Compression and encryption are often performed together for image sharing and/or storage. The order in which the two operations are carried out affects the overall efficiency of digital image services. For example, the encrypted data has less or no compressibility. On the other hand, it is challenging to ensure reasonable security without downgrading the compression performance. Therefore, incorporating one requirement into another is an interesting approach. In this study, we propose a novel hybrid image encryption and compression scheme that allows compression in the encryption domain. The encryption is based on Chaos theory and is carried out in two steps, i.e., permutation and substitution. The lossless compression is performed on the shuffled image and then the compressed bitstream is grouped into 8-bit elements for substitution stage. The lossless nature of the proposed method makes it suitable for medical image compression and encryption applications. The experimental results shows that the proposed method achieves the necessary level of security and preserves the compression efficiency of a lossless algorithm. In addition, to improve the performance of the entropy encoder of the compression algorithm, we propose a data-to-symbol mapping method based on number theory to represent adjacent pixel values as a block. With such representation, the compression saving is improved on average from 5.76% to 15.45% for UCID dataset.

压缩和加密通常一起执行以进行图像共享和/或存储。这两种操作的执行顺序会影响数字图像服务的整体效率。例如，加密数据具有较小的可压缩性或没有可压缩性。另一方面，在不降低压缩性能的情况下确保合理的安全性是一项挑战。因此，将一个需求合并到另一个需求中是一种有趣的方法。在这项研究中，我们提出了一种新颖的混合图像加密和压缩方案，允许在加密域中进行压缩。加密基于混沌理论，分置换和代换两步进行。对混洗后的图像进行无损压缩，然后将压缩后的比特流分组为 8 位元素用于替换阶段。所提出方法的无损特性使其适用于医学图像压缩和加密应用。实验结果表明，所提出的方法达到了必要的安全级别，并保持了无损算法的压缩效率。此外，为了提高压缩算法的熵编码器的性能，我们提出了一种基于数论的数据到符号映射方法，将相邻像素值表示为一个块。通过这种表示，UCID 数据集的压缩节省平均从 5.76% 提高到 15.45%。实验结果表明，所提出的方法达到了必要的安全级别，并保持了无损算法的压缩效率。此外，为了提高压缩算法的熵编码器的性能，我们提出了一种基于数论的数据到符号映射方法，将相邻像素值表示为一个块。通过这种表示，UCID 数据集的压缩节省平均从 5.76% 提高到 15.45%。实验结果表明，所提出的方法达到了必要的安全级别，并保持了无损算法的压缩效率。此外，为了提高压缩算法的熵编码器的性能，我们提出了一种基于数论的数据到符号映射方法，将相邻像素值表示为一个块。通过这种表示，UCID 数据集的压缩节省平均从 5.76% 提高到 15.45%。