## 2 Related Work  
In this section, we discuss a few RDH schemes in encrypted and non-encrypted images. The scheme reported in [21] proposed by [PERSON] in 2011 is the first universally accepted RDH scheme in encrypted images. The scheme is widely used by researchers as a reference work and improved in later years. Here, the secret data are embedded in the three least significant bits (LSB) of the encrypted image. Initially, the image is divided into non-overlapping blocks, with each block being classified into two parts. To embed a bit 1, the last three LSBs of one part of the block were flipped, and the other part of the block was used to embed a bit 0. An improved version of the above work was proposed in [22]. The smoothness measurement used for block recovery was improved, and used a side-match technique to recover the embedded secret data. The vertical absolute difference and the horizontal absolute differences of pixels in a block were considered to calculate the smoothness to bring a significant improvement in block recovery. The RDH scheme proposed in [23] uses a histogram-based approach, where the data-embedding capacity was improved. The histogram of the encrypted image was generated, and the peak value was found. All those pixels whose intensity was the same and higher as compared to that of the pixel which was identified for peak value are incremented to create room for embedding the secret information, whereas two methods called joint method and separable methods were discussed in [24]. In the joint method at the receiver end, an improved adaptive interpolation algorithm was introduced to quantify the relation existing among a pixel and neighborhood pixels. In this method, both the process of extracting data and image recovery are interlinked. In the second method, both these processes were handled separately. The pixel for embedding data is selected in such a way that its neighboring pixels are not altered. In the separable method, the most significant bits of the selected bit are modified to embed data. Hence, a median filter is used to overcome the noise introduced. Compression with encrypted images and data embedded on the compressed portion was introduced by [25]. The encrypted image was classified into the chessboard fashion, where the white locations were selected for compression and data embedding. Half of the fourth LSB was identified to embed the secret data. A bit of secret data is embedded in every block using the data-hiding key [26], but in comparison to earlier schemes, while encrypting the image, all except the fourth bit of each pixel gets encrypted. This fourth bit is hence used to embed the data. Using the smoothness characteristics along the isophote direction, the secret bits are extracted. A reduction in the extracted bit error rate considering the appropriate block size was proposed in [27]. Here, a block complexity function is defined to facilitate the correct recovery of the block. When compared to other schemes, the embedding data ratio is also defined to embed the secret data. A progressive recovery-based RDH technique was proposed by [28], wherein three channels of the encrypted image were made to embed different amounts of secret bits, unlike any other scheme. They used pseudo-random permutation to create three channels of encrypted image pixels. Each pixel in different channels is later compressed to make room for embedding the secret data. Instead of creating different channels as in [28], the encrypted image is partitioned into four equal groups and two data-embedding methods were utilized. A cyclic shifting of bits in a pixel to embed secret data in three groups and a data swapping-based embedding algorithm was used as a second round of embedding. Another method to classify the encrypted image into two by using run-length coding along with Huffman coding was introduced by [29]. Hence, the data hider has to conduct different mechanisms to embed the secret data into the classified blocks using the data-hiding key.