Parametric reversible data hiding in encrypted images using adaptive bit-level data embedding and checkerboard based prediction

Highlights

• We propose an adaptive bit-level data embedding (ABDE) method to embed secret data into the image by bit replacement.

• Using ABDE, we further propose a parametric reversible data embedding method in encrypted images (PRDHEI).

• PRDHEI is able to embed as large as 4.5 bpp of the secret data and obtain an average PSNR larger than 30 dB in the recovered images.

Abstract

In this paper, we first propose an adaptive bit-level data embedding (ABDE) method to embed secret data into a cover image and an adaptive checkerboard based prediction (ACBP) method to predict 3/4 of the pixels in an image using its remaining 1/4 of the pixels. Based on ABDE and ACBP, we further propose a parametric reversible data hiding method in encrypted images (PRDHEI). When parameter $\varepsilon =1$ (ε ∈ [1, 255]), PRDHEI is a full reversible method that both the original image and secret data can be completely recovered. The embedding rate is much higher than state-of-the-art RDHEI methods. Moreover, when ε > 1, the embedding rate of PRDHEI increases significantly. The receiver can fully recover the secret data and reconstruct the original image with very high quality. When $\varepsilon =255,$ PRDHEI reaches its maximum embedding rate of 4.5 bpp while the recovered images are of an average peak signal-to-noise ratio larger than 32 dB.

Introduction

Image encryption and data hiding are two main techniques for privacy protection [1]. The former aims to change the meaningful image into a noise-like one for preventing unauthorized access, while the later conceals secret data into a cover image in an imperceptible way [2], [3]. In image encryption, the original image is the one to be protected, while, in data hiding, the secret data is the information that should be undisclosed. Reversible data hiding (RDH) is a technique that require to perfectly recover the original image after extracting the secret data from the marked image. It can be used in many applications, such as law enforcement, medical imaging and remote sensing, where the original cover image is demanded to be lossless recovered for some legal consideration, medical diagnosis and high-precision nature requirement [4]. A lot of image encryption algorithms [5], [6] and reversible data hiding methods [4], [7], [8], [9] have been proposed in recent years. They both have good performances in their research fields.

Nowadays, reversible data hiding in the encrypted image (RDHEI) has received increasing attentions in the research community, where both the original image and secret data need to be protected [10], [11]. In RDHEI, image encryption and data embedding are accomplished by different users separately. The content-owner first encrypts the original image to a noise-like one, then the data-hider embeds secret data into the encrypted image without knowing its original content. This can be used in many scenarios such as Cloud storage [12], [13], medical image management system [14], [15], law forensics, military applications [1] and secure remote sensing [16]. Taking the medical images as an example, due to the utilization telesurgery and telediagnosis, medical imaging plays an increasing important roles in real applications. The transmission and sharing of medical images must consider the confidentiality, which means that only authorized users (e.g., the attending doctor) are able to access the medical image. Thus, cryptography is needed. For ease of management and protecting the patient privacy, some additional information (hereafter, we call it the secret data) such as patient personal information and image source are added to the encrypted image by the database administrator, who has no right to access the medical image content. At the receiver side, the authorized users, such as doctor and database administrator, are required to reveal the original image or secret data separately. Another example for secure remote sensing are provided in [16], in which the original satellite images are encrypted and sent to the base station(s). Some secret data, such as base station ID, location, local temperature, wind speed, etc., are embedded into the encrypted image before transmission and storage. These images cannot be compressed due to their special utilization. For example, the most commonly used medical image such as the Digital Imaging and Communications in Medicine (DICOM) image is an uncompressed image, and after converting it into JPEG file, a lot of data will be lost [17]. Thus, like other RDHEI methods, we focus on the uncompressed images.

Many RDHEI methods have been proposed in recent years. Depending on whether a preprocessing procedure is needed to reserve room before image encryption, these methods can be divided into two categories, namely: vacating room after encryption (VRAE) and vacating room before encryption (VRBE) [1], [18]. It is more efficient to reserve spare space in the original image than that in the encrypted image because many existing RDH [19], [20], [21], [22], [23] and sparse representation [24] techniques can be used for reserving room. Thus, VRBE methods can reach a larger embedding rate than VRAE methods in general. However, the content-owner may not be willing to perform such extra operation for reserving room because s/he may have difficulty to do such complicated operation due to the limited computation ability [25].

Therefore, VRAE seems to be more applicable in real applications. Hence, many researchers devote to develop efficient VRAE methods. A lot of VRAE methods encrypt the original image using the stream cipher [15], [16], [26], [27], [28], [29], [30], [31], [32]. These methods may cause incorrect extracted data or recovered image when the original image is textured. Because they recover the original image mainly by analyzing the spacial correlations of the directly decrypted image, and textured areas will result in inaccurate estimation results. Other methods encrypt the original image by permutation [33], [34] and Paillier encryption [35], [36], [37]. The former is limited in embedding rate and the later may cause data expansion in the encrypted images. In addition, these existing VRAE methods endure low quality of the final recovered image.

In order to solve these problems, in this paper, we propose a parametric reversible data hiding method in encrypted image. It inherits the merits of VRAE which does not need a reserve room process at the content-owner side. In addition, it is a separable method that data extraction and image recovery can be performed independently. The contributions of this paper are summarized as follows:

• We propose an adaptive bit-level data embedding (ABDE) method to embed secret data into the cover image by bit replacement. Two embedding strategies are designed for data embedding, and ABDE automatically selects the one with a higher embedding rate.

• We propose an adaptive checkerboard based prediction (ACBP) to predict 3/4 of the pixels in an image using its remaining 1/4 of the pixels.

• Based on ABDE and ACBP, we further propose a parametric reversible data embedding method in encrypted images (PRDHEI), where ABDE is used for data embedding, ACBP is adopted for image recovery and parameter ε is to control the embedding rate. It is a full reversible method that both the secret data and original image can be perfectly recovered when parameter $\varepsilon =1$. The embedding rate is much higher than state-of-the-art RDHEI methods.

• In addition, when ε > 1, PRDHEI slightly reduces the recovered image quality while significantly increases the embedding rate. When $\varepsilon =255,$ it is able to embed as large as 4.5 bpp of the secret data and obtain an average PSNR larger than 30 dB in the recovered images.

The rest of this paper is organized as follows: Section 2 reviews the state-of-the-art VRAE methods. Section 3 and Section 5 introduce the proposed adaptive bit-level data embedding and checkerboard based prediction methods. Section 5 describes the proposed parametric reversible data embedding method in encrypted images. Section 6 provides simulation results and comparisons with several related works. Section 7 discusses several issues of the proposed algorithm. Finally, Section 8 concludes this paper.