Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform

Abstract

Abstract. We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations.

Image quality and security through nonlinear joint transform encryption

“…The DRPE implemented with a JTC architecture has been extended from the Fourier domain to the Fresnel domain [14], the fractional Fourier domain [15][16] and the Gyrator domain [17][18][19]. In the nonlinear approaches [14,16,19], the nonlinear operations introduced in the JTC have become essential to correctly decrypt the input signal with satisfactory quality.…”

“…In the nonlinear approaches [14,16,19], the nonlinear operations introduced in the JTC have become essential to correctly decrypt the input signal with satisfactory quality. Moreover, the extension to other domains has increased the security of the overall encryption-decryption system by introducing new parameters that must be adjusted prior to obtaining the hidden information.…”

“…A generalized formulation of the nonlinear JTC-based encryption systems using the fractional Fourier transform and its combination with a nonzero-order JTC were introduced with the purpose of improving the quality of the decrypted images and increasing the security of the processor [16]. The fractional order of the fractional Fourier transform, α, provides and additional parameter to further control the encryption and decryption stages.…”

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

“…We use the GT to improve the security of the original DRPE by adding a new key for the encryption system (the rotation angle of the GT). It has been demonstrated that the nonlinearities introduced in the initial DRPE leading to an improvement in security [3,5,11,14]. The generation of the RPMs by using a chaotic map allows to obtain the chaotic RPMs or CRPMs with a higher security.…”

“…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].…”