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Image Encryption Algorithm based on Wavelet Packet Decomposition and Discrete Linear Canonical Transform. Outline. Introduction Wavelet Packet Decomposition Discrete Fractional Fourier Transform Discrete Linear Canonical Transform Image Encryption Algorithm Simulation Results

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  1. Image Encryption Algorithm based on Wavelet Packet Decomposition and Discrete Linear Canonical Transform

  2. Outline • Introduction • Wavelet Packet Decomposition • Discrete Fractional Fourier Transform • Discrete Linear Canonical Transform • Image Encryption Algorithm • Simulation Results • Security Analysis • Conclusion • References

  3. Introduction(1/3) • Encryption is the process of transforming the information to ensure its security. • With the growth of internet and computer networks, a huge amount of digital data is being exchanged over various types of networks. • The security of digital data including images has attracted more attention, and many different image encryption methods have been proposed to enhance the security of these images .

  4. Introduction(2/3) • One of the techniques existing in the literature for image encryption is based on wavelet packet decomposition (WPD) and bit plane decomposition [2]. • The use of WPD for digital watermarking purpose has also been proposed in [3-5]. • Recently Discrete Linear Canonical Transform has also attracted lots of attention in research community and has been used in number of diverse areas[6].

  5. Introduction(3/3) • In this paper we propose an image encryption technique combining I. Wavelet Packet Decomposition & II. Discrete Linear Canonical Transform (DLCT). • The use of wavelet packet decomposition and DLCT increases the key size significantly making the encryption more robust.

  6. Wavelet Packet Decomposition • WPD is a method of image decomposition which is closely related with the wavelet decomposition. • For a given image, the frequency band has been limited by high frequency and low-frequency part. • In Wavelet Decomposition scheme we successively decompose the low-frequency part of the image whereas in WPD both the low-frequency and high frequency parts are successively decomposed. • It provide more flexible decomposition at any node.

  7. Analysis Structure of Wavelet Packets

  8. Commonly Used Wavelets • Haar Wavelets • Biorthogonal Wavelets • Coiflets • Symmlets • Bathlets • Dmeyer • Daubechies

  9. Discrete Fractional Fourier Transform • The fractional Fourier transform is a generalization for the conventional Fourier transform. • The DFrFT has its own special property of time-frequency analysis, which depends on a parameter p . • The DFrFT has a very close relationship with the Wigner distribution. The DFrFT with order p can be interpreted as a rotation by an angle α (α = pπ / 2 ) in the Wigner distribution of signals.

  10. The kernel matrix of discrete fractional Fourier transform (DFrFT) is defined as follows , where if N is odd, and if N is even is the normalized eigenvector corresponding to the kth-order Hermite function. is defined as follows

  11. Discrete linear canonical transform • The DLCT depends on three independent parameters of the group ad − bc = 1, and its entries are defined as • All the above entries of the DLCT matrix have absolute values of except for b=0, where we adopt • It may also be mention that for parameter values the DLCT reduces to Discrete Fractional Fourier transform.

  12. BLOCK OF IMAGE LL HL Approximation. Horizontal Coefficients Details (X) (Y) LH HH Vertical Diagonal Details Details (Z) (W) Proposed Image Encryption Algo.(1/2) • Step 1 • In the propose technique we divide the original image into blocks of smaller size . • Step 2 • Two level WPD is applied to a block of original image.

  13. Proposed Image Encryption Algo.(2/2) • Step 3 • Construct the complex images with any of two packets, obtained from the different packets of image after two level wavelet packet decomposition. • Step 4 • Successive applications of DLCT/DFRFT with different parameters on the complex images results in an encrypted images. • Similar processing can also be done for the other blocks and encrypt the whole image .The decryption of image is the reverse process of above method. • Here number of levels of decomposition in WPD and choice of combining images out of sixteen images makes additional keys for encryption purpose.

  14. Simulation Results(1/5)

  15. Simulation Results(2/5) Original image Block of an image

  16. Simulation Results(3/5) Wavelet packet decomposition at level 1 of Cameraman image Decomposition tree at First Level Original Image First Level

  17. Simulation Results(4/5) Wavelet packet decomposition at level of Cameraman image Original Image Second Level Decomposition tree at Second Level

  18. Simulation Results(5/5) Encrypted image 1 Encrypted image 2 Decrypted Block of image Decrypted image

  19. Security Analysis • Key space • The number of levels of wavelet packet decomposition and different types of wavelet are used as secret keys. • Moreover, the parameters a, b, c and d of DLCT are also used as the secret keys. • The key space is large enough to resist all kinds of security attacks.

  20. Conclusion • A new scheme of image encryption method using WPD and DLCT is proposed. • The main advantage of the encryption scheme presented is that the increase in number of levels of WPD and different types of wavelet enhances the key size significantly. • The use of DLCT in images encryption increases the security parameters of the encrypted image, due to the sensitivity to any changes made on the parameters used. • The disadvantage of this method is its increased computational cost, but the key size that is enhanced in image encryption is of much more importance as compared to its computational cost.

  21. References • Gupta Kamlesh and Silakari Sanjay, “A Chaos Based Image Encryption Using Block-Based Transformation Algorithm” IJCNS, (2009). • Zheng Wei, Cheng Zhi-gang, Cui Yue-li, “Image Data Encryption and Hiding Based on Wavelet Packet Transform and Bit Planes decomposition”, IEEE (2008) • Alexandre H.P., Rabab K.W., and Pitas I., “Wavelet packets-based digital watermarking for image verification and authentication”, Signal Processing,Vol 83, No. 5, pp. 2117-2132,( 2003). • Kumhom P., On-rit S., and Chamnong thai K, “Image watermarking based on wavelet packet transform with best tree”. ECTI Transactions on Electrical Eng., Electronics, and Communications, Vol. 2, No. 2, pp.23-35, (2004). • Nahla A. Flayh, Syed I. Ahson,“ Wavelet Based Image Encryption” , IEEE,(2008). • Figen S. Oktem and Haldun M. Ozaktas, Member, IEEE, “Exact Relation Between Continuous and Discrete Linear Canonical Transforms” IEEE signal processing letters, vol. 16, no. 8, (august) 2009).

  22. Candan.C, Kutay. M.A, and Ozaktas H.M, “The Discrete Fractional Fourier Transform”, IEEE Trans. on Signal Processing, 48:1329-1337, ( 2000). • Zhu Yu, Zhou Zhe, Yang Haibing, Pan Wenjie, Zhang Yunpeng , “A Chaos-Based Image Encryption Algorithm Using Wavelet Transform”, IEEE(2010). • C.Candan, dFRT: “The Discrete Fractional Fourier Transform,” A Matlab Program, 1998. • Juan M Vilardy 0, Cesar O. Torres M, Lorenzo Mattos V, “Image encryption via Discrete Fractional Fourier Transform and jigsaw transform”, IEEE(2009). • L.Barker. “The discrete fractional Fourier transform and Harper’s equation”, Mathematika,47(1- 2):281–297, 2000.

  23. THANK YOU

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