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A Novel Image Encryption Scheme based on Multiple Parameter Discrete Fractional Fourier Transform

by Deepak Sharma, Rajiv Saxena
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 93 - Number 20
Year of Publication: 2014
Authors: Deepak Sharma, Rajiv Saxena
10.5120/16543-5545

Deepak Sharma, Rajiv Saxena . A Novel Image Encryption Scheme based on Multiple Parameter Discrete Fractional Fourier Transform. International Journal of Computer Applications. 93, 20 ( May 2014), 9-16. DOI=10.5120/16543-5545

@article{ 10.5120/16543-5545,
author = { Deepak Sharma, Rajiv Saxena },
title = { A Novel Image Encryption Scheme based on Multiple Parameter Discrete Fractional Fourier Transform },
journal = { International Journal of Computer Applications },
issue_date = { May 2014 },
volume = { 93 },
number = { 20 },
month = { May },
year = { 2014 },
issn = { 0975-8887 },
pages = { 9-16 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume93/number20/16543-5545/ },
doi = { 10.5120/16543-5545 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:16:17.726189+05:30
%A Deepak Sharma
%A Rajiv Saxena
%T A Novel Image Encryption Scheme based on Multiple Parameter Discrete Fractional Fourier Transform
%J International Journal of Computer Applications
%@ 0975-8887
%V 93
%N 20
%P 9-16
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Security is one of the most challenging aspects in internet and Multimedia applications. Encryption is a process which is used to secure data. The Encryption algorithms and suitable transforms play a crucial role to form efficient security systems. In this regard the original information in the existing security system based on the fractional Fourier transform (FRFT) is protected by only a certain order of FRFT. In this paper, we propose a novel method to encrypt an image by using multiple parameters discrete fractional Fourier transform (DFRFT) with random phase matrices. The multiple-parameter discrete fractional Fourier transform (MPDFRFT) possesses all the desired properties of discrete fractional Fourier transform. The MPDFRFT converts to the DFRFT when all of its order parameters are the same. We exploit the properties of multiple-parameter DFRFT and propose a novel encryption scheme using the double random phase in the MPDFRFT domain for encrypting digital data. The proposed encoding scheme with MPDFRFT significantly enhances the data security compared to DFRFT and FRFT and it shows consistent performance with different images. The scheme offers a high degree of resistance towards bruteforce attack.

References
  1. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing. New York: Wiley, 2000.
  2. L. B. Almeida, "The fractional Fourier transform and time-frequency representations," IEEE Trans. Signal Process. , vol. 42, no. 11, pp. 3084–3091, Nov. 1994.
  3. V. Namias, "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Math. Appl. , vol. 25, pp. 241–265, 1980.
  4. D. Mustard, "The fractional Fourier transform and the Wigner distribution," J. Aust. Math. Soc. B, vol. 38, pp. 209–219, 1996.
  5. R. Tao, B. Deng, and Y. Wang, "Research progress of the fractional Fourier transform in signal processing," Science in China (Ser. F, Information Science), vol. 49, pp. 1–25, Jan. 2006.
  6. G. Unnikrishnan and K. Singh, "Double random fractional Fourier-domain encoding for optical security," Opt. Eng. , vol. 39, pp. 2853–2859, 2000.
  7. G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption by double random phase encoding in the fractional Fourier domain," Opt. Lett. , vol. 25, no. 12, pp. 887–889, 2000.
  8. Zhu B, Liu S, Ran Q: Optical image encryption based on multifractional Fourier transforms. Opt. Lett. 25 (2000) 1159–1161
  9. B. M. Hennelly and J. T. Sheridan, "Image encryption based on the fractional Fourier transform," Proc. SPIE, vol. 5202, pp. 76–87, 2003.
  10. R. Tao, Y. Xin, and Y. Wang, "Double image encryption based on random phase encoding in the fractional Fourier domain," Opt. Express, vol. 15, no. 24, pp. 16067–16079, 2007.
  11. R. Tao, X. M. Li, and Y. Wang, "Generalization of the fractional Hilbert transform," IEEE Signal Process. Lett. , vol. 15, pp. 365–368, 2008.
  12. Hennelly B, Sheridan JT: Optical image encryption by random shifting in fractional Fourier domains. Opt. Lett. 28 (2003) 269–271
  13. S. C. Pei and W. L. Hsue, "Random discrete fractional Fourier transform," IEEE Signal Process. Lett. , vol. 16, no. 12, pp. 1015–1018, Dec. 2009.
  14. L. J. Yan and J. S. Pan, "Generalized discrete fractional Hadamard transformation and its application on the image encryption," in Proc. Int. Conf. Intelligent Information Hiding and Multimedia Signal Processing, 2007, pp. 457–460.
  15. H. Al-Qaheri, A. Mustafi, and S. Banerjee, "Digital watermarking using ant colony optimization in fractional Fourier domain," J. Inf. Hiding Multimedia Signal Process. , vol. 1, no. 3, pp. 179–189, Jul. 2010.
  16. S. C. Pei and M. H. Yeh, "Improved discrete fractional Fourier transform," Opt. Lett. , vol. 22, pp. 1047–1049, 1997.
  17. C. Candan, M. A. Kutay, and H. M. Ozaktas, "The discrete fractional Fourier transform," IEEE Trans. Signal Process. , vol. 48, no. 5, pp. 1329–1337, May 2000.
  18. S. C. Pei and W. L. Hsue, "The multiple-parameter discrete fractional Fourier transform," IEEE Signal Process. Lette. , vol. 13, no. 6, pp. 329–332, Jun. 2006.
  19. B. W. Dickinson and K. Steiglitz, "Eigenvectors and functions of the discrete Fourier transform," IEEE Trans. Acoust. , Speech, Signal Process. , vol. ASSP-30, pp. 25–31, Jan. 1982.
  20. M. T. Hanna, N. P. A. Seif, and W. A. E. M. Ahmed, "Hermite- Gaussian-Like eigenvectors of the discrete Fourier transform matrix based on the singular value decomposition of its orthogonal projection matrices," IEEE Trans. Circuits Syst. I, vol. 51, no. 11, pp. 2245–2254, 2004.
  21. M. T. Hanna, "Direct batch evaluation of optimal orthonormal eigenvectors of the DFT matrix," IEEE Trans. Signal Process. , vol. 56, no. 5, pp. 2138–2143, May 2008.
  22. M. T. Hanna, N. P. A. Seif, and W. A. E. M. Ahmed, "Hermite– Gaussian-Like eigenvectors of the discrete Fourier transform matrix based on the direct utilization of the orthogonal projection matrices on its eigenspaces," IEEE Trans. Signal Process. , vol. 54, no. 7, pp. 2815–2819, Jul. 2006.
  23. P. Refregier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769, (1995).
  24. B. Javidi, A. Sergent, G. Zhang, and L. Guibert, "Fault tolerance properties of a double phase encoding encryption technique," Opt. Eng. 36, 992–998 (1997).
  25. N. Towghi, B. Javidi, and Z. Luo, "Fully phase encrypted image processor," J. Opt. Soc. Am. A 16, 1915 (1999).
  26. O. Matoba and B. Javidi, "Encrypted optical memory system using three-dimensional keys in the Fresnel domain," Opt. Lett. 24, 762-764 (1999).
  27. G. Unnikrishnan and K. Singh, "Optical encryption using quadratic phase systems," Opt. Commun. 193, 51-67, (2001).
  28. Y. Zhang, C. H. Zheng, N. Tanno, "Optical encryption based on iterative fractional Fourier transform," Opt. Commun. 202, 277-285, (2002).
  29. B. Zhu and S. Liu, "Optical Image encryption based on the generalized fractional convolution operation," Opt. Commun. 195, 371-381, (2001).
  30. B. Zhu and S. Liu, "Optical Image encryption with multistage and multichannel fractional Fourier-domain filtering," Opt. Lett. 26, 1242-1244, (2001).
  31. N. K. Nishchal, J. Joseph, and K. Singh, "Fully phase encryption using fractional Fourier transform," Opt. Eng. 42, 1583–1588 (2003).
  32. B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003).
  33. N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption using a localized fractional Fourier transform," Opt. Eng. 42, 3566-3571, (2003).
  34. N. K. Nishchal, J. Joseph, and K. Singh, "Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis," Opt. Eng. 43, 2266-2273 (2004).
  35. J. Zhao, H. Lu, X. S. Song, J. F. Li, and Y. H. Ma, "Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique," Opt. Commun. 249, 493-499, (2005).
  36. A. Sinha, K. Singh, "Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes," Opt. Eng. 44, 057001 (2005).
  37. G. Situ and J. Zhang, "Multiple-image encryption by wavelength multiplexing," Opt. Lett. 30, 1306-1308 (2005).
  38. X. F. Meng, L. Z. Cai, M. Z. He, and G. Y. Dong and X. X. Shen, "Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations" , J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
  39. L. F. Chen and D. M. Zhao, "Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms," Opt. Exp. 14, 8552-8560 (2006),
  40. X. Wang, D. Zhao, F. Jing, and X. Wei, "Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics" Opt. Exp. 14, 1476-1486 (2006).
  41. M. S. Millán, E. Pérez-Cabré, and B. Javidi, "Multifactor authentication reinforces optical security," Opt. Lett. 31, 721-723 (2006).
  42. G. Situ and J. Zhang, "Position multiplexing for multiple-image encryption," J. Opt. A: Pure Appl. Opt. 8, 391 (2006).
  43. Z. Liu and S. Liu, "Double image encryption based on iterative fractional Fourier transform," Opt. Commun. 275, 324–329 (2007).
  44. S. C. Pei, M. H. Yeh, and C. C. Tseng, "Discrete fractional Fourier transform based on orthogonal projections," IEEE Trans. Signal Processing, vol. 47, pp. 1335–1348, May 1999.
  45. Mohammad Monajem and Shahriar Baradaran Shokouhi "A new method of image encryption with multiple-parameter discrete fractional Fourier transform" 2012 International Conference on Information and Computer Networks (ICICN 2012)IPCSIT vol. 27 (2012) (2011) IACSIT Press, Singapore
Index Terms

Computer Science
Information Sciences

Keywords

Discrete Fractional Fourier Transform (DFRFT) Decryption Encryption Fourier Transform (FT) Fractional Fourier Transform (FRFT) Multiple Parameter Discrete Fractional Fourier Transform (MPDFRFT).

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