A lossless probabilistic image encryption algorithm based on QSD decomposition and matrix transformations

With the development of Internet technology, images have become widely used in people's daily life. However, some images carry significant importance and sensitivity, making the security and protection of digital information more crucial. Standard encryption schemes such as RSA, DES, and AES, which have proven effective for textual data, face limitations when applied to images due to their unique features, such as large data capacity and strong pixel correlation. In recent years, numerous effective image encryption schemes utilizing diverse techniques have been proposed. However, the use of integer decomposition in encryption techniques is still underexplored. This paper introduces a novel, lossless, and probabilistic image encryption scheme designed to enhance the security of sensitive images during transmission and storage. This scheme is based on a new integer decomposition technique and utilizes a key with a very large key space. In the proposed approach, an image is encrypted into a pair of images using quasi-square decomposition and new matrix transformations. Security is further reinforced through the use of orthogonal matrices, which enhance diffusion while ensuring data integrity and preservation. Experimental results demonstrate that the proposed scheme is highly secure against most known attacks and cryptanalysis methods. Additionally, a comparison with various existing image encryption techniques shows the effectiveness of the proposed approach. This research provides a significant contribution by introducing new techniques that leverage integer decomposition, which are highly effective against CPA (Chosen Plaintext Attack) and KPA (Known-Plaintext Attack). Moreover, these techniques enhance the entropy value of encrypted images and improve the values of NPCR and UACI, which help prevent differential attacks. The proposed scheme has the potential to advance applications in secure image transmission, storage, and privacy protection.