Secure cryptographic scheme based on generalized Reed–Muller (GRM) codes and Laguerre–Gaussian vortex beams (LGVB) for optical image encryption in Fourier transform

In the era of modern technologies, developing effective crypt-coding systems is crucial when it comes to transmitting huge amounts of protected data quickly. Most encrypted image transmission systems do not sufficiently examine the effect of bit mistakes occurring during transmission. This problem is regarded as one that should be addressed by a competent coding scheme. In this paper, we have proposed an image encryption scheme based on generalized Reed–Muller (GRM) codes, QZ synthesis method, and Laguerre–Gaussian vortex beams (LGVB). In the proposed algorithm, GRM codes encode the image and add redundancy to it which increases its error-resistant quality. An encoded image is decomposed into two square images and each image is phase-encoded and modulated using random phase masks. The modulated image is then propagated through the Fourier domain. Vortex Fresnel array and the QZ decomposition operations are used to add security to generate the private keys. The proposed cryptosystem is robust against basic cryptographic attacks. The use of GRM codes adds on error correction capabilities in the cryptosystem. The correlation coefficient of the original and encrypted images is dropped to 0.3% , demonstrating the effectiveness of the encryption in randomizing the image data. System performance is tested by evaluating the mean-squared error, peak signal-to-noise ratio, structural similarity index measure and correlation coefficients.