New Approach to Image Encryption Based on Large Invertible Pseudo-Random Matrices

In the digital age, where secure image transmission is essential, we present an improved image encryption scheme based on large scalable Hill matrices defined over the Z/256Z ring.The encryption matrix is constructed by multiplying two triangular matrices generated from chaotic maps, providing a high degree of randomness and unpredictability.Each block incorporates arbitrary square submatrices, enhancing the structural complexity of the encryption.Experiments conducted on a diverse set of images validate the robustness of our approach: the correlation between the clear and encrypted images is close to zero, the entropy reaches 7.99 bits per pixel, and the performance achieves an NPCR of 99.64%, a UACI of 33.45%, and an avalanche effect of 50.33%.These results significantly outperform those of traditional variants of the Hill cipher, highlighting the effectiveness of the combination of evolving matrices and chaotic sequences for reliable and efficient image encryption.