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A new method in encryption of gray scale images using chaos game representation

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Abstract

In recent years, digital images have gained special significances due to increasing growth of mass media systems. Security of confidential information against unauthorized access during transmission is a serious issue for users of such media and the required level of security must be provided according to different applications. This paper uses chaos game for encryption. The proposed algorithm converts image pixels into binary digits, and produces a binary string with combining them. Taking each pair of bits as one letter of DNA sequence, you can produce an artificial DNA string and draw a Chaos Game Representation (CGR) image. The process also uses a static S-box technique for the substitution process through a Hilbert fractal. The advantage of this method is that it provides a large key space(2418), which is a significant amount to prevent various attacks. Besides that, in Lena, Baboon, Pepper images, the acquired average amount for entropy is 7.9988, NPCR is 99.625, UACI is 35.597.The use of one-dimensional chaos function, and static s-box makes the model more complicated. But it has been proved that the proposed method is capable of providing a high level of security.

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References

  1. Alawida M, Samsudin A, The JS, Alkhawaldeh RS (2019) A new hybrid digital chaotic system with applications in image encryption. Signal Process 160:45–58

    Article  Google Scholar 

  2. Almeida JS, Carriço JA, Maretzek A, Noble PA, Fletcher M (2001) Analysis of genomic sequences by chaos game representation. Bioinformatics 17:429–437

    Article  Google Scholar 

  3. Arun KS, Nair AS, Oommen VO (2013) A novel DNA sequence compression method based on chaos game representation. Int J Comput Biol (IJCB) 2:1–11

    Article  Google Scholar 

  4. Asgari-Chenaghlu M, Balafar M-A, Feizi-Derakhshi M-R (2019) A novel image encryp- tion algorithm based on polynomial combination of chaotic maps and dynamic function generation. Signal Process 157:1–13

    Article  Google Scholar 

  5. Ayubi P, Setayeshi S, Rahmani A (2020) Deterministic chaos game: a new fractal based pseudo-random number generator and its cryptographic application. J Inform Sec Appl 52:1–20

    Google Scholar 

  6. 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

    Article  Google Scholar 

  7. Çavusoglu Ü, Kaçar S, Pehlivan I, Zengin A (2017) Secure image encryption algorithm design using a novel chaos based S-box. Chaos, Solitons Fractals 95:92–101

    Article  Google Scholar 

  8. Chai X, Fu X, Gan Z, Lu Y, Chen Y (2019) A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Process 155:44–62

    Article  Google Scholar 

  9. Chen J, Zhu Z-l, Zhang L-b, Zhang Y, Yang B-q (2018) Exploiting self-adaptive per- mutation–diffusion and DNA random encoding for secure and efficient image encryption. Signal Process 142:340–353

    Article  Google Scholar 

  10. Cheng G, Wang G, Chen H (2019) A novel color image encryption algorithm based on hyper chaotic system and permutation-diffusion architecture. Int J Bifurcation Chaos 29:1–17

    Article  Google Scholar 

  11. Girdhar A, Kapur H, Kumar V (2021) A novel grayscale image encryption approach based on chaotic maps and image blocks. Appl Phys B 127

  12. Hsiao H, Lee J (2015) Finger print image cryptography based on multiple chaotic systems. Signal Process 113:169–181

    Article  Google Scholar 

  13. Hussain I, Shah T, Gondal MA (2012) Image encryption algorithm based on PGL (2, GF (28)) S-boxes and TD-ERCS chaotic sequence. Nonlinear Dyn, 70.

  14. Hussain I, Anees A, AlKhaldi AH, Algarni A, Aslam M (2018) Construction of chaotic quantum magnets and matrix Lorenz systems S-boxes and their applications. Chin J Phys 56:1609–1621

    Article  Google Scholar 

  15. Jeffrey HJ (1990) Chaos game representation of gene structure. Nucleic Acids Res 18:2163–2170

    Article  Google Scholar 

  16. Joseph J (2010) Chaos game representation for genome sequence analysis. Introduction to Chaos Game Representation, Thiruvananthapuram, Kerala, India, 1–23

  17. Khalil N, Sarhan A, Alshewimy M (2021) An efficient color/grayscale image encryption scheme based on hybrid chaotic maps. Optics Laser Technol. 143

  18. Khan M, Shah T (2014) A novel statistical analysis of chaotic S-box in image encryption. 3D Res Center. 5: 1-8

  19. Khan M, Shah T, Mahmood H, Gondal MA, Hussain I (2012) A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems. Nonlinear Dynamics 70:2303–2311

    Article  MathSciNet  Google Scholar 

  20. Liu H, Wang X (2010) Color image encryption based on one-time keys and robust chaotic maps. Comput Math Appl 59:3320–3327

    Article  MathSciNet  Google Scholar 

  21. Liu H, Wang X, & Kadir A, (2012).Image encryption using DNA complementary rule and chaotic maps. Appl Soft Comput. 12:1457–1466

  22. Liu Y, Tang S, Liu R, Zhang L, Ma Z (2017) Secure and robust digital image watermarking schem using logistic and RSA encryption. Expert Syst Appl 97:95–105

    Article  Google Scholar 

  23. Peitgen, H., JUrgens,H., Saupe, D.,(2004). Chaos and fractals new Frontiers of science second edition. Springer.

  24. Prombutr N, Akkaraaektharin P (2008) Analysis and design Hilbert curve fractal antenna feed with co-planar waveguide for multi-band wireless communications. Int J Eng 2:1–11

    Google Scholar 

  25. Ramezanipoor N, Yaghoobi M (2019) A new approach in DNA sequence compression: fast DNA sequence compression using parallel chaos game representation. Expert Syst Appl 116:487–493

    Article  Google Scholar 

  26. Saravana Kumar G et al (2009) Fractal raster tool paths for layered manufacturing of porous objects. Virtual Phys Prototyping 4:91–104

    Article  Google Scholar 

  27. Shaji V, Vani VP (2015) Medical image watermarking using CGR. Int J Eng Res Gen Sci 3:580–586

    Google Scholar 

  28. Sulistyo B, Mahayana D, Rahardjo B (2009) On applicability of chaos game method for block cipher randomness analysis. Int Conf Eng Inform. ICEEI '09

  29. Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187:1076–1085

    MathSciNet  MATH  Google Scholar 

  30. Wang J, Zhi X, Chai X, Lu Y (2021) Chaos-based image encryption strategy based on random number embedding and DNA-level self-adaptive permutation and diffusion. Multimed Tools Appl 80:16087–16122, 10.1007/s11042-020-10413-7

  31. Wang S, Wang C, Xu C (2020) An image encryption algorithm is based on a hidden attractor chaos system and the Knuth–Durstenfeld algorithm. Opt Lasers Eng 128:1–14

    Google Scholar 

  32. Wu J, Liao X, Yang B (2018) Image encryption using 2d hénon-sine map and DNA approach. Signal Process 153:11–23, 10.1016/j.sigpro.2018.06.008

  33. Yang F, Mou J, Liu J et al (2020) Characteristic analysis of the fractional-order hyper chaotic complex system and its image encryption application. Signal Process 169:1–16

    Article  Google Scholar 

  34. Zhang Q, Guo L, Wei X (2010) Image encryption using DNA addition combining with chaotic maps. Math Comput Modell 52: 2028-2035

  35. Zhou S, Wang B, Zheng X, Zhou C, (2014). Digital watermarking based on chaos game representation and discrete cosine transform. 2014 7th Int Congr Image Signal Process. 335–339

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Authors and Affiliations

  1. Computer Engineering Department, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Nafise Ramezani Pour & Mahdi Yaghoobi

Authors
  1. Nafise Ramezani Pour
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  2. Mahdi Yaghoobi
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All authors including Nafise Ramezanipour and Mahdi Yaghoobi contributed equally in developing the main idea of the research, writing the initial draft of manuscript, replying to the reviewer’s comments and revising the final version.

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Correspondence to Nafise Ramezani Pour.

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Nafise Ramezanipour and Mahdi Yaghoobi declare that they have no conflict of interest.

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Pour, N.R., Yaghoobi, M. A new method in encryption of gray scale images using chaos game representation. Multimed Tools Appl 81, 29653–29672 (2022). https://doi.org/10.1007/s11042-022-12779-2

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  • DOI: https://doi.org/10.1007/s11042-022-12779-2

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