## 2 Related Work
As in many other schemes, the room-vacating approach is explored to embed secret data. Another RDH scheme which also accommodates secret data via vacating room was proposed by [30]. To mask the original image contents, block-level permutation and stream cipher encryption were used. The most significant bit (MSB) layers where the secret data could be embedded are adaptively compressed based on the frequency of MSB, thus embedding additional data. Unlike most of the existing schemes, ref. [31] reserved the data-embedding space before encrypting the original image via the prediction error estimation method. A location map is also used to justify whether the information could be embedded in a particular location. Anyway, the MSBs of selected location pixels are used for secret data hiding as many other schemes. Machine learning models are also used in RDH. In [32], a convolutional neural network (CNN) framework supports recovering the cover image and hence the embedded data from the marked image. Here, the data embedding is made possible through an image-scrambling algorithm called the Arnold transform algorithm. Secret data can also be embedded in a non-encrypted domain. The quality of the stego image is very important as the original pixels are modified while embedding the data [33]. Unlike in the encrypted domain, CNN is also used as a predictor for predicting a set of pixels from another set in RDH in non-encrypted images [34]. The RDH scheme utilized the feature extraction potential with multiple receptive fields and the global optimization capability of the CNN model. The experimental results proved that the CNN-based predictor is more accurate in predicting the pixels over the linear predictors. RDH on non-encrypted images is also exploited in the compressed domain [35]. Here, the first level of embedding is carried out using the mean and standard deviation values obtained through the absolute moment block truncation coding (AMBTC) on the image blocks [36]. The second level embedding is attained via (7,4) hamming code on the AMBTC-based image. Histogram shifting for embedding additional information in non-smooth regions of an image introduces a higher distortion. A technique to reduce the pixel's invalid shifting will produce a higher-quality stego image [37]. The image pixels are classified into two groups accounting for a checkerboard pattern. Fluctuations in each group are calculated and combined with prediction errors helps to achieve a higher embedding rate with information being embedded by modifying the prediction errors. A similar kind of approach is discussed in [38]. Here, an efficient embedding capacity is computed while reducing the distortions introduced with the embedding of additional data. They identify multiple peaks from regions with less local complexity from the histogram and are expanded to hide the additional information. The focus of the experiment relied upon achieving better embedding with the least distortion. To embed the secret information, most of the existing schemes have been utilizing the vacant room created by compression or by shifting or finding pixel differences, and a few have tried modifying the original bits of the pixel, either MSBs or LSBs. A sufficient amount of redundant space is required to improve the embedding capacity. We should also reduce the complexity that leads to errors during the recovery process. Here, we propose a novel \(MPSA\) scheme that particularly retains the encrypted image pixel's intensities as such to embed the secret information. A detailed literature review reveals that the existing RDH schemes in encrypted images have low embedding rate, and there is wide scope to improve this parameter without compromising the image restoration capability. Another important observation is that the majority of the pre-existing works on RDH in encrypted images distort the encrypted pixel values, which may result in a new pixel distribution in the marked image.