Grayscale Image Encryption using Generalized Lucas Matrices and HillCipher

Secure and effective methods of image encryption are increasingly important in protecting sensitive
digital content from being attacked by today's increasingly knowledgeable and aggressive adversaries.
This is no exception to attacks carried out on the secret content generated by grayscale images.
Stemming from this problem, this research introduces a new approach to encrypt grayscale images using
a combination of the Generalized Lucas Matrix and Hill Cipher (GLMHC) with a self-invertible
encryption key. This type of encryption key eliminates the need to find the inversion key during the
decryption process and reduces the computational burden. Encrypted image quality is measured using
entropy, Mean Two-Dimensional Error (MSE), Signal to Peak Noise ratio (PSNR), Number of Pixels
Change Rate (NPCR), and Average Integrated Change Intensity (UACI). This measure is compared
with two other methods which is based on Elliptical Curve Cryptography (ECC) that also consider the
scope of the self-invertible key matrix 4 × 4 dimension and using a 256 × 256-pixel image. The
results of the experiment showed that the GLMHC-based scheme achieved a standard value of entropy
close to 8, indicating a strong randomness in the encryption process. The high MSE value of 8493.8882
compared to the lower PSNR of 8.8397 for certain images indicates the level of distortion in the
decrypted image compared to the original one that has complied with the standards and even the quality
is better than the other two methods. However, a UACI value of 29.7454% lower than the standard may
imply less effective encryption, as certain pixels on the encrypted image still retain the same structure
as the original image. This highlights the potential to improve the diffusion process in the certain area
of image for future studies.