An Improved Reversible Data Hiding in Encrypted Images using Parametric Binary Tree Labeling

05/23/2019 ∙ by Youqing Wu, et al. ∙ 0

This work proposes an improved reversible data hiding scheme in encrypted images using parametric binary tree labeling(IPBTL-RDHEI), which takes advantage of the spatial correlation in the entire original image not in small image blocks to reserve room for embedding data before image encryption, then the original image is encrypted with a secret key and parametric binary tree labeling is used to label image pixels in two different categories. According to the experimental results, compared with several state-of-the-art methods, the proposed IPBTL-RDHEI method achieves higher embedding rate and outperforms the competitors. Due to the reversibility of IPBTL-RDHEI, the original content of the image and the secret information can be restored and extracted losslessly and separately.

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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 compression-based

[5, 6], difference expansion-based [7, 8, 9] and histogram shifting-based [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 content-owner, data-hider and receiver. The content-owner, that is, the original image provider, encrypts the original plaintext image before sending it to the data-hider. The data-hider 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.

Fig. 1: The frameworks of RDHEI methods.

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 one-MSB, 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 two-MSB (MSB and second MSB) planes substitution so that the embedding rate can exceed 1 bpp. Chen [21] adopted the extended run-length coding and block-based 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], IPBTL-RDHEI is proposed in this paper, which is a novel RRBE separable RDHEI method with high capacity. First, IPBTL-RDHEI reserves embedding space in the plaintext image before encryption by the content-owner. Second, at the data-hider end, the proposed IPBTL-RDHEI 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 IPBTL-RDHEI 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 IPBTL-RDHEI 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.

Fig. 2: The distribution of binary codes in a full binary tree.

For pixels with 8-bit 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 sub-categories according to and , where is calculated by:

(1)

When , the nodes from right to left in the layer are selected to label different sub-categories in G1. When , the nodes from right to left in the layer are selected to label different sub-categories in G1, that is, when , the selected binary codes that are not derived from the node of ’0…0’. Moreover, pixels in the same sub-category are labeled with the same -bit binary code, and pixels in different sub-categories 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.

Fig. 3: Illustrative example of labeling bits selection when = 1 to 3 and = 1 to 7
Fig. 4: The framework of the proposed IPBTL-RDHEI method.

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 sub-categories 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 IPBTL-RDHEI method is composed of three main phases: 1) Generation of encrypted image with labels done by the content-owner, 2) Generation of marked encrypted image done by the data-hider, and 3) Data-extraction/image-recovery done by the receiver. In the first phase, the content-owner 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 data-hiding 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 data-hiding 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 IPBTL-RDHEI method.

Iii-a 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.

Fig. 5: The context of the MED predictor.

Iii-A1 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)

Iii-A2 Image Encryption

After obtaining the predicted error of the 8-bit depth original image , we convert all pixels in the original image into 8-bit 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 pseudo-random matrix

of the same size as the original image is generated by an encryption key, similarly, each pixel value of is converted into 8-bit binary sequence using Eq. (4). Then the encrypted 8-bit binary sequence can be obtained through the bitwise exclusive-or (XOR) operation:

(5)

where is the bitwise XOR operation, and denotes the encrypted 8-bit binary sequence. Finally, Eq. (6) is used to calculate the encrypted pixel

(6)
Fig. 6: Example of prediction and image encryption: (a) original image, (b) predicted value, (c) predicted error and (d) encrypted image.

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 .

Iii-A3 pixel grouping

We separate all pixels in into four sets, namely: reference pixel (), special pixel (), embeddable pixel () and non-embeddable 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 .

Fig. 7: Pixel grouping.

Iii-A4 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 sub-categories according to the different value of prediction error, pixels in the same sub-category are labeled with the same -bit binary code, and pixels in different sub-categories 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 8-bit binary of each pixel in reverse order before pixel labeling using PBTL.

Iii-B 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.

Fig. 8: Illustrative example of the pixel labeling and payload embedding when and : (a) Labeling bits selection, (b) The 8-bit binary representation of Fig. 6(d), (c) Reverse order of 8-bit binary in and , (d) Pixel bits after pixel labeling, (e) Encrypted image with labels and (f) Marked encrypted image.
Fig. 9: Test images: (a) , (b) , (c) , (d) , and (e) .

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 8-bit 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 3-bit 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’.

Iii-C 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 data-hiding 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.

Iii-C1 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 8-bit 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 data-hiding key .

Iii-C2 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 data-hiding 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 IPBTL-RDHEI method. Five common 8-bit 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 BOWS-2 [24]

are also tested, respectively, for an average result. We use two metrics with PSNR (peak signal-to-noise 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.

Fig. 10: Simulation relsuts of applying the proposed IPBTL-RDHEI method to image when and : (a) the original image, (b) encrypted image, (c) encrypted image with labels, (d) marked encrypted image,, (e) recovered image, and , (f) the difference between (a) and (e)

Iv-a Performance and Security Analysis

We perform the proposed IPBTL-RDHEI method on the test images separately to evaluate the performance, Tables I-III 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 I-III represents the auxiliary information is larger than the reserved room, so no secret data can be embedded. As shown in tables I-III, 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
TABLE I: Embedding rates of test images when = 2 and = 1 to 7.
(,) (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
TABLE II: Embedding rates of test images when = 3 and = 1 to 7.
(,) (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
TABLE III: Embedding rates of test images when = 4 and = 1 to 7.

Fig. 10 takes as an example to show different images in different phases generated by the proposed IPBTL-RDHEI 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 noise-like 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 IV-VI 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 IPBTL-RDHEI 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
TABLE IV: Encrypted images’ PSNR and SSIM with the original images when and .
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
TABLE V: Encrypted images with labels’ PSNR and SSIM with the original images when and .
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
TABLE VI: Marked encrypted images’ PSNR and SSIM with the original images when and .

Iv-B Comparisons with Related Methods and Analysis

In this subsection, we compare the maximal embedding rate of the proposed IPBTL-RDHEI method with several state-of-the-art methods, the parameters and in IPBTL-RDHEI are set to 5 and 2. In order to achieve a better performance, we set the length of fixed-length 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 IPBTL-RDHEI method achieves higher embedding rate and outperforms the competitors.

Fig. 11: Comparison of maximal ER (bpp) of test images between our method and four state-of-the-art methods.
Fig. 12: Comparison of the average ER (bpp) of three datasets between our method and four state-of-the-art methods.

Moreover, in order to reduce the influence caused by the random selection of test images, the detailed embedding rates of IPBTL-RDHEI 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 IPBTL-RDHEI method and these four state-of-the-art methods. The average embedding rate of the EPE-HCRDH method in [19] is close to 1 bpp but no more than 1 bpp in the three datasets. The method of two-MSB 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 BOWS-2 dataset. Both Yi ’s method [18] and our method are based on PBTL, the results in Fig. 12 show that the proposed IPBTL-RDHEI method significantly improves the embedding rate compared with Yi ’s method [18], there are two reasons for this. First, the proposed IPBTL-RDHEI 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 IPBTL-RDHEI 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
BOWS-2 ER 2.9883 0.0484 2.5194
PSNR + + +
SSIM 1 1 1
TABLE VII: Detailed ER (bpp) of our method on the three datasets when = 5 and = 2 .

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 data-hiding 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 IPBTL-RDHEI 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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