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Multi-layer color image encryption using random matrix affine cipher, RP2DFrHT and 2D Arnold map

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Abstract

Confidentiality, integrity, authenticity, non-repudiation and storing and transmitting images over the unsecured channel has become a challenging task nowadays. In this scenario, a robust image encryption technique over open network has grasped a great deal of attention. In this paper to meet this challenge, we have established a new multi-layer robust color image encryption using random matrix affine cipher (RMAC), reality preserving two dimensional discrete fractional Hartley transform (RP2DFrHT) and two dimensional Arnold map. The first stage of encryption is designed through RMAC. RMAC provides security in co-ordinate domain as well as in geometrical domain. So if a hacker has knowledge about all the pixels of an image, but has no information about the mechanism of co-ordinate domain he/she cannot steal any information. The second stage of encryption is obtained incorporating the concept of RP2DFrHT. The reality preserving transform eliminates the complex-valued coefficients and provides the real-valued coefficients of encrypted image. The real-valuedness of data provides convenient platform for display, storage and transmission in digital domain. The third stage of encryption is done using 2D Arnold map, which not only enhances the security but also enlarges key space. Therefore, the proposed technique provides security in geometrical, co-ordinate, frequency and time domains simultaneously. The security of our proposed technique depends upon the secret keys as well as their correct arrangements. Simulation analysis provides the complete visual results of all stages of encrypted and decrypted images. Sensitivity analysis validates that our proposed technique is highly sensitive towards its secret keys and their arrangements. Statistical analysis such as histogram analysis, MSE, PSNR, correlation coefficient, entropy analysis and resistivity of classical attacks validates the effectiveness and feasibility of our proposed work. Moreover, comparison analysis testifies that our proposed technique functions significantly well as compared to existing similar techniques.

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References

  1. Abdulla AA (2015) Exploiting similarities between secret and cover images for improved embedding efficiency and security in digital steganography. Ph.D. thesis, University of Buckingham

  2. Abuturab MR (2012) Securing color information using Arnold transform in gyrator transform domain. Opt Lasers Eng 50(5):772–779

    Article  Google Scholar 

  3. Abuturab MR (2013) Color image security system based on discrete Hartley transform in gyrator transform domain. Opt Lasers Eng 51(3):317–324

    Article  Google Scholar 

  4. Abuturab MR (2015) An asymmetric single-channel color image encryption based on Hartley transform and gyrator transform. Opt Lasers Eng 69:49–57

    Article  Google Scholar 

  5. Candan C, Kutay MA, Ozaktas HM (2000) The discrete fractional Fourier transform. IEEE Trans Signal Process 48(5):1329–1337

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen H, Du X, Liu Z, Yang C (2013) Color image encryption based on the affine transform and gyrator transform. Opt Lasers Eng 51(6):768–775

    Article  Google Scholar 

  7. Chen L, Zhao D (2005) Optical image encryption based on fractional wavelet transform. Opt Commun 254(4-6):361–367

    Article  Google Scholar 

  8. Chen L, Zhao D (2006) Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms. Opt Express 14(19):8552–8560

    Article  Google Scholar 

  9. Chen L, Zhao D (2008) Image encryption with fractional wavelet packet method. Optik 119(6):286–291

    Article  Google Scholar 

  10. Guleria V, Sabir S, Mishra D (2020) Security of multiple RGB images by RSA cryptosystem combined with FRDCT and Arnold transform. J Inform Secur Appl 54:102524

    Google Scholar 

  11. Guo Q, Liu Z, Liu S (2010) Color image encryption by using Arnold and discrete fractional random transforms in IHS space. Opt Lasers Eng 48 (12):1174–1181

    Article  Google Scholar 

  12. Hennelly B, Sheridan JT (2003) Fractional Fourier transform-based image encryption: Phase retrieval algorithm. Opt Commun 226(1-6):61–80

    Article  Google Scholar 

  13. Huang JJ, Hwang HE, Chen CY, Chen CM (2012) Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain. Opt Laser Technol 44(7):2238–2244

    Article  Google Scholar 

  14. Hussain I (2016) Optical image encryption based on S-box transformation and fractional Hartley transform. J Vib Control 22(4):1143–1146

    Article  MathSciNet  Google Scholar 

  15. Hwang HE (2011) An optical image cryptosystem based on Hartley transform in the Fresnel transform domain. Opt Commun 284(13):3243–3247

    Article  Google Scholar 

  16. Joshi M, Chandrashakher K (2007) Singh, Color image encryption and decryption using fractional Fourier transform. Opt Commun 279(1):35–42

    Article  Google Scholar 

  17. Kang XJ, Han Z, Yu AW, Duan PQ (2017) Double random scrambling encoding in the RPMPFrHT domain. IEEE Int Conf Image Process (ICIP)4362–4366

  18. Kumar M, Mishra D, Sharma R (2014) A first approach on an RGB image encryption. Opt Lasers Eng 52:27–34

    Article  Google Scholar 

  19. Lang J (2012) Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform. Opt Commun 285(10-11):2584–2590

    Article  Google Scholar 

  20. Liu Z, Dai J, Sun X, Liu S (2010) Color image encryption by using the rotation of color vector in Hartley transform domains. Opt Lasers Eng 48 (7-8):800–805

    Article  Google Scholar 

  21. Liu Z, Xu L, Lin C, Dai J, Liu S (2011) Image encryption scheme by using iterative random phase encoding in gyrator transform domains. Opt Lasers Eng 49(4):542–546

    Article  Google Scholar 

  22. Liu Z, Xu L, Liu T, Chen H, Li P, Lin C, Liu S (2011) Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains. Opt Commun 284(1):123–128

    Article  Google Scholar 

  23. Mehra I, Nishchal NK (2015) Wavelet-based image fusion for securing multiple images through asymmetric keys. Opt Commun 335:153–160

    Article  Google Scholar 

  24. Mishra DC, Sharma R (2016) An approach for security of color image data in coordinate, geometric, and frequency domains. Inform Secur J A Global Perspect 25(4-6):213–234

    Article  Google Scholar 

  25. Nishchal NK, Joseph J, Singh K (2004) Securing information using fractional Fourier transform in digital holography. Opt Commun 235(4-6):253–259

    Article  Google Scholar 

  26. Pei SC, Hsue WL (2006) The multiple-parameter discrete fractional Fourier transform. IEEE Signal Process Lett 13(6):329–332

    Article  Google Scholar 

  27. Pei SC, Tseng CC, Yeh MH, Shyu JJ (1998) Discrete fractional Hartley and Fourier transforms. IEEE Trans Circ Syst II: Analog Digit Signal Process 45(6):665–675

    MATH  Google Scholar 

  28. Prasad A, Kumar M, Choudhury DR (2012) Color image encoding using fractional Fourier transformation associated with wavelet transformation. Opt Commun 285(6):1005–1009

    Article  Google Scholar 

  29. Refregier P, Javidi B (1995) Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 20(7):767–769

    Article  Google Scholar 

  30. Singh P, Yadav A, Singh K (2017) Color image encryption using affine transform in fractional Hartley domain. Opt Appl 47(3):421–433

    Google Scholar 

  31. Singh P, Yadav A, Singh K, Saini I (2017) Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition. Math Sci Appl AIP Conf Proc 1802:020017–1–7

    Google Scholar 

  32. Situ G, Zhang J (2004) Double random-phase encoding in the Fresnel domain. Opt Lett 29(14):1584–1586

    Article  Google Scholar 

  33. Soleymani A, Nordin MJ, Sundararajan E (2014) A chaotic cryptosystem for images based on Henon and Arnold cat map. The Scientif World J 2014

  34. Tao R, Lang J, Wang Y (2009) The multiple-parameter discrete fractional Hadamard transform. Opt Commun 282(8):1531–1535

    Article  Google Scholar 

  35. Tao R, Meng XY, Wang Y (2010) Image encryption with multiorders of fractional Fourier transforms. IEEE Trans Inform Forens Secur 5(4):734–738

    Article  Google Scholar 

  36. Vashisth S, Singh H, Yadav A, Singh K (2014) Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval. Optik 125(18):5309–5315

    Article  Google Scholar 

  37. Venturini I, Duhamel P (2004) Reality preserving fractional transforms, International Conference on Acoustics. Speech Signal Process 5:205–208

    Google Scholar 

  38. 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 349-350:137–153

    Article  Google Scholar 

  39. Wu J, Zhang L, Zhou N (2010) Image encryption based on the multiple-order discrete fractional cosine transform. Opt Commun 283(9):1720–1725

    Article  Google Scholar 

  40. Yadav PL, Singh H (2018) Optical double image hiding in the fractional Hartley transform using structured phase filter and Arnold transform. 3D Research 9(2):20

    Article  Google Scholar 

  41. Zhang Y, Xiao D (2013) Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform. Opt Lasers Eng 51(4):472–480

    Article  Google Scholar 

  42. Zhao D, Li X, Chen L (2008) Optical image encryption with redefined fractional Hartley transform. Opt Commun 281(21):5326–5329

    Article  Google Scholar 

  43. Zhou N, Wang Y, Gong L (2011) Novel optical image encryption scheme based on fractional Mellin transform. Opt Commun 284(13):3234–3242

    Article  Google Scholar 

  44. Zhou N, Wang Y, Wu J (2011) Image encryption algorithm based on the multi-order discrete fractional Mellin transform. Opt Commun 284 (24):5588–5597

    Article  Google Scholar 

  45. Zhu Z, Wu C, Wang J, Hu K, Chen XD (2020) A novel 3D vector decomposition for color-image encryption. IEEE Photonics J 12(2):1–14

    Article  Google Scholar 

  46. Zhu H, Zhao C, Zhang X, Yang L (2014) An image encryption scheme using generalized Arnold map and affine cipher. Optik 125(22):6672–6677

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology Mesra, Ranchi, India

    Shazia Sabir & Vandana Guleria

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  1. Shazia Sabir
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  2. Vandana Guleria
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Correspondence to Vandana Guleria.

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Sabir, S., Guleria, V. Multi-layer color image encryption using random matrix affine cipher, RP2DFrHT and 2D Arnold map. Multimed Tools Appl 80, 27829–27853 (2021). https://doi.org/10.1007/s11042-021-11003-x

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  • DOI: https://doi.org/10.1007/s11042-021-11003-x

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