I Introduction
Reversible data hiding (RDH) is a technique to embed secret data into the cover data in a reversible way, while the secret data can be extracted without any error and the cover data can be reconstructed losslessly [1, 2, 3, 4]
. In the last decade, reversible data hiding has attracted extensive research interest from the information hiding community, due to this technology is quite useful for some special applications in which images are not allowed to be disturbed, such as military, medical, fine art work, law forensics and so on. As of now, many methods have been designed, which can be mainly classified into three categories: lossless compressionbased
[5, 6], difference expansionbased [7, 8, 9] and histogram shiftingbased [10, 11]. These methods are designed to ensure the secret data is not detected and the change of the original image is not perceptible.With the development of cloud storing and cloud computing, many reversible data hiding schemes in encrypted images (RDHEI) have been published since Puech [12] proposed the first RDHEI method. The RDHEI technology embeds data into encrypted images rather than plaintext images [13, 14, 15, 16], there are three end users: the contentowner, datahider and receiver. The contentowner, that is, the original image provider, encrypts the original plaintext image before sending it to the datahider. The datahider embeds secret data into encrypted image without knowing the content of the original image or the encryption key. At the receiver side, the original content of the image can be restored and the secret information can be extracted. More precisely, as shown in Fig. 1.
In general, the reported RDHEI techniques can be mainly classified into three categories, 1) vacating room after encryption (VRAE) [13, 17]; 2) vacating room by encryption (VRBE) [18]; and 3) reserving room before encryption (RRBE) [19, 20, 21]. Since encryption would minimize the redundancy of images, it is difficult for VRAE methods to achieve a satisfactory capacity of embedding in encrypted images. The VRBE methods use some speciﬁc encryption algorithms to encrypt the original image while keeping spatial redundancy in the encrypted image. Different from VRBE and VRAE, RRBE methods have been proposed that reserve room before image encryption, which exploit spatial correlation in plaintext image so as to obtain a larger embedding capacity.
In the previous RDHEI methods, image recovery and secret information extraction should be processed jointly [13]. To separate the processes of image recovery and secret information extraction, separable reversible data hiding schemes in encrypted images have been reported [17, 18, 19, 20, 21]. Zhang [17] proposed a separable RDHEI scheme to creat a sparse space to accommddate additional data by compressing the least significant bits. In[19], the secret data were embedded by MSB substitution. Due to the local correlation between a pixel and its neighbors in a plaintext image, the values of adjacent pixels are very close. For this reason, during the decoding process, the secret information must be extracted without error from the MSB plane and the original image must be perfectly restored based on MSB prediction, but the method in [19] only substitute oneMSB, so the embedding rate is lower than one bit per pixel (bpp). Based on [19], an improved method proposed in [20] to embed the secret data into the encrypted image by twoMSB (MSB and second MSB) planes substitution so that the embedding rate can exceed 1 bpp. Chen [21] adopted the extended runlength coding and blockbased MSB plane rearrangement scheme to compress multiple MSB planes of the original image to embed secret data. Yi [18] proposed a VRBE separable RDHEI method using parametric binary tree labeling scheme to embed secret information into encrypted image by exploiting local correlation within small image blocks.
Based on Yi ’s method [18], IPBTLRDHEI is proposed in this paper, which is a novel RRBE separable RDHEI method with high capacity. First, IPBTLRDHEI reserves embedding space in the plaintext image before encryption by the contentowner. Second, at the datahider end, the proposed IPBTLRDHEI method uses parametric binary tree labeling scheme to label encrypted pixels in two different categories for hiding secret information. And then at the receiver end, according to different permissions, one can obtain the original image, secret information or both. Compared with Yi ’s method [18], the proposed IPBTLRDHEI method take full advantage of the redundancy of image so that the embedding rate can be increased.
The rest of this paper is organized as follows. Section II introduces parametric binary tree labeling scheme. The proposed IPBTLRDHEI method is discussed in detail in Section III. Section IV shows the experimental results and analysis. Finally, in Section V, the conclusions are drawn and future works are proposed.
Ii Parametric binary tree labeling scheme
Parametric binary tree labeling scheme (PBTL) [18] can be used to label image pixels in two different categories, namely G1 and G2, and a full binary tree is used to illustrate the distribution of binary labeling bits, as shown in Fig. 2.
For pixels with 8bit depth, the full binary tree has 7 layers, and the layer has nodes, where . Given two parameters and , where . For G2, all pixels are labeled by the same bits of ’0…0’, which is the first node of the layer. For G1, all pixels are classified into different subcategories according to and , where is calculated by:
(1) 
When , the nodes from right to left in the layer are selected to label different subcategories in G1. When , the nodes from right to left in the layer are selected to label different subcategories in G1, that is, when , the selected binary codes that are not derived from the node of ’0…0’. Moreover, pixels in the same subcategory are labeled with the same bit binary code, and pixels in different subcategories are labeled with different bit binary codes. Fig. 3 is an illustrative example of labeling bits selection when = 1 to 3 and = 1 to 7.
As can be seen from Fig. 3, for example, when , , the G2 pixels are labeled by the same 2 bits of ’00’, the nodes from right to left in layer are selected to label different subcategories in G1, the selected nodes are ’111’, ’110’, ’101’, ’100’, ’011’ and ’010’, which are not derived from the node of ’00’, that is, ’000’ and ’001’ that derived from ’00’ are ignored and the remaining nodes in layer are kept.
Iii Proposed Scheme
The proposed IPBTLRDHEI method is composed of three main phases: 1) Generation of encrypted image with labels done by the contentowner, 2) Generation of marked encrypted image done by the datahider, and 3) Dataextraction/imagerecovery done by the receiver. In the first phase, the contentowner detects the prediction error of the original plaintext image and encrypts the original plaintext image by an encryption key. Then, PBTL is used to label encrypted image. In the second phase, after using a datahiding key, the secret information can be hidden by bit replacement. In the third phase, the secret information must be extracted without error from the marked encrypted image with only the datahiding key, and the original image must be reconstructed losslessly by exploiting the spatial correlation in plaintext image with only the encryption key. When using both of the keys, the original image and the secret information can be restored and extracted losslessly. Fig. 4 shows the framework of the proposed IPBTLRDHEI method.
Iiia Generation of Encrypted Image with labels
Generation of encrypted image with labels includes four steps: prediction error, image encryption, pixel grouping and pixel labeling using PBTL. Next, these four steps are described one by one.
IiiA1 Prediction Error
For an original image, the pixels in the first row and first column are retained as reference pixels. The MED predictor [8] as shown in Fig. 5 can exploit the left, upper and upper left neighboring pixels to predict an image pixel:
(2) 
where is the predicted value of . Hence the predicted error is calculated by:
(3) 
IiiA2 Image Encryption
After obtaining the predicted error of the 8bit depth original image , we convert all pixels in the original image into 8bit binary sequence using
(4) 
where k is the corresponding bit of the binary sequence, and , is the size of the original image and
is floor operation. A pseudorandom matrix
of the same size as the original image is generated by an encryption key, similarly, each pixel value of is converted into 8bit binary sequence using Eq. (4). Then the encrypted 8bit binary sequence can be obtained through the bitwise exclusiveor (XOR) operation:(5) 
where is the bitwise XOR operation, and denotes the encrypted 8bit binary sequence. Finally, Eq. (6) is used to calculate the encrypted pixel
(6) 
In this way, the encrypted image is generated. An example of the prediction and image encryption process is described in Fig. 6. Fig. 6(a) is taken as the original image, where and . The corresponding predicted value of Fig. 6(a) is shown in Fig. 6(b). Fig. 6(c) is the predicted error from the subtraction of Fig. 6(a) and Fig. 6(b). Fig. 6(d) is an encrypted image of Fig. 6(a) by an encryption key .
IiiA3 pixel grouping
We separate all pixels in into four sets, namely: reference pixel (), special pixel (), embeddable pixel () and nonembeddable pixel (). Here, the pixels on the first row and first column are retained as reference pixels (), which will be kept unmodiﬁed during data embedding phase. contains only one pixel which will be utilized to store the parameters and . Then, for the remaining pixels , according to the corresponding predicted error calculated by Eq. (3), if satisﬁed the condition of Eq. (7), the pixel belongs to ; otherwise, it is in set . Pixels in can be utilized to embed secret data while cannot.
(7) 
is a positive integer, calculated by the parameters and , and are the ceil and floor operations. Let , and represent the number of pixels in , and , respectively. Thus, = +++1, and = .
Fig. 7 is the pixel grouping of Fig. 6 when and . According to aforementioned, we pick pixels on first row and column as . Without loss of generality, the last pixel is selected as . By the Eq. (1) and Eq. (7). if the predicted error satisﬁed the condition: , the pixel belongs to ; otherwise, it is in set .
IiiA4 Pixel labeling using PBTL
Since the pixel positions of and are predefined, they must be easy to distinguish. We only need to label the pixels in and using PBTL scheme. Given two parameters and , all pixels in are labeled by the same bits of ’0…0’, and the remaining bits are kept unmodified. For , all pixels are classified into different subcategories according to the different value of prediction error, pixels in the same subcategory are labeled with the same bit binary code, and pixels in different subcategories are labeled with different bit binary codes. What should be noticed is that because of the spatial correlation of the original image, the prediction error values and labels of the adjacent pixels are likely to be the same, which may reveal the original image content. To avoid this situation, the last few bits of each pixel are adopted instead of the first few bits for labeling, that is, for and , we arrange the 8bit binary of each pixel in reverse order before pixel labeling using PBTL.
IiiB Generation of Marked Encrypted Image
The parameters and are first stored in , Since , is sufficient to store them by bit replacement, the original 8 bits of pixel in are stored as auxiliary information. In addition, for all pixels in , the replaced original bits of each pixel need to be recorded as auxiliary information. Thus, the auxiliary information contains two parts: the original 8 bits of pixel in and the replaced original bits of each pixel in . The payload consists of auxiliary information and the secret data.
Each pixel in are labeled with bit binary code during pixel labeling, then the remaining (8) bits are reserved to embed payload bits by bit replacement. Therefore, totally bits of the payload can be successfully embedded, including bits of the auxiliary information and bits of the secret data, for data security, the secret data is first encrypted by using the data hiding key before the embedding operation. In this way, the marked encrypted image is generated.
The effective embedding rate under different settings of parameters and can be calculated as follows:
(8) 
In practice, we further obtain the maximum embedding rate (bpp) as
(9) 
The example of the pixel labeling and payload embedding when and is described in Fig. 8. Fig. 8(a) is the labeling bits selection of and . ’00’ is adopted to label each pixel in , ’111’, ’110’, ’101’, ’100’, ’011’ and ’010’ are applied to label pixels in when the predicted error equal to 2, 1, 0, 1, 2 and 3, respectively. Fig. 8(b) is the 8bit binary sequence of Fig. 6(d). Fig. 8(c) is the reverse order of each pixel in and . Fig. 8(d) shows pixel bits after pixel labeling. Fig. 8(e) is the encrypted image with labels and Fig. 8(f) is the marked encrypted image after payload embedding. As can be seen, the pixels in remain unchanged, the first 4 bits of are utilized to store and the last 4 bits of are utilized to store . Each pixel in are labeled with ’00’ and each pixel in are labeled with 3bit binary code according to different predicted error. ’—–’ represents the bits that have been embedded payload. It is observed that the payload contains the auxiliary information of ’00000001’,’00’,’10’ and ’01’.
IiiC Data Extraction and Image Recovery
At the receiver end, the secret information must be extracted without error from the marked encrypted image with only the datahiding key , the original image must be restored losslessly with only the encryption key . According to different permissions, one can obtain the original image, secret information or both.
IiiC1 Data extraction
After obtaining the marked encrypted image. Firstly, we remain the pixels in unmodiﬁed and extract the parameters and from . Secondly, for the rest pixels, we check the labels of their or bits in the 8bit binary value in reverse order and classify them into sets and . Next, we extract bits of the payload from the pixel in sequentially and obtain the encrypted secret data. Finally, the plaintext secret data can be obtained by decrypting using the datahiding key .
IiiC2 Image recovery
On the other hand, the replaced bits of each pixel in and 8 bits of the pixel in can be restored using the auxiliary information from the extracted payload, the original values of and must be obtained by decrypting using the encryption key . The original value of must be obtained by decrypting directly using the encryption key as the pixels in remain unmodiﬁed. For each pixel in , according to its labeling bits, we obtain the corresponding predicted error, then the original value of each pixel in can be obtained with the corresponding predicted error and the restored pixels in . By now the original content of the image is fully recovered.
Due to the invertibility of each step above, the secret information must be extracted without error using datahiding key and the original content of the image must be restored losslessly using the encryption key . The process of data extraction and image restoration is independent and separable.
Iv experimental results and analysis
Several experiments are performed to evaluate the performance of the proposed IPBTLRDHEI method. Five common 8bit depth images are used, as shown in Fig. 9. Moreover, in order to reduce the influence caused by the random selection of test images, three datasets including UCID [22], BOSSBase [23], and BOWS2 [24]
are also tested, respectively, for an average result. We use two metrics with PSNR (peak signaltonoise ratio) and SSIM (structural similarity) to evaluate the similarity between images. The embedding rate (ER) is expressed in bpp and is expected to be as large as possible to hide the maximal amount of information.
Iva Performance and Security Analysis
We perform the proposed IPBTLRDHEI method on the test images separately to evaluate the performance, Tables IIII show the maximal embedding rates of test images , , , and when = 2 to 4 and = 1 to 7. From the results, we can observe that when is set to small values, e.g., = 1 or 2, it indicates that the encrypted image with labels cannot or can only embed few secret data, ’/’ int the tables IIII represents the auxiliary information is larger than the reserved room, so no secret data can be embedded. As shown in tables IIII, different images should choose different parameters set to achieve the maximal embedding rate. In addition, the effect of image texture complexity on embedding capacity is significant, a smooth image can obtain a larger maximal embedding rate, this is because smooth images have more pixels belong to . For example, image can reach the maximal embedding rate of 3.0589 bpp when and .
(,)  (1,2)  (2,2)  (3,2)  (4,2)  (5,2)  (6,2)  (7,2) 

Lena  /  0.3933  1.6609  2.6867  2.6447  1.9285  0.9919 
Man  /  /  0.8173  2.0024  2.4790  1.9094  0.9894 
Jetplane  /  1.5395  2.6098  3.0250  2.6726  1.9223  0.9925 
Baboon  /  /  /  0.2039  0.9692  1.2402  0.8615 
Tiffamy  /  0.7108  1.9811  2.8478  2.6515  1.9288  0.9928 
(,)  (1,3)  (2,3)  (3,3)  (4,3)  (5,3)  (6,3)  (7,3) 

Lena  /  /  1.7087  2.7872  2.6770  1.9407  0.9929 
Man  /  /  0.6546  2.0924  2.5517  1.9925  0.9915 
Jetplane  /  0.9849  2.6962  3.0589  2.6900  1.9347  0.9939 
Baboon  /  /  /  /  0.8789  1.2502  0.8896 
Tiffamy  /  0.0525  2.0743  2.9204  2.6793  1.9416  0.9946 
(,)  (1,4)  (2,4)  (3,4)  (4,4)  (5,4)  (6,4)  (7,4) 

Lena  /  /  1.2997  2.7703  2.6693  1.9423  0.9933 
Man  /  /  0.1126  2.0374  2.5516  1.9226  0.9919 
Jetplane  /  0.4303  2.4107  3.0266  2.6778  1.9360  0.9942 
Baboon  /  /  /  /  0.6866  1.2002  0.8953 
Tiffamy  /  /  1.7111  2.8941  2.6703  1.9436  0.9949 
Fig. 10 takes as an example to show different images in different phases generated by the proposed IPBTLRDHEI method. Fig. 10(a) shows the original image. Fig. 10(b) shows the encrypted image obtained by the encryption key . Encrypted Image with labels is shown in Fig. 10(c). Fig. 10(d) presents the marked encrypted image. Fig. 10(e) gives the recovered image, which is completely the same as the original image in Fig. 10(a). Fig. 10(f) is the difference between Fig. 10(a) and Fig. 10(e), where all pixels are 0. The images shown in Fig. 7(b), (c) and (d) are noiselike images, it is difficult to detect the content of the plaintext image from its encrypted versions, which means they have a high perceptual security level.
Table IVVI perform the encrypted version images’ PSNR and SSIM with each original image to test the security of our method. As shown in the tables, the PSNR of each encrypted version image is very low and SSIM of each encrypted version image is almost 0, so no information can be obtained from the encrypted version images, which means the proposed IPBTLRDHEI method securely protects the privacy of the original image and can be applied to the RDH in the encryption domain.
Encrypted image  Lena  Man  Jetplane  Baboon  Tiffany 

PSNR  9.2255  7.9937  8.0077  9.5108  6.8839 
SSIM  0.0341  0.0681  0.0346  0.0299  0.0389 
Encrypted image  Lena  Man  Jetplane  Baboon  Tiffany 

with labels  
PSNR  9.2256  8.0096  7.9935  9.5215  6.8741 
SSIM  0.0347  0.0695  0.0353  0.0306  0.0391 
Marked encrypted  Lena  Man  Jetplane  Baboon  Tiffany 

image  
PSNR  9.2222  8.0176  7.9941  9.5182  6.8838 
SSIM  0.0351  0.0694  0.0359  0.0325  0.0375 
IvB Comparisons with Related Methods and Analysis
In this subsection, we compare the maximal embedding rate of the proposed IPBTLRDHEI method with several stateoftheart methods, the parameters and in IPBTLRDHEI are set to 5 and 2. In order to achieve a better performance, we set the length of fixedlength codewords to 3 and block size to in [21]. In [18] the block size is set to , and are also set to 5 and 2.
Fig. 11 shows the maximal embedding rate of test images, and results are compared with four competitors [18], [19], [20] and [21]. As can be seen, the proposed IPBTLRDHEI method achieves higher embedding rate and outperforms the competitors.
Moreover, in order to reduce the influence caused by the random selection of test images, the detailed embedding rates of IPBTLRDHEI on the three datasets is shown in Table VII. For the best cases, the embedding rates are 2.9759 bpp, 2.9883 bpp and 2.9883 bpp, respectively. Since is set to 5, that is, each pixel in is labeled with 5 bits and the remaining 3 bits can be embeded payload bits by bit replacement, so the best embedding rates approache 3. In UCID dataset, the worst embedding rate is 0, which means that the auxiliary information is larger than the reserved room, so no secret information can be embedded when and . and in table VII indicate each image can be recovered without any error.
Fig. 12 compares the average embedding rate of the three datasets between the proposed IPBTLRDHEI method and these four stateoftheart methods. The average embedding rate of the EPEHCRDH method in [19] is close to 1 bpp but no more than 1 bpp in the three datasets. The method of twoMSB planes substitution in [20] has a better performance than [19]. In addition, the average embedding rate of Chen ’s method [21] is higher, reaching 1.8768 bpp in the UCID dataset, 2.3226 bpp in the BOSSBase dataset and 2.2447 bpp in the BOWS2 dataset. Both Yi ’s method [18] and our method are based on PBTL, the results in Fig. 12 show that the proposed IPBTLRDHEI method signiﬁcantly improves the embedding rate compared with Yi ’s method [18], there are two reasons for this. First, the proposed IPBTLRDHEI method reserves room in the plaintext images before encryption, which can take full advantage of the redundancy of images. Second, we take advantage of the spatial correlation in the entire original images not in small image blocks to reserve room for embedding data, which reduces the number of reference pixels , that results in less ancillary information. Through the above analysis, it is verified that the proposed IPBTLRDHEI method has better performance.
Datasets  Indicators  Best case  Worst case  Average 

UCID  ER  2.9759  0  2.2683 
PSNR  +  +  +  
SSIM  1  1  1  
BOSSbase  ER  2.9883  0.0713  2.5613 
PSNR  +  +  +  
SSIM  1  1  1  
BOWS2  ER  2.9883  0.0484  2.5194 
PSNR  +  +  +  
SSIM  1  1  1 
V Conclusion
In this paper, we propose an efficient method of reversible data hiding in encrypted images using parametric binary tree labeling, which is an improved method based on Yi ’s works [18]. A higher embedding rate can be achieved and during the decoding phase, the secret information must be extracted without error using datahiding key and the original content of the image must be restored losslessly using the encryption key. The process of data extraction and image restoration is independent and separable. In addition, we see that the proposed IPBTLRDHEI method provides a good level of security that can be used to protect the confidentiality of the original image content while providing authenticity or integrity checks.
In the future, we also will try to modify and improve the proposed method, in order to have a much higher embedded capacity. In future research, we will test other error predictors in order to reduce the value of prediction errors, then more pixels can be utilized to embed secret data.
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