordingly, the use of chaotic maps and XOR operation provides a dual layer of security. Depending on the average absolute value of horizontal, vertical, and diagonal correlation coefficient of plain image as well as bifurcation properties of chaotic maps, one of the mentioned chaotic maps is selected for diffusion phase. First, original gray scale image matrix is extended to square matrix by adding the sequences generated with proper chaotic maps to implement the first step of diffusion phase. Then the Arnold’s cat map changes pixels location of new extended matrix by means of certain equation as confusion phase. The encrypted image is generated after applying XOR, exchange and transform operations on the content of pixels as second step of diffusion phase. Thus the system is able to build several more complicated chaotic structures. In addition the encryption and decryption processing time directly depend on the value of correlation coefficient of original image. Plain images with less correlation coefficient have less encryption and decryption processing time, and vice versa. Compared with several existing methods, the proposed scheme has more better properties, including wider chaotic ranges and more complex chaotic behavior. Experimental results show that the proposed system has proper encryption and decryption processing time, unified average changing intensity (UACI), number of pixel change rate (NPCR), and extensive security analysis for kind of images.

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References

  1. Abbas NAM (2016) Image encryption based on Independent Component Analysis and Arnold’s Cat Map. Egypt Inform J 17:139–146

    Google Scholar 

  2. Souyah Amina, Mohamed FK (2017) An efficient and secure chaotic cipher algorithm for image content preservation, Signal processing, https://doi.org/10.1016/j.cnsns.2017.12.017, PII: S1007–5704(17)30439–2

  3. Bakhshandeh A, Eslami Z (2013) An authenticated image encryption scheme based on chaotic maps and memory cellular automata. Opt Lasers Eng 51(6):665–673

    Google Scholar 

  4. Borujeni SE, Eshghi M (2013) Chaotic image encryption system using phasemagnitude transformation and pixel substitution. Telecommun Syst 52(2):525–537

    Google Scholar 

  5. Chapaneri S, Chapaneri R, Sarode T (2014) Evaluation of Chaotic Map Lattice systems for image encryption, Circuits, Systems, Communication and Information Technology Applications (CSCITA), 2014 International Conference on IEEE. p. 59–64

  6. 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 

  7. Chen J-x, Zhu Z-l, Fu C et al (2015) An image encryption scheme using nonlinear inter-pixel computing and swapping based permutation approach. Commun Nonlinear Sci Numer Simul 23(1):294–310

    MathSciNet  MATH  Google Scholar 

  8. Chen J-x, Zhu Z-l, Fu C et al (2015) A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism. Commun Nonlinear Sci Numer Simul 20(3):846–860

    Google Scholar 

  9. Chen J-x, Zhu Z-l, Fu C et al (2015) An efficient image encryption scheme using gray code based permutation approach. Opt Lasers Eng 67:191–204

    Google Scholar 

  10. Cheng G, Wang C, Chen H (2019) A novel color image encryption algorithm based on hyper chaotic system and permutation-diffusion architecture. Int J Bifurcation Chaos 29(09):1950115

    MATH  Google Scholar 

  11. Del Rey AM, Sánchez GR, De la Villa Cuenca A (2015) A protocol to encrypt digital images using chaotic maps and memory cellular automata. Log J IGPL 23(3):485–494

    MathSciNet  MATH  Google Scholar 

  12. Dhall S, Pal SK, Sharma K (2017) Cryptanalysis of image encryption based on a new 1D chaotic system, Signal processing, PII S0165–1684(17)30434–6, https://doi.org/10.1016/j.sigpro.2017.12.021

  13. El Assad S, Farajallah M (2016) A new chaos-based image encryption system. Signal Process Image Commun 41:144–157

    Google Scholar 

  14. François M, Grosges T, Barchiesi D et al (2012) Image encryption algorithm based on a chaotic iterative process. Appl Math 3(12):1910

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  16. Fu C, Chen J-j, Zou H et al (2012) A chaos-based digital image encryption scheme with an improved diffusion strategy. Opt Express 20(3):2363–2378

    Google Scholar 

  17. Fu C, Meng W-h, Zhan Y-f et al (2013) An efficient and secure medical image protection scheme based on chaotic maps. Comput Biol Med 43(8):1000–1010

    Google Scholar 

  18. Gong L, Qiu K, Deng C, Zhou N (2019) An image compression and encryption algorithm based on chaotic system and compressive sensing. Opt Laser Technol 115:257–267

    Google Scholar 

  19. Hua Z, Zhou Y (2016) Image encryption using 2D Logistic-adjusted-Sine map. Inf Sci 339:237–253

    Google Scholar 

  20. Kanso A, Ghebleh M (2015) An efficient and robust image encryption scheme for medical applications. Commun Nonlinear Sci Numer Simul 24(1):98–116

    MathSciNet  MATH  Google Scholar 

  21. Khanzadi H, Eshghi M, Borujeni SE (2014) Image encryption using random bit sequence based on chaotic maps. Arab J Sci Eng 39(2):1039–1047

    MATH  Google Scholar 

  22. Lan R, He J, Wang S, Gu T, Luo X (2018) Integrated Chaotic Systems for Image Encrypion, Signal processing, PII S0165–1684(18)30041–0, https://doi.org/10.1016/j.sigpro.2018.01.026

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

    Google Scholar 

  24. Liao X, Lai S, Zhou Q (2010) A novel image encryption algorithm based on self-adaptive wave transmission. Signal Process 90(9):2714–2722

    MATH  Google Scholar 

  25. Liu H, Wang X (2013) Triple-image encryption scheme based on one-time key stream generated by chaos and plain images. J Syst Softw 86(3):826–834

    Google Scholar 

  26. Liu Y, Zhang LY, Wang J, Zhang Y, Wong K-w (2016) Chosen-plaintext attack of an image encryption scheme based on modified permutation–diffusion structure. Nonlinear Dynamics 84(4):2241–2250

    MATH  Google Scholar 

  27. Mohamed FK (2014) A parallel block-based encryption schema for digital images using reversible cellular automata. Eng Sci Technol Int J 17(2):85–94

    Google Scholar 

  28. Norouzi B, Seyedzadeh SM, Mirzakuchaki S et al (2015) A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos. Multimed Tools Appl 74(3):781–811

    Google Scholar 

  29. Pan SM, Wen RH, Zhou ZH, Zhou NR (2017) Optical multi-image encryption scheme based on discrete cosine transform and nonlinear fractional Mellin transform. Multimed Tools Appl 76:2933–2953

    Google Scholar 

  30. Shannon CE (2001) A mathematical theory of communication. ACM SIGMOBILE Mobile Comput Commun Rev 5(1):3–55

    MathSciNet  Google Scholar 

  31. Sha-ShaYu N-RZ, Gong L-H, Nieb Z (2020) Optical image encryption algorithm based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system. Opt Lasers Eng 124:105816

    Google Scholar 

  32. Song C-Y, Qiao Y-L, Zhang X-Z (2013) An image encryption scheme based on new spatiotemporal chaos. Optik-Int J Light Electron Optics 124(18):3329–3334

    Google Scholar 

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

    MathSciNet  Google Scholar 

  34. Wang X, Guo K (2014) A new image alternate encryption algorithm based on chaotic map. Nonlinear Dynamics 76(4):1943–1950

    MATH  Google Scholar 

  35. Wang X, Xu D (2014) A novel image encryption scheme based on Brownian motion and PWLCM chaotic system. Nonlinear Dynamics 75(1–2):345–353

    Google Scholar 

  36. Wang X, Zhang H-l (2015) A color image encryption with heterogeneous bit-permutation and correlated chaos. Opt Commun 342:51–60

    Google Scholar 

  37. Wang Y, Wong K-W, Liao X et al (2011) A new chaos-based fast image encryption algorithm. Appl Soft Comput 11(1):514–522

    Google Scholar 

  38. Wang H, Xiao D, Chen X, Huang H (2017) Cryptanalysis and Enhancements of Image Encryption Using Combination of the 1D Chaotic Map, Signal processing, PII: S0165–1684(17)30394–8, https://doi.org/10.1016/j.sigpro.2017.11.005

  39. Wong K-W, Kwok BS-H, Yuen C-H (2009) An efficient diffusion approach for chaosbased image encryption. Chaos, Solitons Fractals 41(5):2652–2663

    MATH  Google Scholar 

  40. Wu Y, Yang G, Jin H et al (2012) Image encryption using the two-dimensional logistic chaotic map. J Electron Imaging 21(1):013014-1-013014-15

    Google Scholar 

  41. Wu J, Liao X, Yang B (2017) Color Image Encryption Based on Chaotic Systems and Elliptic Curve ElGamal Scheme, Signal processing, PII: S0165–1684(17)30134–2, https://doi.org/10.1016/j.sigpro.2017.04.006

  42. Xu L, Gou X, Li Z et al (2017) A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion. Opt Lasers Eng 91:41–52

    Google Scholar 

  43. Yavuz E, Yazici R, Kasapbaşi MC et al (2015) A chaos-based image encryption algorithm with simple logical functions, Comput Electric Eng

  44. Yu F , Li L , Tang Q , Cai S , Song Y , Xu Q (2019) A Survey on True Random Number Generators Based on Chaos, Discrete Dynamics in Nature and Society, 2019 Article ID 2545123, p. 10

  45. Zhang G, Liu Q (2011) A novel image encryption method based on total shuffling scheme. Opt Commun 284(12):2775–2780

    Google Scholar 

  46. Zhang Y-Q, Wang X-Y (2014) A symmetric image encryption algorithm based on mixed linear– nonlinear coupled map lattice. Inf Sci 273:329–351

    Google Scholar 

  47. Zhang X, Zhao Z (2014) Chaos-based image encryption with total shuffling and bidirectional diffusion. Nonlinear Dynamics 75(1–2):319–330

    Google Scholar 

  48. Zhang W, Wong K-w, Yu H et al (2013) A symmetric color image encryption algorithm using the intrinsic features of bit distributions. Commun Nonlinear Sci Numer Simul 18(3):584–600

    MathSciNet  MATH  Google Scholar 

  49. Zhang Y, Xiao D, Wen W, Nan H (2014) Cryptanalysis of image scrambling based on chaotic sequences and vigen’ere cipher. Nonlinear Dynamics 78(1):235–240

    MathSciNet  Google Scholar 

  50. Zhang LY, Liu Y, Wang C, Zhou J, Zhang Y, Chen G (2018) Improved known-plaintext attack to permutation-only multimedia ciphers. Inf Sci 430:228–239

    MathSciNet  Google Scholar 

  51. Zhi-Jing H, Cheng S, Li-Hua G, Nan-Run Z (2020) Nonlinear optical multi-image encryption scheme with two-dimensional linear canonical transform. Opt Lasers Eng 124:105821

    Google Scholar 

  52. Zhou Y, Bao L, Chen CLP (2014) A new 1D chaotic system for image encryption. Signal Process 97:172–182

    Google Scholar 

  53. 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(4):1193–1213

    MathSciNet  MATH  Google Scholar 

  54. 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) article id. 338, 36 pp.

  55. Zhu Z-l, Zhang W, Wong K-w et al (2011) A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf Sci 181(6):1171–1186

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran

    Ahmad Pourjabbar Kari & Amir Massoud Bidgoli

  2. Department of Computer Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran

    Ahmad Habibizad Navin

  3. Department of Mathematics and Computer Sciences, University of Tabriz, Tabriz, Iran

    Mirkamal Mirnia

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  1. Ahmad Pourjabbar Kari
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  2. Ahmad Habibizad Navin
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  3. Amir Massoud Bidgoli
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  4. Mirkamal Mirnia
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Correspondence to Ahmad Pourjabbar Kari.

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Pourjabbar Kari, A., Habibizad Navin, A., Bidgoli, A.M. et al. A new image encryption scheme based on hybrid chaotic maps. Multimed Tools Appl 80, 2753–2772 (2021). https://doi.org/10.1007/s11042-020-09648-1

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  • DOI: https://doi.org/10.1007/s11042-020-09648-1

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