ORCID
- Ji-Jian Chin: 0000-0001-9809-6976
Abstract
Secure and effective methods of image encryption are increasingly important in protecting sensitivedigital 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 usinga combination of the Generalized Lucas Matrix and Hill Cipher (GLMHC) with a self-invertibleencryption key. This type of encryption key eliminates the need to find the inversion key during thedecryption process and reduces the computational burden. Encrypted image quality is measured usingentropy, Mean Two-Dimensional Error (MSE), Signal to Peak Noise ratio (PSNR), Number of PixelsChange Rate (NPCR), and Average Integrated Change Intensity (UACI). This measure is comparedwith two other methods which is based on Elliptical Curve Cryptography (ECC) that also consider thescope of the self-invertible key matrix 4 × 4 dimension and using a 256 × 256-pixel image. Theresults of the experiment showed that the GLMHC-based scheme achieved a standard value of entropyclose to 8, indicating a strong randomness in the encryption process. The high MSE value of 8493.8882compared to the lower PSNR of 8.8397 for certain images indicates the level of distortion in thedecrypted image compared to the original one that has complied with the standards and even the qualityis better than the other two methods. However, a UACI value of 29.7454% lower than the standard mayimply less effective encryption, as certain pixels on the encrypted image still retain the same structureas the original image. This highlights the potential to improve the diffusion process in the certain areaof image for future studies.
Publication Date
2025-12-08
Publication Title
Menemui Matematik (Discovering Mathematics)
Volume
47
Issue
3
ISSN
3083-8452
Acceptance Date
2025-12-08
Deposit Date
2026-01-22
Funding
As authors, we acknowledge the support from PUTRA GRANT GP/2023/9753100 the Special Postgraduate Scheme (SGRA) provided by Universiti Putra Malaysia.
Additional Links
https://persama.org.my/images/Menemui_Matematik/2025/MMv473_113_133.pdf, https://einspem.upm.edu.my/dismath/
Keywords
Generalized Lucas Matrices, Hill Cipher, Self-invertible, Entropy, MSE, PSNR, NPCR, UACI
First Page
113
Last Page
133
Recommended Citation
Johar, P., Yunos, F., Chin, J., & Asbullah, M. (2025) 'Grayscale Image Encryption using Generalized Lucas Matrices and HillCipher', Menemui Matematik (Discovering Mathematics), 47(3), pp. 113-133. Retrieved from https://pearl.plymouth.ac.uk/secam-research/2198
