## 1 Introduction  
With the phenomenal expansion of social networks and the remarkable progress of communication networks, image transfer has become an established standard since images are highly expressive and informative forms of communication. As a result, there is a necessity for cryptographic techniques to maintain image security. It is critical to consider the unique properties of image data while constructing an encryption method, such as substantial redundancy and significant correlation among neighboring pixels. Because of the uniqueness of image properties, traditional cryptographic algorithms are not suited for visual cryptography. Many methods, including chaotic systems [1, 2], DNA encoding [3], cellular automata [4], quantum image encryption [5], and transforms, such as FRFT [6, 7], Affine [5], etc., have been proposed to solve the obstacles provided by the distinctive visual features. On the contrary, encryption alone is insufficient to meet today's demandsfor rapid transmission and reduced storage space. As a result, numerous scientists have made significant contributions in this area and have successfully presented compression encryption techniques. Some very promising and related works are discussed further. Compression and encryption are performed concurrently, fastening calculations and bringing more security. Using the spark concept, [PERSON] [8] established the uniqueness criteria of 2D sparse recovery. The uniqueness criteria are improved by the regularity of sparse parameters in columns and rows, resulting in better compression and sparse rebuilding. The sparse depiction is disrupted by chaotic confusion. This phase aids in fulfilling the said criteria and increases the cryptographic safety index. The chaos pattern is then applied to form two orthogonal measuring matrices. The sparse encrypted form is compressed in two dimensions using the singular value decomposition. Further, a compressed-encrypted matrix built on chaos-based uncertainty is utilized to diminish the correlation across neighboring pixels in the compressed matrices, creating a homogenous allocation in the ciphered image. Finally, the XOR procedure is used to encrypt the data. Depending on the smoothing standard in the decryption procedure, researchers have incorporated the variation restriction to the 2D sparse recovery problem in order to improve compression performance. In another work, [PERSON] et al. [9] presented a technique based on compression encryption. Here, the column-wise scan-optimization compression approach is employed instead of zigzag scanning. The Huffman encoding of JPEG compression is then replaced with arithmetic coding in entropy stage encoding. As with the one-time pad, an image is encrypted with XOR encryption, which is unbreakable in security. Moreover, the compressed information is XORed with a random integer. In a DCT-based compression encryption technique, [PERSON] et al. suggest employing DCT and chaos to provide high-quality image encryption. In this work, the image hash value is first utilized to create a plaintext-correlated encryption key, and then lightweight chaos is created to build a pseudo-random sequence. Second, to construct the DCT coefficient matrix, DCT and quantize \(8\times 8\) subblocks are created. Then, using the DCT matrix, extraction of the DC and AC coefficients for compression coding are achieved. Reconstruction of the ciphertext takes place after permuting the DC coefficient bitstream with the chaotic sequence. By diffusing the ciphertext and hiding the hash value, the final ciphertext is acquired. The algorithm features a good compression rate, and a vast key space [10]. Yet another approach by [PERSON] et al. [11] proposed quantum cosine transform-based image compression-encryption. Here, the quantum discrete cosine transform and 5D hyperchaotic system are used for compression and encryption with the zigzag technique. It is important to compress and encrypt multimedia information, particularly digital images, simultaneously.