# A Novel Adaptive Image Data Hiding and Encryption Scheme Using Constructive Image Abstraction
## 1 Introduction
[13] utilized a two-dimensional prediction-error histogram to decrease the distortion from data hiding and provide between 1.202 and 2.85 embedding rates in bpp. [PERSON] et al. [14] introduced an adaptive method to carry secret message in RGBE images, which takes into consideration of the exponent channel distribution when converting from OpenEXR image format. Their method keeps the exponent channel intact during the message concealment. Their scheme supports embedding rates from 7.30 to 9.29 bpp. [PERSON] et al. [15] partitioned the pixels into three groups according to their luminance, and selected low luminance pixels to conceal a greater number of messages. Depending on the specific parameters used, their approach yielded the embedding rates of 2.433 to 20.002 bpp. Most of the above-mentioned works embed messages by altering pixels of the cover image, thereby generating stego pixels with different degrees of distortion, depending on the number of secret messages injected into the cover images. In this scenario, the format remains consistent between the cover and stego images. As a result, concealing a greater message results in a larger image distortion, making it challenging to withstand steganalytic attacks, which aim to identify any hidden messages in an innocent-looking image. To address the issue of possible steganalytic vulnerabilities, researchers have proposed a novel data hiding scheme that conceals confidential messages by creating a stego image directly, instead of modifying an existing cover image. This method is known as \"constructive data hiding\" or \"constructive steganography\" [16]. [PERSON] and [PERSON] [17], evaluated the EC-MV steganalysis of their WCTCIS algorithm using the BOSSbase2 image data base containing 10,000 color images. Their algorithm, which uses the constructive image steganography (CIS) approach, can resist the steganalysis attack. Their experimental results demonstrate that the detection rate in the receiver operating characteristic (ROC) curve is linear and the area under the curve (AUC) is around 0.50, which is no better than a random guess. They also reported that in contrast, the steganographic algorithm by cover modification (SCM) approach has a high detection rate, resulting in the AUC being as high as 0.9984. [PERSON] and [PERSON] concluded that the stego images produced by the CIS approach can resist modern power attacks, such as EC-MV steganalysis, RS steganalysis, pixel value difference (PVD) attacks, and an attack through statistical analysis. Similar to data hiding methods, encryption algorithms for HDR images are limited in the literature. Some techniques have been proposed to encrypt different aspects of HDR images. [PERSON] et al. [18] applied elementary cellular automata (ECA) to encrypt HDR RGBE images, while [PERSON] et al. [19] generated pseudo-random numbers by utilizing a logistic map to encrypt HDR images in the format of LogLUV. [PERSON] and [PERSON] [20] prioritized achieving good performance by only encrypting the exponent field bits in OpenEXR images. [PERSON] and [PERSON] [21] presented a scheme for encrypting and authenticating OpenEXR images using torus automorphism and Vernam cipher. [PERSON] et al. [22] employed random binary digits to encrypt images, and [PERSON] et al. [14] proposed an image encryption algorithm utilizing a 2D sine logistic modulation map (2D-SLMM) and a random permutation technique. In addition, they introduced a set of metrics to comprehensively evaluate the security of the encrypted image in six different aspects. Research in the combination of data hiding and encryption has also received considerable attention, particularly with the rise of cloud computing and privacy-preserving applications. One such field is reversible data hiding in encrypted images (RDHEI), which can be divided into two approaches: vacating room after encryption (VRAE) and reserving room before encryption (RRBE). In the VRAE approach, [PERSON] et al.