### International Journal of Computer Network and Information Security(IJCNIS)

*ISSN: *2074-9090 (Print), *ISSN: *2074-9104 (Online)

*Published By: *MECS Press

*IJCNIS Vol.6, No.10, Sep. 2014*

#### Hybrid Encryption-Compression Scheme Based on Multiple Parameter Discrete Fractional Fourier Transform with Eigen Vector Decomposition Algorithm

Full Text (PDF, 734KB), PP.1-12

Views:94 Downloads:1

#### Author(s)

#### Index Terms

#### Abstract

Encryption along with compression is the process used to secure any multimedia content processing with minimum data storage and transmission. The transforms plays vital role for optimizing any encryption-compression systems. Earlier 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 article, a novel method for encryption-compression scheme based on multiple parameters of discrete fractional Fourier transform (DFRFT) with random phase matrices is proposed. 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-compression scheme using the double random phase in the MPDFRFT domain for encryption and compression data. The proposed scheme with MPDFRFT significantly enhances the data security along with image quality of decompressed image compared to DFRFT and FRFT and it shows consistent performance with different images. The numerical simulations demonstrate the validity and efficiency of this scheme based on Peak signal to noise ratio (PSNR), Compression ratio (CR) and the robustness of the schemes against bruit force attack is examined.

#### Cite This Paper

Deepak Sharma, Rajiv Saxena, Narendra Singh,"Hybrid Encryption-Compression Scheme Based on Multiple Parameter Discrete Fractional Fourier Transform with Eigen Vector Decomposition Algorithm", IJCNIS, vol.6, no.10, pp.1-12, 2014. DOI: 10.5815/ijcnis.2014.10.01

#### Reference

[1]V. Namias. The fractional order Fourier transform and its application to quantum mechanics. In Journal of the Institute of Mathematics and Its Applications, March 1980. 25 (3): p. 241–265.

[2]L. B. Almeida. The fractional Fourier transform and time-frequency representations. In IEEE Trans. Signal Processing, November 1994. 42(11): p. 3084–3091.

[3]D. Mustard. The fractional Fourier transform and the Wigner distribution. In Journal of the Australian Mathematical Society series-B, 1996. 38: p. 209–219.

[4]H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay. The Fractional Fourier Transform with Applications in Optics and Signal Processing. New York: Wiley, 2000.

[5]Kulbir Singh, Navdeep Singh, Parvinder Kaur and Rajiv Saxena. Image Compression By Using Fractional Transforms. In International Conference on Advances in Recent Technologies in Communication and Computing 2009. p. 411-413.

[6]R. Tao, B. Deng, and Y. Wang. Research progress of the fractional Fourier transform in signal processing. In Science in China (Ser.F, Information Science), January 2006. 49: p. 1–25.

[7]G. Unnikrishnan and K. Singh. Double random fractional Fourier-domain encoding for optical security. In Optical. Eng. journal, 2000. 39: p. 2853–2859.

[8]G. Unnikrishnan, J. Joseph, and K. Singh. Optical encryption by double random phase encoding in the fractional Fourier domain. In opt. Letter, 2000. 25(12): p. 887–889.

[9]B. Zhu, S. Liu, and Q. Ran. Optical image encryption based on multifractional Fourier transforms. In Opt. Letter 2000. 25: p.1159–1161.

[10]B. M. Hennelly and J. T. Sheridan. Image encryption based on the fractional Fourier transform. In Proc. SPIE, 2003. 5202: p.76–87.

[11]R. Tao, Y. Xin, and Y. Wang. Double image encryption based on random phase encoding in the fractional Fourier domain. In Opt. Express, 2004. 15(24): p. 16067–16079.

[12]R. Tao, X. M. Li, and Y.Wang, “Generalization of the fractional Hilbert transform,” IEEE Signal Process. Lett., vol. 15, pp. 365–368, 2008.

[13]B. Hennelly and J. T. Sheridan. Optical image encryption by random shifting in fractional Fourier domains. In Opt. Letter, 2003. 28: p. 269–271.

[14]S. C. Pei and W. L. Hsue. Random discrete fractional Fourier transform. In IEEE Signal Process. Letter, December 2009. 16(12): p. 1015–1018.

[15]L. J. Yan and J. S. Pan. Generalized discrete fractional Hadamard transformation and its application on the image encryption. In Proceeding of International Conference on Intelligent Information Hiding and Multimedia Signal Processing, 2007. p. 457–460.

[16]H. Al-Qaheri, A. Mustafi, and S. Banerjee. Digital watermarking using ant colony optimization in fractional Fourier domain. In Journal of Information Hiding Multimedia Signal Processing, July 2010. 1(3): p. 179–189.

[17]S. C. Pei and M. H. Yeh. Improved discrete fractional Fourier transform. In Opt. Letter, 1997. 22: p. 1047–1049.

[18]C. Candan, M. A. Kutay and H. M. Ozaktas. The discrete fractional Fourier transform. In IEEE Transaction Signal Processing, May 2000. 48(5): p. 1329–1337.

[19]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.

[20]B. W. Dickinson and K. Steiglitz. Eigenvectors and functions of the discrete Fourier transform. In IEEE Trans. Acoustic, Speech, Signal Processing, January 1982. ASSP-30 (1): p. 25–31.

[21]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. In IEEE Transaction on Circuits and Systems, November 2004. 51(11): p. 2245–2254.

[22]M. T. Hanna. Direct batch evaluation of optimal orthonormal eigenvectors of the DFT matrix. In IEEE Transaction on Signal Processing, May 2008. 56(5): p. 2138–2143.

[23]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. In IEEE Transaction on Signal Processing, July 2006. 54(7): p. 2815–2819.

[24]P. Refregier and B. Javidi. Optical image encryption based on input plane and Fourier plane random encoding. In Opt. Letter, 1995. 20: p. 767-769.

[25]B. Javidi, A. Sergent, G. Zhang, and L. Guibert. Fault tolerance properties of a double phase encoding encryption technique. In Opt. Eng., April 1997. 36(4): p. 992–998.

[26]N. Towghi, B. Javidi, and Z. Luo. Fully phase encrypted image processor. In The Journal of the Optical Society of America-A, 1999. 16 (8): p.1915-1927.

[27]O. Matoba and B. Javidi. Encrypted optical memory system using three-dimensional keys in the Fresnel domain. In Optics Letters, 1999. 24(11): p.762-764.

[28]G. Unnikrishnan and K. Singh. Optical encryption using quadratic phase systems. In Elsevier Optics Communications, June 2001. 193(1-6): p.51-67.

[29]Y. Zhang, C. H. Zheng and N. Tanno. Optical encryption based on iterative fractional Fourier transform. In Elsevier Optics Communications, Feburary 2002. 202 (4-6): p. 277-285.

[30]B. Zhu and S. Liu. Optical Image encryption based on the generalized fractional convolution operation In Elsevier Optics Communications, August 2001. 195 (5-6): p.371-381.

[31]B. Zhu and S. Liu. Optical Image encryption with multistage and multichannel fractional Fourier-domain filtering. In Optics Letters, 2001. 26(16): p.1242-1244.

[32]N. K. Nishchal, J. Joseph, and K. Singh. Fully phase encryption using fractional Fourier transform. In Optical Engineering, June 2003. 42(6): p.1583–1588.

[33]B. Hennelly and J. T. Sheridan. Optical image encryption by random shifting in fractional Fourier domains. In Optics Letters, 2003. 28(4): p. 269-271.

[34]N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh. Optical encryption using a localized fractional Fourier transform. In Optical Engineering, January 2003. 42(12): p. 3566-3571.

[35]N. K. Nishchal, J. Joseph, and K. Singh. Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis. In Optical Engineering, January 2004.43 (10): p. 2266-2273.

[36]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. In Optics Communications, May 2005. 249 (4-6): p.493-499.

[37]A. Sinha and K. Singh. Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes. In Optical Engineering, May 2005. 44(5): 057001.

[38]G. Situ and J. Zhang. Multiple-image encryption by wavelength multiplexing. In Optics Letters, 2005. 30(11): p. 1306-1308.

[39]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. In Journal of Optics A: Pure and Applied Optics, October 2005. 7(11): p. 624.

[40]L. F. Chen and D. M. Zhao. Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms. In Optics Express, 2006. 14(19): p. 8552-8560.

[41]X. Wang, D. Zhao, F. Jing and X. Wei. Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics. In Optics Express, February 2006. 14(4): p.1476-1486.

[42]M. S. Millán, E. Perez-Cabre and B. Javidi, “Multifactor authentication reinforces optical security,” In Optics Letters, March 2006. 31(6): p.721-723.

[43]G. Situ and J. Zhang. Position multiplexing for multiple-image encryption. In Journal of Optics A: Pure and Applied Optics, 2006. 8(5): p. 391.

[44]Z. Liu and S. Liu. Double image encryption based on iterative fractional Fourier transform. In Elsevier Optics Communications, July 2007. 275(2): p.324-329.

[45]H. Cheng and X. Li. Partial encryption of compressed images and videos. In IEEE Transactions on Signal Processing, August 2000. 48(8): p. 2439-2451.

[46]C. Vijaya and J. S. Bhat. Signal compression using discrete fractional Fourier transform and set partitioning in hierarchical tree. In Elsevier Signal Processing, August 2006. 86(8): p.1976–1983.

[47]K. Nagamani and A. G. Ananth. Image Compression Techniques for High Resolution Satellite Imageries using Classical Lifting Scheme. In International Journal of Computer Applications, February 2011. 15(3): p. 25-28.

[48]Rajinder Kumar, Kulbir Singh and Rajesh Khanna Satellite Image Compression using Fractional Fourier Transform. In International Journal of Computer Applications, July 2012. Volume 50 (3): p. 20-25.

[49]E. Celikel and M. E. Dalkilic. Experiments on a secure compression algorithm. In Proceedings of the International Conference on Information Technology: Coding and Computing, April 2004. 2: p.150-152.

[50]Bryan Usevitch. A Tutorial on Modern Lossy Wavelet Image Compression: Foundations of JPEG 2000. In IEEE Signal Processing Magazine, September 2001. p. 22-35.

[51]A. S. Lewis and G. Knowles. Image Compression Using the 2-D Wavelet Transform. In IEEE Transaction on Image Processing, April 1992. 1(2): p. 244-250.

[52]S. C. Pei, M. H. Yeh, and C. C. Tseng. Discrete fractional Fourier transform based on orthogonal projections. In IEEE Transaction on Signal Processing, May 1999. 47(5): p. 1335–1348.

[53]Mohammad Monajem and Shahriar Baradaran Shokouhi. A new method of image encryption with multiple-parameter discrete fractional Fourier transform. In International Conference on Information and Computer Networks (ICICN 2012), Singapore. Vol. 27, IACSIT Press.