Image encryption using the Gyrator transform and random phase masks generated by using chaos

Abstract

Abstract. The Gyrator transform (GT), chaotic random phase masks (CRPMs) and a random permutation of the Jigsaw transform (JT) are utilized to design an images encryption-decryption system. The encryption-decryption system is based on the double random phase encoding (DRPE) in the Gyrator domain (GD), this technique uses two random phase masks (RPMs) to encode the image to encrypt (original image) into a random noise. The RPMs are generated by using chaos, these masks are CRPMs. The parameters of the chaotic function have the control of the generation of the CRPMs. We apply a random permutation to the resulting image of the DRPE technique, with the purpose of obtaining an encrypted image with a higher randomness. In order to successfully retrieve the original image (without errors or noise-free) at the output of the decryption system is necessary to have all the proper keys, which are: the rotation angles of the GTs, the parameters of the chaotic function utilized to generate the two CRPMs and the random permutation of the JT. We check and analyze the validity of the image encryption and decryption systems by means of computing simulations. IntroductionThe image encryption is different from traditional cryptology because the spatial, frequency and redundancy features of the image to encrypt are analysed and processed by the image encryption system [1]. The double random phase encoding (DRPE) is a successful method for optical image encryption [1][2][3], the DRPE uses two random phase masks (RPMs) with the purpose of encoding the image to encrypt (original image) into a stationary white noise pattern (encrypted image). One of the main drawbacks of the image encryption systems based on the initial DRPE is that the security of the system is vulnerable to attacks, this weakness is due to the linear property of the DRPE scheme [1][2][3]. The DRPE has been further extended from the Fourier domain to the Fresnel domain [4][5][6], the fractional Fourier domain [7][8][9][10][11][12], the Gyrator domain (GD) [13][14][15][16] and other domains [17][18][19][20], with the purpose of adding more keys and increasing the security of the DRPE system.The Gyrator transform (GT) is a mathematical tool for analysis and processing of twodimensional signals [21]. The GT has been used in optics [22], signal processing [13] and image encryption [13][14][15][16].In this paper, we propose a nonlinear image encryption-decryption system based on the DRPE, the GT, the chaotic random phase masks (CRPMs) and the Jigsaw transform (JT), in order to overcome the security vulnerabilities of the initial DRPE proposed in Ref. [2]. We use the GT to improve the security of the original DRPE by adding a new key for the encryption system (the

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“…A DNA arrangement is used as a key sequence to permute and diffuse the plain image matrix [30]. To encrypt an image, the author utilized chaotic random phase masks, Gyrator transform and Jigsaw transform along with the random permutation of resulting image [31]. A new phenomenon, i.e.…”

Bidimensional uncertainty product associated with two specific Gyrator domains

“…The Gyrator transform (GT) is a new mathematical tool for analysis and processing of twodimensional signals, which belongs to the linear canonical transform [6,7]. The GT describes rotations in the phase space and it has been used in image processing [8,9], optics [10] and image encryption [8,[11][12][13][14][15].…”