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Optical Double Image Hiding in the Fractional Hartley Transform Using Structured Phase Filter and Arnold Transform

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3D Research

Abstract

To maintain the security of the image encryption and to protect the image from intruders, a new asymmetric cryptosystem based on fractional Hartley Transform (FrHT) and the Arnold transform (AT) is proposed. AT is a method of image cropping and edging in which pixels of the image are reorganized. In this cryptosystem we have used AT so as to extent the information content of the two original images onto the encrypted images so as to increase the safety of the encoded images. We have even used Structured Phase Mask (SPM) and Hybrid Mask (HM) as the encryption keys. The original image is first multiplied with the SPM and HM and then transformed with direct and inverse fractional Hartley transform so as to obtain the encrypted image. The fractional orders of the FrHT and the parameters of the AT correspond to the keys of encryption and decryption methods. If both the keys are correctly used only then the original image would be retrieved. Recommended method helps in strengthening the safety of DRPE by growing the key space and the number of parameters and the method is robust against various attacks. By using MATLAB 8.3.0.52 (R2014a) we calculate the strength of the recommended cryptosystem. A set of simulated results shows the power of the proposed asymmetric cryptosystem.

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References

  1. Matoba, O., Nomura, T., Perez-Cabre, E., Millan, M. S., & Javidi, B. (2009). Optical techniques for information security. Proceedings of IEEE, 97, 1128–1148.

    Article  Google Scholar 

  2. Alfalou, A., & Brosseau, C. (2009). Optical image compression and encryption methods. Advances in Optics and Photonics, 1, 536–589.

    Article  Google Scholar 

  3. Chen, W., Javidi, B., & Chen, X. (2014). Advances in Optical security system. Advances in Optics and Photonics, 6, 120–155.

    Article  Google Scholar 

  4. Javidi, B., et al. (2016). Roadmap on optical security. Journals of Optics, 18, 1–39.

    Google Scholar 

  5. Refregier, P., & Javidi, B. (1995). Optical image encryption based on input plane and Fourier plane random encoding. Optics Letters, 20, 767–769.

    Article  Google Scholar 

  6. Kumar, P., Joseph, J., & Singh, K. (2016). Double random phase encoding based optical encryption systems using some linear canonical transforms: Weaknesses and countermeasures. Springer Series in Optical Sciences, 198, 367–396.

    Article  MathSciNet  MATH  Google Scholar 

  7. Unnikrishnan, G., & Singh, K. (2000). Double random fractional Fourier domain encoding for optical security. Optical Engineering, 39(11), 2853–2859.

    Article  Google Scholar 

  8. Unnikrishnan, G., Joseph, J., & Singh, K. (2000). Optical encryption by double random phase encoding in the fractional Fourier domain. Optics Letters, 25, 887–889.

    Article  Google Scholar 

  9. Nishchal, N. K., Joseph, J., & Singh, K. (2003). Fully phase encryption using Fractional Fourier transform. Optical Engineering, 42(6), 1583–1588.

    Article  Google Scholar 

  10. Hennelly, B. M., & Sheridan, J. T. (2003). Image encryption and fractional Fourier transform. Optik, 114, 251–265.

    Article  Google Scholar 

  11. Tao, R., Xin, Y., & Wang, Y. (2007). Double image encryption based on random phase encoding in the fractional Fourier domain. Optics Express, 15–24, 16067–16079.

    Article  Google Scholar 

  12. Sinha, A., & Singh, N. (2008). Optical image encryption using fractional Fourier transform and chaos. Optics and Lasers in Engineering, 46(2), 117–123.

    Article  Google Scholar 

  13. Rajput, S. K., & Nischal, N. K. (2012). Image encryption based on interference that uses fractional Fourier domain asymmetric keys. Applied Optics, 51(10), 1446–1452.

    Article  Google Scholar 

  14. Dahiya, M., Sukhija, S., Singh, H. (2014). Image encryption using Quad phase masks in fractional Fourier domain and Case study. In: IEEE, 2014, 978-1-4799-2572-8.

  15. Girija, R., & Singh, H. (2018). A cryptosystem based on deterministic phase masks and fractional Fourier transform deploying singular value decomposition. Optical and Quantum Electronics, 50(210), 1–24.

    Google Scholar 

  16. Matoba, O., & Javidi, B. (1999). Encrypted optical memory system using three dimensional keys in the Fresnel domain. Optics Letters, 24, 762–764.

    Article  Google Scholar 

  17. Hennelly, B. M., & Sheridan, J. T. (2004). Random phase and jigsaw encryption in the Fresnel domain. Optical Engineering, 10(1117/1), 1790502.

    Google Scholar 

  18. Situ, G., & Zhang, J. (2004). Double random-phase encoding in the Fresnel domain. Optics Letters, 29, 1584–1586.

    Article  Google Scholar 

  19. Rajput, S. K., & Nischal, N. K. (2014). Fresnel domain nonlinear optical encryption scheme based on Gerchberg-Saxton phase retreival algorithm. Applied Optics, 53, 418–425.

    Article  Google Scholar 

  20. Singh, H., Yadav, A. K., Vashisth, S., & Singh, K. (2015). Optical image encryption using devil’s vortex toroidal lens in the Fresnel transform domain. International Journal of Optics, 2015, 1–13. https://doi.org/10.1155/2015/926135.

    Article  Google Scholar 

  21. Rodrigo, J. A., Alieva, T., & Calvo, M. L. (2007). Gyrator Transform: properties and applications. Optics Express, 15, 2190–2203.

    Article  Google Scholar 

  22. Singh, N., & Sinha, A. (2009). Gyrator Transform- based optical image encryption, using chaos. Optics and Lasers in Engineering, 47(5), 539–546.

    Article  Google Scholar 

  23. Liu, Z., Xu, L., Lin, C., Dai, J., & Liu, S. (2011). Image encryption scheme by using iterative random phase encoding in gyrator transform domains. Optics and Lasers in Engineering, 49(4), 542–546.

    Article  Google Scholar 

  24. Abuturab, M. R. (2012). Color image security system using double random structured phase encoding in gyrator transform domain. Applied Optics, 51, 3006–3016.

    Article  Google Scholar 

  25. Singh, H., Yadav, A. K., Vashisth, S., & Singh, K. (2014). Fully-phase image encryption using double random—structured phase masks in gyrator domain. Applied Optics, 53, 6472–6481.

    Article  Google Scholar 

  26. Singh, H., Yadav, A. K., Vashisth, S., & Singh, K. (2015). Double phase- image encryption using gyrator transforms, and structured phase mask in the frequency plane. Optics and Lasers in Engineering, 67, 145–156.

    Article  Google Scholar 

  27. Vashisth, S., Yadav, A. K., Singh, H., Singh, K. (2015). Watermarking in Gyrator domain using asymmetric cryptosystem. In: International conference on optics and photonics. Proceedings of SPIE, 96542E-1-8, https://doi.org/10.1117/12.2183394.

  28. Zhou, N. R., Wang, Y., & Gong, L. (2011). Novel optical image encryption scheme based on fractional Mellin transform. Optics Communication, 284, 3234–3242.

    Article  Google Scholar 

  29. Vashisth, S., Singh, H., Yadav, A. K., & Singh, K. (2014). Devil’s vortex phase structure as frequency plane mask for image encryption using the fractional Mellin transform. International Journal of Optics, 728056, 1–9.

    Article  Google Scholar 

  30. Wu, J., Zhang, L., & Zhou, N. (2010). Image encryption based on the multiple order discrete fractional cosine transform. Optics Communication, 283(9), 1720–1725.

    Article  Google Scholar 

  31. Hartley, R. V. L. (1942). A more symmerical Fourier analysis applied to transmission problems. Proceedings of IRE, 30(3), 144–150.

    Article  MATH  Google Scholar 

  32. Chen, L., & Zhao, D. (2006). Optical image encryption with Hartley transforms. Optics Letters, 31, 3438–3440.

    Article  Google Scholar 

  33. Singh, N., & Sinha, A. (2009). Optical image encryption using Hartley transform and logistic map. Optics Communication, 282, 1104–1109.

    Article  Google Scholar 

  34. Singh, N., & Sinha, A. (2010). Optical image encryption using improper Hartley transforms and chaos. Optik, 121, 918–925.

    Article  Google Scholar 

  35. Zhao, D., Li, X., & Chen, L. (2008). Optical image encryption with redefined fractional Hartley transform. Optics Communication, 281, 5326–5329.

    Article  Google Scholar 

  36. Jimenez, C., Torres, C., & Mattos, L. (2011). Fractional Hartley transform applied to optical image encryption. Journal of Physics, 274, 012041.

    Google Scholar 

  37. Singh, P., Yadav, A. K., & Singh, K. (2017). Color image encryption using affine transform in fractional Hartley domain. Optica Applicata. https://doi.org/10.5277/ol170308.

    Google Scholar 

  38. Yadav, A. K., Singh, P., & Singh, K. (2017). Cryptosystem based on devil’s vortex Fresnel lens in fractional Hartley domain. Journal of Optics, 1–12. https://doi.org/10.1007/s12596-017-0435-9.

  39. Singh, H. (2017) Non linear optical double image encryption using random-optical vortex in fractional Hartley domain. Optica Applicata, 47(4), 557–578. https://doi.org/10.5277/oa170406.

    Google Scholar 

  40. Vilardy, J. M., Torres, C. O., Jimenez, C. J. (2013) Double image encryption method using the Arnold transform in the fractional Hartley domain. Proceedings of SPIE, 8785. https://doi.org/10.1117/12.2022216.

  41. Abutturab, M. R. (2013). Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain. Optics & Laser Technology, 45, 524–532.

    Article  Google Scholar 

  42. Singh, P., Yadav, A. K., Singh, K., & Saini, I. (2017). Optical image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition. AIP. https://doi.org/10.1063/1.4973267.

    Google Scholar 

  43. Zhou, N., Dong, T., & Wu, J. (2010). Novel image encryption algorithm based on multiple—parameter discrete fractional random transform. Optics Communication, 283(15), 3037–3042.

    Article  Google Scholar 

  44. Singh, H. (2016). Optical cryptosystems of color images using random phase masks in fractional wavelet transform domain. In: AIP conference proceedings, Vol. 1728, 2016, pp. 020063-1/4.

  45. Carnicer, A., Montes- Usategui, M., Arcos, S., & Juvells, I. (2005). Vulnerability to chosen-ciphertext attacks of optical encryption schemes based on double random phase keys. Optics Letters, 30, 1644–1646.

    Article  Google Scholar 

  46. Frauel, Y., Castro, A., Naughton, T. J., & Javidi, B. (2007). Resistance of the double random phase encryption against various attacks. Optics Express, 15(16), 10253–10265.

    Article  Google Scholar 

  47. Peng, X., Zhang, P., Wei, H., & Yu, B. (2006). Known plaintext attack on optical encryption based on double random phase keys. Optics Letters, 31, 1044–1046.

    Article  Google Scholar 

  48. Rajput, S. K., & Nishchal, N. K. (2013). Known plaintext attack on encryption domain independent optical Asymmetric cryptosystem. Optics Communication, 309, 231–235.

    Article  Google Scholar 

  49. Qin, W., & Peng, X. (2010). Asymmetric cryptosystem based on phase truncated Fourier transforms. Optics Letters, 35, 118–120.

    Article  Google Scholar 

  50. Wang, X., & Zhao, D. (2011). Security enhancement of a phase truncation based image encryption algorithm. Applied Optics, 50, 6645–6651.

    Article  Google Scholar 

  51. Wang, X., & Zhao, D. (2012). Double images encrypted method with resistance against the specific attack based on an asymmetric algoirthm. Optics Express, 20, 11994–12003.

    Article  Google Scholar 

  52. Wang, X., & Zhao, D. (2012). A special attack on the asymmetric cryptosystem based on phase truncated Fourier transform. Optics Communication, 285(6), 1078–1081.

    Article  Google Scholar 

  53. Wang, Q., Guo, Q., & Zhaou, J. (2013). Color image hiding based on phase truncation and phase retrieval technique in fractional fourier domain. Optik, 124, 1224–1229.

    Article  Google Scholar 

  54. Wang, X., Chen, Y., Dai, C., & Zhao, D. (2014). Discussion and a new attack of the asymmetric cryptosystem based on phase truncated Fourier transform. Applied Optics, 53(2), 208–213.

    Article  Google Scholar 

  55. Mehra, I., & Nischal, N. K. (2014). Image fusion using wavelet transform and its application to asymmetric cryptosystem and hiding. Optics Express, 22, 5474–5482.

    Article  Google Scholar 

  56. Anshula, H. S. (2016). Asymmetric image encryption scheme by using random phase masks in Fourier transform domain. The International Conference on Fibre and Photonic. https://doi.org/10.1364/photonics.2016.W3A.4.

    Google Scholar 

  57. Sinha, A. (2016). Non linear optical cryptosystem resistant to standard and hybrid attacks. Optics and Lasers in Engineering, 81, 79–86.

    Article  Google Scholar 

  58. Khurana, M., Singh, H. (2017). An asymmetric image encryption based on phase truncated hybrid transform. 3D Research, 8:28, 1–17.

    Google Scholar 

  59. Liu, H., Lin, D., & Kadir, A. (2013). A novel data hiding method based on deoxyribonucleic acid coding. Computers & Electrical Engineering, 39, 1164–1173.

    Article  Google Scholar 

  60. Rajput, S. K., & Nishchal, N. (2012). Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask. Applied Optics, 51, 5377–5786.

    Article  Google Scholar 

  61. Singh, H. (2016). Cryptosystem for securing image encryption using structured phase masks in Fresnel Wavelet transform domain. 3D Res 7-34:1-18

  62. Kumar, R., & Bhaduri, B. (2017). Optical image encryption using Kronecker product and hybrid phase masks. Opitcs and Laser Technology, 95, 51–55.

    Article  Google Scholar 

  63. Barrera, J. F., Henao, R., & Torroba, R. (2005). Fault tolerances using toroidal zone plate encryption. Optics Communications, 256, 489–494.

    Article  Google Scholar 

  64. Davis, J. A., McNamara, D. E., & Cottrell, D. M. (2000). Image Processing with the radial Hilbert transform:theory and experiments. Optics Letters, 25, 0146–9592.

    Article  Google Scholar 

  65. Joshi, M., Shakher, C., & Singh, K. (2010). Image encryption using radial Hilbert transform filter bank as an additional key in the modified double random fractional Fourier encoding architecture. Optics and Lasers in Engineering, 48, 605–615.

    Article  Google Scholar 

  66. Joshi, M., Shakher, C., & Singh, K. (2010). Fractional fourier plane image encryption technique using radial Hilbert and Jigsaw transform. Optics and Lasers in Engineering, 48, 754–759.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Sciences, Singhania University, Pacheri Beri, Rajasthan, India

    Poonam Lata Yadav

  2. Department of Applied Sciences, The NorthCap University, Gurgaon, India

    Hukum Singh

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  1. Poonam Lata Yadav
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  2. Hukum Singh
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Correspondence to Poonam Lata Yadav.

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Yadav, P.L., Singh, H. Optical Double Image Hiding in the Fractional Hartley Transform Using Structured Phase Filter and Arnold Transform. 3D Res 9, 20 (2018). https://doi.org/10.1007/s13319-018-0172-0

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  • DOI: https://doi.org/10.1007/s13319-018-0172-0

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