In the present paper the fractional Fourier transform was used to make phase encryption of color digital images. The image to encrypt is placed as the phase of a complex exponential, then is fractionally transformed three times and multiplied in intermediate steps by two statistically independent random phase masks thus to obtain the encrypted image, to decrypt the coding image the encryption procedure is applied in the inverse sense to the conjugated complex of the encrypted image, then is taken the negative of the phase of the resulting function from the decryption process and the original image is obtained this way that had been encrypted. The use of the fractional Fourier transform and the phase encryption of the image add much more complexity to the decryption of the image to who wants decrypt it without being authorized. In the cryptographic algorithm implemented five keys are used, made up of three fractional orders and two random phase masks, all these keys are necessary for proper decryption affording reliability to image transference via transmission networks

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.

Zinc oxide (ZnO) is a wide bandgap semiconductor of great scientific and technological interest due to its high exciton binding energy and outstanding structural and optical properties, making it an ideal material for applications in optoelectronics, sensors, and photocatalysis. This study presents the rapid synthesis of highly crystalline ZnO nanostructures using two alternative routes: (1) direct thermal decomposition of zinc acetate and (2) a physical-green route assisted by Mangifera indica extract. Both routes were subjected to identical calcination thermal conditions (400 °C for 2 h), allowing for an objective comparison of their effects on structural, vibrational, morphological, and optical characteristics. X-ray diffraction analyses confirmed the formation of a pure hexagonal wurtzite phase in both samples, highlighting a higher crystallinity index (91.6%) and a larger crystallite size (35 nm) in the sample synthesized using the physical-green route. Raman and FTIR spectra supported these findings, revealing greater structural order. Electron microscopy showed significant morphological differences, and UV-Vis analysis showed a red shift in the absorption peak, associated with a decrease in the optical bandgap (from 3.34 eV to 2.97 eV). These results demonstrate that the physical-green route promotes significant improvements in the structural and functional properties of ZnO, without requiring changes in processing temperature or the use of additional chemicals.

We propose the use of the Jigsaw transform (JT) and the iterative cosine transform over a finite field in order to encrypt and decrypt images. The JT is a nonlinear operation that allows one to increase the security over the encrypted images by adding new keys to the encryption and decryption systems. The finite field is a finite set of integer numbers where the basic mathematical operations are performed using modular arithmetic. The finite field used in the encryption and decryption systems has an order given by the Fermat prime number 257. The iterative finite field cosine transform (FFCT) was used in our work with the purpose of obtaining images that had an uniform random distribution. We used a security key given by an image randomly generated and uniformly distributed. The JT and iterative FFCT was utilized twice in the encryption and decryption systems. The encrypted images presented a uniformly distributed histogram and the decrypted images were the same original images used as inputs in the encryption system. The resulting decrypted images had a high level of image quality in comparison to the image quality of the decrypted images obtained by the actual optical decryption systems. The proposed encryption and decryption systems have three security keys represented by two random permutations used in the JTs and one random image. The key space of the proposed encryption and decryption systems is larger. The previous features of the security system allow a better protection of the encrypted image against brute force and statistical analysis attacks.