## 1 Introduction
[19] applied the multiple-base notational system and homogeneity index modification and proposed an authentication algorithm for RGBE images. With the aid of the distortion tolerance, the embedding rate reached 2.27 bpp. Finally, [PERSON] et al. [20] extended the multi-MSB prediction and Huffman coding developed for LDR image and proposed reversible data hiding in encrypted RGBE images. Their scheme offered an embedding rate of 6.19-7.03 bpp. Adaptive message embedding is an effective way for hiding data in LDR or HDR images. Since an HDR image can represent a large range of luminance and human eyes are not sensitive to the dark luminance, the darker pixels are better candidates than the brighter ones to carry more messages. [PERSON] and [PERSON]'s algorithm [11] classified pixels of RGBE images into flat or boundary areas to embed different quantities of secret messages. [PERSON] et al. [15] used the homogeneous representations inherent in the RGBE pixels to conceal different numbers of messages. [PERSON] et al. [18] employed a two-level pixel prediction mechanism in complex regions of an RGBE image to reduce the distortion caused by message embedding. Targeting the OpenEXR images, [PERSON] et al. [16] divided pixels into three categories based on the luminance and embedded more messages in low luminance pixels. In the above works, secret messages were embedded by modifying pixels in a cover HDR image in order to generate a stego pixel, where the cover image and the stego image share the same image format. Data hiding using pixel modification inevitably produces interference with the natural features of a cover image, even though the modification is minor and even subtle. Consequently, the more that the information is concealed, the greater the image reveals distortion, which makes it difficult for these classical data hiding schemes to resist the attack of steganalysis, which intends to detect any secret messages hidden in an innocuous image. To resolve the potential steganalytic risk, a new data hiding scheme has been designed, which conceals secret messages by directly constructing a stego image rather than modifying the existing covers. This approach is termed \"constructivedata hiding\" or \"constructive steganography\". Technical algorithms developed to construct a stego image include texture synthesis [21] and color transfer [22], among others. Image encryption [23; 24] is an effective way for preserving privacy and maintaining security. While a number of low dynamic range (LDR) image encryption schemes have been presented [25; 26], and unfortunately, research works on HDR encryption are limited. [PERSON] et al. [27] used the elementary cellular automata (ECA) as an encryption tool to cipher RGBE images. [PERSON] et al. [28] used a logistic map to generate a pseudo-random number sequence in order to encrypt an HDR image with the LogLuv format. [PERSON] and [PERSON] [29] encrypted the bits in the exponent field in OpenEXR images and obtain good encryption performance. [PERSON] and [PERSON] [30] proposed an encryption and authentication scheme for OpenEXR images; they made use of the torus automorphism as the permutation function and Vernam cipher as the stream cipher, where the plaintext is combined with a pseudo-random stream of data to generate the ciphertext using the Boolean \"exclusive or\" (XOR) function. Finally, [PERSON] et al. [20] reserved room for data hiding in the RGBE image, and then encrypted the image using a series of random binary digits. Their scheme is one of few algorithms in the extant literature that can conceal a secret message and encrypt an HDR image. Security is perhaps the most important issue for image encryption [31; 32]. However, the current state-of-the-art HDR encryption algorithms fail to analyze the security comprehensively. Some algorithms only present visual perception metric without further analysis, for example, [PERSON] et al. [28] and [PERSON] et al. [20].