Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain

Abstract. A double-image encryption scheme is proposed based on an asymmetric technique, in which the encryption and decryption processes are different and the encryption keys are not identical to the decryption ones. First, a phase-only function (POF) of each plain image is retrieved by using an iterative process and then encoded into an interim matrix. Two interim matrices are directly modulated into a complex image by using the convolution operation in the fractional Fourier transform (FrFT) domain. Second, the complex image is encrypted into the gray scale ciphertext with stationary white-noise distribution by using the FrFT. In the encryption process, three random phase functions are used as encryption keys to retrieve the POFs of plain images. Simultaneously, two decryption keys are generated in the encryption process, which make the optical implementation of the decryption process convenient and efficient. The proposed encryption scheme has high robustness to various attacks, such as brute-force attack, known plaintext attack, cipher-only attack, and specific attack. Numerical simulations demonstrate the validity and security of the proposed method.

[1]  Jingjuan Zhang,et al.  Multiple-image encryption by wavelength multiplexing. , 2005, Optics letters.

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

[3]  Huijuan Li,et al.  Double-image encryption based on discrete fractional random transform and chaotic maps , 2011 .

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

[5]  Huijuan Li,et al.  Information security system based on iterative multiple-phase retrieval in gyrator domain , 2008 .

[6]  Wen-Nung Lie,et al.  Multiple-image encryption and multiplexing using a modified Gerchberg-Saxton algorithm and phase modulation in Fresnel-transform domain. , 2009, Optics letters.

[7]  Arturo Carnicer,et al.  Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. , 2005, Optics letters.

[8]  Ayman Alfalou,et al.  Double random phase encryption scheme to multiplex and simultaneous encode multiple images. , 2009, Applied optics.

[9]  Muhammad Rafiq Abuturab,et al.  Securing color image using discrete cosine transform in gyrator transform domain structured-phase encoding , 2012 .

[10]  Zhengjun Liu,et al.  Double image encryption by using iterative random binary encoding in gyrator domains. , 2010, Optics express.

[11]  Wen Chen,et al.  Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain. , 2012, Optics express.

[12]  Xiaogang Wang,et al.  Fully phase multiple-image encryption based on superposition principle and the digital holographic technique , 2012 .

[13]  Xiaogang Wang,et al.  Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval , 2011 .

[14]  Peng Zhang,et al.  Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain. , 2006, Optics letters.

[15]  Ailing Tian,et al.  Single-channel color image encryption using phase retrieve algorithm in fractional Fourier domain , 2013 .

[16]  Ayman Alfalou,et al.  Optical image compression and encryption methods , 2009 .

[17]  Li-Hua Gong,et al.  Novel single-channel color image encryption algorithm based on chaos and fractional Fourier transform , 2011 .

[18]  Daomu Zhao,et al.  Multiple-image encryption using phase retrieve algorithm and intermodulation in Fourier domain , 2012 .

[19]  John T. Sheridan,et al.  Optical image encryption by random shifting in fractional Fourier domains. , 2003, Optics letters.

[20]  Lu Xi,et al.  Information hiding based on double random-phase encoding and public-key cryptography. , 2009, Optics express.

[21]  Muhammad Rafiq Abuturab.  Color information security system using discrete cosine transform in gyrator transform domain radial-Hilbert phase encoding , 2012 .

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

[23]  Di Xiao,et al.  Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform , 2013 .

[24]  Jianhua Wu,et al.  Image encryption algorithm based on the multi-order discrete fractional Mellin transform , 2011 .

[25]  Hone-Ene Hwang,et al.  Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain. , 2011, Applied optics.

[26]  Xiaogang Wang,et al.  A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms , 2012 .

[27]  Huijuan Li,et al.  Double-image encryption based on iterative gyrator transform , 2008 .

[28]  Qiaofeng Tan,et al.  Security enhanced optical encryption system by random phase key and permutation key. , 2009, Optics express.

[29]  Xiang Peng,et al.  Asymmetric cryptosystem based on phase-truncated Fourier transforms. , 2010, Optics letters.

[30]  A. Alfalou,et al.  Simultaneous fusion, compression, and encryption of multiple images. , 2011, Optics express.

[31]  Daomu Zhao,et al.  Double images encryption method with resistance against the specific attack based on an asymmetric algorithm. , 2012, Optics express.

[32]  Wen Chen,et al.  Space-based optical image encryption. , 2010, Optics express.

[33]  Peng Zhang,et al.  Known-plaintext attack on optical encryption based on double random phase keys. , 2006, Optics letters.

[34]  Hone-Ene Hwang,et al.  Position multiplexing multiple-image encryption using cascaded phase-only masks in Fresnel transform domain , 2011 .