Nonlinear Encryption for Multiple Images Based on a Joint Transform Correlator and the Gyrator Transform

Abstract

A novel nonlinear encryption–decryption system based on a joint transform correlator (JTC) and the Gyrator transform (GT) for the simultaneous encryption and decryption of multiple images in grayscale is proposed. This security system features a high level of security for the single real-valued encrypted image and a high image quality for the multiple decrypted images. The multispectral or color images are considered as a special case, taking each color component as a grayscale image. All multiple grayscale images (original images) to encrypt are encoded in phase and placed in the input plane of the JTC at the same time without overlapping. We introduce two random-phase masks (RPMs) keys for each image to encrypt at the input plane of the JTC-based encryption system. The total number of the RPM keys is given by the double of the total number of the grayscale images to be encrypted. The use of several RPMs as keys improves the security of the encrypted image. The joint Gyrator power distribution (JGPD) is the intensity of the GT of the input plane of the JTC. We obtain only a single real-valued encrypted image with a high level of security for all the multiple grayscale images to encrypt by introducing two new suitable nonlinear modifications on the JGPD. The security keys are given by the RPMs and the rotation angle of the GT. The decryption system is implemented by two successive GTs applied to the encrypted image and the security keys given by the RPMs and considering the rotation angle of the GT. We can simultaneously retrieve the various information of the original images at the output plane of the decryption system when all the security keys are correct. Another result due to the appropriate definition of the two nonlinear operations applied on the JGPD is the retrieval of the multiple decrypted images with a high image quality. The numerical simulations are computed with the purpose of demonstrating the validity and performance of the novel encryption–decryption system.