Image encryption using radial Hilbert transform filter bank as an additional key in the modified double random fractional Fourier encoding architecture

We propose a method for image encryption using a radial Hilbert transform (RHT) filter bank in the factional Fourier transform (FRT) domain. The filter bank comprises of multiple integral order RHT filters. The scheme is implemented using the well-known double random phase encoding technique. The random phase functions, fractional orders of the FRT, and integral orders of the multiple RHT filters forming the filter bank are used as key parameters for encryption and decryption. Simulation results have been presented to analyze the performance of the proposed scheme with respect to variation in key parameters, and the schematic for its optical implementation has been presented. Effectiveness of the scheme is also shown against the noise, occlusion and attacks using partially correct random phase keys. The effect on decryption, of rotation of the RHT filter bank as well as some of the RHT filters of the filter bank has been studied. Simulation results are also presented to exhibit the performance of the technique against reshuffling the positions of the RHT filters during the decryption. Investigations have also been carried out to analyze the proposed technique against the chosen- and the known-plain-text attacks.

[1]  Claudio Iemmi,et al.  Optical encoding of color three-dimensional correlation , 2002 .

[2]  Ran Tao,et al.  Double image encryption based on random phase encoding in the fractional Fourier domain. , 2007, Optics express.

[3]  Generation of dark hollow beams by using a fractional radial Hilbert transform system , 2007 .

[4]  A W Lohmann,et al.  Optical implementation of the fractional Hilbert transform for two-dimensional objects. , 1997, Applied Optics.

[5]  John T. Sheridan,et al.  Image encryption and the fractional Fourier transform , 2003 .

[6]  Xiangfeng Meng,et al.  Cross-talk-free double-image encryption and watermarking with amplitude–phase separate modulations , 2005 .

[7]  G Unnikrishnan,et al.  Fractional fourier domain encrypted holographic memory by use of an anamorphic optical system. , 2001, Applied optics.

[8]  Huijuan Li,et al.  Image encryption based on gyrator transform and two-step phase-shifting interferometry , 2009 .

[9]  Yan Zhang,et al.  Optical encryption based on iterative fractional Fourier transform , 2002 .

[10]  Aloka Sinha,et al.  Gyrator transform-based optical image encryption, using chaos , 2009 .

[11]  Xiang Peng,et al.  Double-lock for image encryption with virtual optical wavelength. , 2002, Optics express.

[12]  Bahram Javidi,et al.  Resistance of the double random phase encryption against various attacks. , 2007, Optics express.

[13]  Z. Zalevsky,et al.  The Fractional Fourier Transform: with Applications in Optics and Signal Processing , 2001 .

[14]  Hone-Ene Hwang,et al.  Fast algorithm of phase masks for image encryption in the Fresnel domain. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[15]  Kehar Singh,et al.  Securing information using fractional Fourier transform in digital holography [rapid communication] , 2004 .

[16]  Chandra Shakher,et al.  Image encryption and decryption using fractional Fourier transform and radial Hilbert transform , 2008 .

[17]  Valerij Rozouvan,et al.  Modulo image encryption with fractal keys , 2009 .

[18]  Huijuan Li,et al.  Double-image encryption by iterative phase retrieval algorithm in fractional Fourier domain , 2008 .

[19]  J Campos,et al.  Image processing with the radial Hilbert transform: theory and experiments. , 2000, Optics letters.

[20]  D Mendlovic,et al.  Fractional Hilbert transform. , 1996, Optics letters.

[21]  José A. Rodrigo,et al.  Applications of gyrator transform for image processing , 2007 .

[22]  G. Unnikrishnan,et al.  Optical encryption by double-random phase encoding in the fractional Fourier domain. , 2000, Optics letters.

[23]  H. Ozaktas,et al.  Fractional Fourier transforms and their optical implementation. II , 1993 .

[24]  R. Dorsch,et al.  Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm. , 1996, Applied optics.

[25]  S Liu,et al.  Optical image encryption based on multifractional Fourier transforms. , 2000, Optics letters.

[26]  Madhusudan Joshi,et al.  Color image encryption and decryption using fractional Fourier transform , 2007 .

[27]  B Javidi,et al.  Optical image encryption based on input plane and Fourier plane random encoding. , 1995, Optics letters.

[28]  Bahram Javidi,et al.  Polarization encoding for optical security systems , 2000 .

[29]  D Mendlovic,et al.  Anamorphic fractional Fourier transform: optical implementation and applications. , 1995, Applied optics.

[30]  Linfei Chen,et al.  Color information processing (coding and synthesis) with fractional Fourier transforms and digital holography. , 2007, Optics express.

[31]  Narendra Singh,et al.  Optical image encryption using fractional Fourier transform and chaos , 2008 .

[32]  J. Davis,et al.  Analysis of the fractional hilbert transform. , 1998, Applied optics.

[33]  Fan Ge,et al.  A half-blind color image hiding and encryption method in fractional Fourier domains , 2008 .

[34]  Claudio Iemmi,et al.  Encoding 3D correlation in an optical processor , 2005 .

[35]  Zhengjun Liu,et al.  Double image encryption based on iterative fractional Fourier transform , 2007 .