# Enhanced Steganography for High Dynamic Range Images with Improved Security and Capacity
## 2 Preliminary
### Security by Statistical Analysis  
The scheme proposed by [PERSON] et al. serves the dual purpose of image annotation and image steganography. In the context of steganography, the primary objective is to ensure security against statistical analysis. As in the case of cryptography, steganography algorithms are assumed to be publicly available, and the security of the scheme is based on the concealment of secret data without detection. If it can be demonstrated that an algorithm can determine, with a higher success rate than random guessing, whether a given image contains embedded secret data, then the steganography scheme is deemed to have been compromised. Steganalysis, akin to cryptanalysis in cryptography, involves identifying concealed messages that have been concealed through steganography using various techniques, including perceptual, statistical, specific, and universal blind analysis [22]. While [PERSON] et al. have shown promising results in perceptual analysis, which pertains to the level of distortion, their scheme has a clear vulnerability in specific analysis. The specific analysis concentrates on identifying weaknesses in a particular steganography scheme. While [PERSON] et al. have asserted that stego-HDR-images do not arouse suspicion among eavesdroppers, our findings demonstrate that this claim is not always valid. **Artificial Distribution of Pixels' Values**  
Two categories of pixels are identified (see Table 3) as suitable for the embedding of secret messages based on the following definitions [13]: _embeddable_ and _promising_. \[P(R,G,B,E)\ is\ \left\{ \begin{array}{l}\emph{embeddable, }2\leq HV_{p}\leq 7\\ \emph{promising,}\left\{\begin{array}{l}\max(R,G,B)=127\ and\ HV_{p}=2\\ \max(R,G,B)=254,\ R,G,B\ \in\emph{even and\ HV_{p}=2}\end{array}\right.\end{array} \right. \tag{3}\]  
In the context of the \"_embeddable_\" category, a pixel is considered _embeddable_ if its HV value falls within the range from 2 to 7. An _embeddable_ pixel may also be designated as \"_promising_\", which can be further divided into two specific categories. The first category corresponds to pixels with a maximum value of 127 in any of the Red, Green, or Blue channels, while the second category requires that the maximum value be 254 and that all three channel values be even. Specifically, the first category of \"_promising_\" pixels with \begin{table}
\begin{tabular}{c c} \hline \hline
**Pixel Category** & **Satisfied Condition** \\ \hline Regular & \(\max(R,G,B)\geq 128\) \\ \hline Irregular & \(\max(R,G,B)\leq 127\) \\ \hline Embeddable & \(2\leq HV_{p}\leq 7\) \\ \hline Promising & \(\max(R,G,B)=127\ \left(HV_{p}=2\right)\) \\ \(\max(R,G,B)=254\ R,G,B\ \in\emph{even}\left(HV_{p}=2\right)\) \\ \hline Singular & \(HV_{p}=1\) \\ \hline Null & \(R=G=B=0\ \left(HV_{p}>8\right)\) \\ \hline Neutral & \(HV_{p}=8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The categories of pixels in an HDR image encoded by the RGBE format. \(\max(R,G,B)=127\) can facilitate one multiplication operation, while the second category with \(\max(R,G,B)=254\) can facilitate one division operation. Therefore, the \"_promising_\" pixels with an HV value of 2 (\(HV_{p}=2\)) have the ability to convey one bit of a secret message. [PERSON] et al. 's image steganography scheme employs the technique of utilizing \"_promising_\" pixels to conceal secret messages, thereby ensuring that the magnitude of change resulting from embedding the secret data remains within a reasonable range in each case. However, upon conducting a detailed analysis, two potential vulnerabilities have been identified in [PERSON] et al. 's steganography approach. **Observation 1**. : _The proportion of even-valued integers present in the three color channels where \(max(R,G,B)=254\) will be altered from 25% to 12.5% following the embedding procedure in Ref. [13]._  
As noted in Ref. [13], the capacity is primarily attributable to pixels with a homogeneity value of 2. These pixels make up roughly 11% of the pixels.