Novel image encryption algorithm based on multiple-parameter discrete fractional random transform

A new method of digital image encryption is presented by utilizing a new multiple-parameter discrete fractional random transform. Image encryption and decryption are performed based on the index additivity and multiple parameters of the multiple-parameter fractional random transform. The plaintext and ciphertext are respectively in the spatial domain and in the fractional domain determined by the encryption keys. The proposed algorithm can resist statistic analyses effectively. The computer simulation results show that the proposed encryption algorithm is sensitive to the multiple keys, and that it has considerable robustness, noise immunity and security.

[1]  Y Zhang,et al.  Fractional Gabor transform. , 1997, Optics letters.

[2]  Byoungho Lee,et al.  Optical implementation of iterative fractional Fourier transform algorithm. , 2006, Optics express.

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

[4]  Ran Tao,et al.  The multiple-parameter discrete fractional Hadamard transform , 2009 .

[5]  Shutian Liu,et al.  The discrete fractional random cosine and sine transforms , 2006 .

[6]  J García,et al.  Fractional wavelet transform. , 1997, Applied optics.

[7]  Dong-Wook Kim,et al.  Digital Hologram Encryption using Discrete Wavelet Packet Transform , 2008 .

[8]  C. Shih.  Fractionalization of Fourier transform , 1995 .

[9]  Linfei Chen,et al.  Image encryption with fractional wavelet packet method , 2008 .

[10]  Hong-Yi Fan,et al.  Eigenmodes of fractional Hankel transform derived by the entangled-state method. , 2003, Optics letters.

[11]  Xiaogang Wang,et al.  Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry , 2006 .

[12]  Zhengjun Liu,et al.  Random fractional Fourier transform. , 2007, Optics letters.

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

[14]  Linfei Chen,et al.  Optical image encryption with redefined fractional Hartley transform , 2008 .

[15]  Shutian Liu,et al.  Watermarking based on discrete fractional random transform , 2007 .

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

[17]  Soo-Chang Pei,et al.  The discrete fractional cosine and sine transforms , 2001, IEEE Trans. Signal Process..

[18]  Ran Tao,et al.  Optical image encryption based on the multiple-parameter fractional Fourier transform. , 2008, Optics letters.

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

[20]  Zeev Zalevsky,et al.  Some important fractional transformations for signal processing , 1996 .

[21]  Zhengjun Liu,et al.  A discrete fractional random transform , 2005, math-ph/0605061.