Nonlinear image encryption using a fully phase nonzero-order joint transform correlator in the Gyrator domain

Abstract A novel nonlinear image encryption scheme based on a fully phase nonzero-order joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption–decryption scheme.

[1]  M. L. Calvo,et al.  Gyrator transform: properties and applications. , 2007, Optics express.

[2]  Xudong Chen,et al.  Optical authentication via photon-synthesized ghost imaging using optical nonlinear correlation , 2015 .

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

[4]  Shi Liu,et al.  Iterative phase retrieval algorithms. I: optimization. , 2015, Applied optics.

[5]  Bahram Javidi,et al.  Advances in optical security systems , 2014 .

[6]  Elisabet Pérez-Cabré,et al.  Optical Data Encryption , 2011 .

[7]  Myrian Tebaldi,et al.  Experimental multiplexing of encrypted movies using a JTC architecture. , 2012, Optics express.

[8]  Muhammad Rafiq Abuturab.  Securing color information using Arnold transform in gyrator transform domain , 2012 .

[9]  Jingjuan Zhang,et al.  Double random-phase encoding in the Fresnel domain. , 2004, Optics letters.

[10]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

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

[12]  J. Goodman.  Introduction to Fourier optics , 1969 .

[13]  Myrian Tebaldi,et al.  Known-plaintext attack on a joint transform correlator encrypting system. , 2010, Optics letters.

[14]  John Fredy Barrera,et al.  Optical encryption with a reference wave in a joint transform correlator architecture , 2009 .

[15]  María S. Millán,et al.  Joint transform correlator-based encryption system using the Fresnel transform and nonlinear filtering , 2013, Iberoamerican Meeting of Optics and the Latin American Meeting of Optics, Lasers and Their Applications.

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

[17]  Dafne Amaya,et al.  Experimental color encryption in a joint transform correlator architecture , 2011 .

[18]  María S. Millán,et al.  Improved decryption quality and security of a joint transform correlator-based encryption system , 2013 .

[19]  Rafael C. González,et al.  Digital image processing using MATLAB , 2006 .

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

[21]  Muhammad Rafiq Abuturab.  Noise-free recovery of color information using a joint-extended gyrator transform correlator , 2013 .

[22]  Zhengjun Liu,et al.  Image encryption scheme by using iterative random phase encoding in gyrator transform domains , 2011 .

[23]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[24]  Elisabet Pérez-Cabré,et al.  Nonlinear optical security system based on a joint transform correlator in the Fresnel domain. , 2014, Applied optics.

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

[26]  María S. Millán,et al.  Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform , 2014 .

[27]  Bahram Javidi,et al.  Fully phase encrypted image processor , 1999 .

[28]  Myrian Tebaldi,et al.  Chosen-plaintext attack on a joint transform correlator encrypting system , 2010 .

[29]  B Javidi,et al.  Encrypted optical memory system using three-dimensional keys in the Fresnel domain. , 1999, Optics letters.

[30]  Shizhuo Yin,et al.  NONZERO-ORDER JOINT TRANSFORM CORRELATOR , 1998 .

[31]  M. Sagrario Millán Garcia-Varela,et al.  Images encryption system based on a fractional joint transform correlator and nonlinear filtering , 2014 .

[32]  Chenggong Zhang,et al.  Ciphertext-only attack on a joint transform correlator encryption system. , 2013, Optics express.

[33]  Weimin Jin,et al.  Color image encryption based on joint fractional Fourier transform correlator , 2011 .

[34]  José A Rodrigo,et al.  Experimental implementation of the gyrator transform. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[35]  María S. Millán,et al.  Optical pattern recognition with adjustable sensitivity to shape and texture , 2002 .

[36]  Shi Liu,et al.  Iterative phase retrieval algorithms. Part II: Attacking optical encryption systems. , 2015, Applied optics.

[37]  Bahram Javidi,et al.  Optical encryption using a joint transform correlator architecture , 2000 .

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

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

[40]  María S. Millán,et al.  Dual nonlinear correlator based on computer controlled joint transform processor: Digital analysis and optical results , 1997 .

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

[42]  Jinpeng Ma,et al.  Fast algorithm of discrete gyrator transform based on convolution operation , 2011 .