A novel reversible image authentication scheme for digital images

Signal Processing 98 (2014) 174–185

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Signal Processing journal homepage: www.elsevier.com/locate/sigpro

A novel reversible image authentication scheme for digital images Chun-Chi Lo a, Yu-Chen Hu b,n a

Department of Computer Science and Information Engineering, Providence University, 200 Chung Chi Road, Taichung 43301, Taiwan, ROC Department of Computer Science and Information Management, Providence University, 200 Chung Chi Road, Taichung 43301, Taiwan, ROC b

a r t i c l e in f o

abstract

Article history: Received 20 August 2013 Received in revised form 28 October 2013 Accepted 24 November 2013 Available online 1 December 2013

Image authentication is to protect the image integrity when the digital image is illegally modified. Most of the image authentication schemes proposed so far employed the irreversible data hiding approach to embed the authentication data into the cover images. In this paper, a novel reversible image authentication scheme for digital images is proposed. In the proposed scheme, the authentication codes are generated by using the random number values induced by the selected random number seed. Then, the authentication codes are embedded into the cover image. Experimental results show that the proposed scheme achieves good detecting accuracy while keeping good image quality of the embedded image. The proposed reversible image authentication can be employed to protect the image integrity of the general-purposed images as well as the specialpurposed images such as the medical and military images. & 2013 Elsevier B.V. All rights reserved.

Keywords: Tamper detection Image authentication Random number generator Digital signature Fragile watermark

1. Introduction In recent decades, the research issue towards the image integrity protection becomes more and more important because the digital images can be easily copied and modified by using the image processing software such as Adobe PhotoShop and PhotoImpact. The traditional cryptography approach can only be used to protect the security of digital images. When one cryptograph scheme, such as RSA, AES, MD5, or RSA, is employed to process the digital image, any change from the encrypted data can be detected. However, the tampered areas in the image cannot be located by using the cryptograph scheme. In other words, the cryptography approach is not suitable for the image integrity protection.

n Corresponding author. Tel.: þ886 4 26328001x18112; fax: þ 886 4 26324045. E-mail addresses: [email protected] (C.-C. Lo), [email protected] (Y.-C. Hu).

0165-1684/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sigpro.2013.11.028

The research toward image authentication [1] for image integrity protection had thus been proposed. In general, the image authentication schemes can be classified into two main categories: signature-based schemes [2–5] and fragile watermark-based schemes [6–16]. In a signaturebased scheme, the given image is processed by using the hash function and the hashed result is encrypted by using the public key cryptosystem to generate the digital signature. Then, the digital signature of the image to be protected is stored in a trust third party. When the given image is to be authenticated, the digital signature is extracted from the trust third party and it is compared to the other signature that is generated from the image to detect the tampered areas. In a fragile watermark-based scheme, the watermark data is embedded into the cover image. Typically, the watermark data is generated by using either the image features extracted from the cover image or the random values induced by the selected random number seed. When the desired image is to be authenticated, the watermark data is extracted from the image to detect the tampered

C.-C. Lo, Y.-C. Hu / Signal Processing 98 (2014) 174–185

areas. The detection accuracy and the image quality of the embedded image are the two major considerations for the fragile watermark-based image authentication approach. In 2001, Lin and Chang proposed a semi-fragile watermarking scheme [6] which can be resistant to lossy compression for JPEG images. Wong and Memon proposed the secret and public key image watermarking schemes [7] for image authentication and ownership verification in 2001. Lee and Lin proposed the dual watermark for both image tamper detection and image recovery [8] in 2008. Ahmed and Siyal proposed an image authentication scheme [9] based on the hash function in 2010. Qi and Xin proposed a quantization-based semi-fragile watermarking scheme [10] for image content authentication in 2011. Chan proposed the image authentication method by applying the Hamming code to the rearranged bits in 2011 [11]. A novel watermarking scheme with flexible selfrecovery quality had been proposed in 2011 [12]. In this scheme, the embedded watermark data for content recovery are computed from the original discrete cosine transform coefficients of the host image. When a part of a watermarked image is tampered, the watermark data in the area without any modification can be extracted. In addition, a novel fragile watermarking scheme with content restoration capability had been proposed in 2012 [13]. In this scheme, authentication bits are generated using the image hashing method with a folding operation. The low-frequency component of the non-subsampled contourlet transform coefficients is used to encode the restoration bits for each block by adaptive bit allocation mechanism. The fragile watermarking schemes [6–13] had been proposed to protect the image integrity of the digital images in raw format. In addition to the raw images, the compressed images of vector quantization and block truncation coding had been studied to design the image authentication schemes. Chung and Hu proposed an adaptive image authentication scheme for the compressed images of vector quantization in 2011 [14]. In this scheme, the authentication codes are generated by the random values induced by the selected random seed. Then, the authentication codes are embedded into the indices of the compressed images of vector quantization. In 2013, a tamper detection scheme [15] for block truncation coding had been proposed. In this scheme, 1-bit authentication code of each image block is generated from the quantization levels. Multiple copies of the authenticaiton data are embedded into the bit maps of compressed image blocks based on the block permutations. These block permutations are generated by using the random sequences induced by the selected random number seeds. In 2013, a joint image coding and image authentication scheme for block truncation coding had been introduced [16]. In this scheme, the digital image in raw format is compressed by block truncation coding. While the image coding process is executed, the authentication code of each image block is embedded into the compressed codes to protect the image integrity. In addition to the signature-based schemes and the fragile watermark-based schemes for image authentication mentioned above, a robust image hashing scheme using

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ring-based entropies had been proposed [17] for image authentication. In this scheme, the image hashing is achieved by converting the input image into a normalized image. The normalized image is then divided into different rings and the ring-based entropies are extracted to produce a hash. In general, data hiding schemes can be classified into two categories: irreversible data hiding schemes and reversible data hiding schemes [18]. In the irreversible data hiding schemes, secret data is first embedded into the original cover images to generate the stego-images. Then, secret data can be extracted when it is needed by executing the secret extraction procedure. However, the original cover images cannot be restored. The reversible data hiding schemes are also called the lossless data hiding schemes. The reversible data hiding schemes can extract the secret data and recover the original cover images simultaneously. Two main approaches of the reversible data hiding schemes had been introduced. They are the histogram shifting approach [19–22] and the difference expansion approach [23–25]. Some reversible data hiding schemes [26–28] that use the mix of these two approaches had also been proposed. Ni et al. proposed the histogram shifting scheme (HS) [19] for reversible data hiding in 2006. In this scheme, the occurrences of all possible pixel values in the cover image are calculated to generate the image histogram. The required pairs of peak and zero points from the image histogram are searched. Secret data is embedded into the pixels in the peak point. Those pixels whose values ranges from the peak point to the zero point have to be modified. By contrast, those pixels whose values are out of the range are not changed. The hiding capacity of HS equals the number of pixels in the peak point. The larger the number of pixels in the peak point is, the higher hiding capacity the scheme has. To increase the hiding capacity of HS, more pairs of peak and zero points can be used. Sometimes, it is impossible to find out more pairs of peak and zero points because the zero points are not searched. Tsai et al. proposed a prediction-based histogram shifting scheme (PBHS) [20] in 2009. The goal of PBHS is to improve the hiding capacity of the HS scheme. In PBHS, the host image is partitioned into non-overlapped image blocks. The center pixel in each block is selected as the basic pixel for predictive coding. For any block, the difference between each pixel and the basic pixel is calculated to generate the prediction error. No prediction error is generated for the basic pixel. After processing all image blocks, the residual image is generated. Then, the residual image histogram can then be produced. Finally, the residual image histogram is employed to embed the secret data. Similarly, multiple pairs of peak and zero points can be selected to embed secret data into the host image. For a reversible data hiding scheme based on histogram shifting, overflow and underflow problems are unavoidable. For example, it is not allowed to modify the pixel whose value is 0 or 255 in the HS scheme. To solve the overflow and underflow problems, the location map that records the overflow and underflow pixels can be generated. The location map can be viewed as the overhead of the

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histogram shifting scheme. The storage cost of the location map can be reduced by losslessly encoding it by any lossless data compression technique and then embed the compressed data into the host image. In addition to the location map method, one possible solution to solve the overflow and underflow problems is described here. If the number of the overflow and underflow pixels is quite small, the positions of these pixels can be recorded. For example, 18 bits are needed to record the position of one pixel in the grayscale image of 512 512 pixels. The position information can then be embedded into the host image. From the literature concerning the fragile watermarkbased image authentication schemes, we find that the irreversible data hiding approach is employed in most schemes to embed the authentication data into the cover images. As far as we know, the irreversible data hiding approach provides a higher hiding capacity than the reversible data hiding approach. In other words, the design of the irreversible image authentication scheme is much easier than that of the reversible image authentication because more authentication data can be embedded into the cover image. However, the irreversible image authentication approach is not suitable for image integrity protection of some important images, such as the remote sensing images, the medical images, the military images, because any alterations of these images are not permitted. To protect the image integrity for the general-purposed images as well as the special-purposed images, a reversible image authentication scheme for digital images is proposed in this paper. This scheme is a kind of the fragile watermark-based image authentication scheme. A blockbased data embedding process is designed and the authentication data of each image block is embedded into the embeddable positions based on the prediction-based histogram shifting. The rest of this paper is organized as follows. Section 2 will present the proposed scheme. The experimental results are discussed in Section 3. Finally, the conclusions is given in Section 4. 2. The proposed scheme The goal of the proposed scheme is to detect the tampered areas for the digital images. If the image is not tampered, the authentication data can be extracted and the embedded image can be recovered back to the original image. If the image is tampered, the tamper areas of the image will be detected. The proposed scheme consists of three procedures: authentication codes generation procedure, the authentication codes embedding procedure, and the tamper detection procedure which are described in the following subsections.

w h random values. Each random value v is then converted to the 1-bit authentication code (c) by using the following equation: c ¼ v mod 2:

ð1Þ

As we know, the hiding capacities of the reversible data hiding schemes are generally much less than those of the irreversible data hiding schemes. Therefore, only 1-bit authentication code is generated for each image block. 2.2. The authentication codes embedding procedure Basically, the authentication codes embedding procedure is similar to the data embedding procedure in the PBHS scheme. The difference between them is to embed the authentication codes or secret data into the embeddable positions in the residual image. In the PBHS scheme,

Authentication codes

Cover image Predictive coding

Generate residual histogram

Search p pairs of peak point and zero point

Block-based data embedding

Inverse predictive coding Stego-image Fig. 1. Flowchart of the proposed authentication codes embedding procedure.

p pairs of peak and zero points

Stego-image

seed S

Predictive coding Generate residual histogram

Generate the authentication code for each block

Extract authentication codes

2.1. The authentication codes generation procedure Suppose the grayscale image of W H pixels is to be processed. It is divided into non-overlapping image blocks of n n pixels. A total of w h image blocks are divided where w¼W/n and h ¼H/n. A total number of w h authentication codes will be generated. To generate the authentication codes, the pseudo random number generator (PRNG) with a predefined seed S is used to generate

Generate residual image

Collect authentication codes for each block

Inverse predictive coding

Tamper detection of each block

Cover image

Detected image

Fig. 2. Flowchart of the proposed tamper detection procedure.


1-bit secret data is embedded into each embeddable residual value, but 1-bit authentication code is embedded into the embeddable locations of each image block in the proposed authentication codes embedding procedure.

b

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The flowchart of authentication codes embedding procedure is depicted in Fig. 1. In the proposed scheme, the cover image is first processed by the predictive coding process. In this process, the cover image is divided into

b

b

b

Fig. 3. Four test cases for tamper refinement. (a) Case 1, (b) Case 2, (c) Case 3 and (d) Case 4.

Fig. 4. Six testing images of 512 512 pixels. (a) Airplane; (b) boat; (c) girl; (d) goldhill; (e) lenna; and (f) pepper.

Table 1 Hiding capacity (unit: bits) of the proposed scheme when the block size is set to 4 4. Images

p¼ 1

p ¼2

p¼3

p¼ 4

p¼5

Airplane Boat Girl Goldhill Lenna Pepper

36,532 23,047 22,442 16,463 24,447 22,345

63,616 44,631 43,746 31,903 46,009 42,960

63,620 44,637 43,767 31,909 46,014 42,966

63,623 44,641 43,767 31,911 46,018 42,969

63,625 44,644 43,782 31,913 46,022 42,971

Average

24,212.667

45,477.500

45,485.500

45,488.167

45,492.833

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non-overlapping image blocks of n n pixels. The center pixel in each block is chosen as the basic pixel for predictive coding. For any block, the difference between each pixel and the basic pixel is computed to generate the prediction error. After processing all image blocks, the residual image is generated. The occurrences of all possible

Fig. 5. Image qualities of the embedded images of the proposed scheme.

values in the residual image are calculated to generate the residual image histogram. Let p denote the pair of peak and zero points that will be used to embed the authentication data. The value of p in the residual histogram are searched before the actually data embedding process is executed. A block-based data embedding process that is similar to that in the PBHS scheme is employed here. In the PBHS scheme, the secret data is randomly generated and each embeddable residual value is used to carry 1-bit secret data. In the proposed authentication codes embedding process, the residual values are divided into non-overlapping image blocks. Let c denote the 1-bit authentication code that will be embedded into the embeddable residual values in each residual block. The same authentication code c is embedded into these embeddable residual values in each residual block. By sequentially embedding the 1-bit authentication code of each block in the same way, the embedded residual values are generated. Finally, the stego-image is produced by performing the inverse predictive coding process on the embedded residual values.

Fig. 6. Embedded images “Lenna” of the proposed scheme when the block size equals 4 4. (a) p ¼1 with 51.454 dB; (b) p ¼2 with 48.826 dB; (c) p ¼3 with 48.826 dB; and (d) p ¼4 with 48.826 dB.


Recall that (n n 1) residual values are generated in the predictive coding process when image size equals n n. The total number of embeddable residual values is

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ranged between 0 and (n n 1). It may happen that there is no embeddable residual value in some image blocks. In other words, no authentication codes can be embedded

Fig. 7. The tampered object of the test. (a) The tampered object of 6217 pixels and (b) the binary tampered object.

Fig. 8. Tampered images “Lenna” of the proposed scheme when the block size equals 4 4. (a) p ¼1; (b) p ¼ 2; (c) p ¼3; and (d) p¼ 4.

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Fig. 9. The difference images for the tamper test. (a) Pixel difference image (p ¼1); (b) block difference image (p¼ 1); (c) pixel difference image (p ¼2); (d) block difference image (p ¼2); (e) pixel difference image (p ¼3); (f) block difference image (p ¼3); (g) pixel difference image (p ¼4); and (h) block difference image (p ¼4).


into some image blocks where their residual values are not located at the peak points.

2.3. The tamper detection procedure The goal of the tamper detection procedure is to detect whether the given image of W H pixels is modified or not. If this image is modified, the tamper areas of the image will be detected. If this image is not tampered, the authentication codes can be extracted and the original cover image can be recovered. Some system parameters, such as W, H, n, p, and the random number seed S, should be known in advnace. In addition, p pairs of peak and zero points should be available. The flowchart of the tamper detection procedure is shown in Fig. 2. To determine whether these w h image blocks are tampered or not, two sets of authentication codes of the image block are to be generated. The PRNG with the random seed S is employed to generate w h random values. Each random value v is then converted to 1-bit authentication code c by using Eq. (1). By collecting all the authentication codes of the image blocks, the first set of authentication codes is generated. The second set of the authentication codes will be extracted by using the data extraction procedure of the PBHS scheme. To extract the authentication codes, the predictive coding is performed on the given image to generate the residual image. Then, the residual histogram is produced. The authentication codes are then extracted by processing the residual values with the use of p pairs of peak and zero point. The residual values are recovered to generate the residual image. Then, the cover image is rebuilt by performing inverse predictive coding. To generate the second set of the authentication codes, the authentication codes that are extracted by using the PBHS data extraction procedure are processed. All the authentication codes in each block are collected together. The number of the authentication codes that are classified as the same block ranges between 0 and (n n 1). After collecting the authentications codes of the image blocks, the second set of the authentication codes is generated. When two sets of authentication codes are available, we can determine whether each image block is tampered or not. Let t denote the total number of extracted authentication codes of the block in the second set, where 0 rtrn n. If t copies of the extracted authentication codes and c in the first set are equal, this block is classified as a clear block. Otherwise, it is classified as a modified block. Here, a white pixel and a black one are used in the detected image for a clear block and a modified block, respectively. When these two sets of the authentication codes for each image block are sequentially checked by the same way, the detected image is generated. The above detected result needs to be further refined because it is possible that some modified blocks may not be detected in the above-mentioned process. In the proposed scheme, some image blocks without embedding any authentication codes can be found due to the limited hiding capacity. In addition, it may happen that the extracted authentication codes of some image blocks in the tampered image have the

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same values as their corresponding authentication codes generated by using PRNG with the random seed S. To further improve the detecting accuracy, an iterative tamper refinement process is employed to process the roughly detected image of size w h. In each round, four test cases as shown in Fig. 3 are sequentially checked to decide whether each white pixel will be changed to a black one or not. Here, b denotes the selected white pixel to be processed. In the first case of Fig. 3(a), if the adjacent up and down pixels of b are black, b will be changed to a black pixel. In the second case of Fig. 3(b), if the adjacent left and right pixels of b are black, b is changed to a black one. Similarly, two additional cases for the 451 and 1351 splay black pixels of b are listed in Fig. 3(c) and (d), respectively. After checking each white pixel in the current detected image to determine whether it will be changed to a black one or not, the total number of modified pixels in each round is calculated. If the number of modified pixels is greater than or equal to 1, the same tamper refinement process is iterated by using the modified detected image. Otherwise, the tamper refinement process is stopped. 3. Experimental results Our experiments are performed on windows 7 PC with an Intel Core i5 2.8 GHz CPU and the 2 GB RAM. The testing programs are implemented by using Bloodshed Dev C þ þ. In our experiments, six grayscale images of 512 512 pixels, “Airplane”, “Boat”, “Girl”, “Goldhill”, “Lenna”, and “Pepper” as shown in Fig. 4, are used. In the simulations, the block size is set to 4 4. Table 1 lists the hiding capacities of the proposed scheme. It is shown that the hiding capacity increases as p increases. Average hiding capacities of 24,212.667, 45,477.5, and 45,485.5 bits are achieved by the block-based histogram shifting scheme with 4 4 blocks when p values are set to 1, 2, and 3, respectively. The gain of hiding capacity is quite small when p is increased from 2 to 3 or more. Therefore, it is suggested that the maximal p value should be set to 2. Results of the embedded image qualities of the proposed scheme are listed in Fig. 5. It is shown that the average embedded image quality decreases with the increase of the p value. Average image quality of 51.475 dB is achieved by the proposed scheme with p set to 1. Besides, average image quality of 48.830 dB is achieved by the proposed scheme with p set to 2. The embedded images “Lenna” of the proposed scheme with different p values are shown in Fig. 6. In these four embedded images, the p values are set to 1 to 4, respectively. In the tamper test, a butterfly as shown in Fig. 7(a) is added on the shoulder of each embedded image. The tampered object in the binary form is shown in Fig. 7(b). In the tamper Table 2 Total numbers of different pixels and different blocks in the tamper test. p

No. of different pixels

No. of different blocks

p¼1 p¼2 p¼3 p¼4

6146 6148 6148 6148

456 456 456 456

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Fig. 10. Detected images of the proposed scheme. (a) Roughly detected image (p ¼1); (b) the refined image (p ¼ 1); (c) roughly detected image (p ¼ 2); (d) the refined image (p ¼ 2); (e) roughly detected image (p ¼ 3); (f) the refined image (p¼ 3); (g) roughly detected image (p ¼4); and (h) the refined image (p ¼4).


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test, there are 6217 pixels within the tampered object and 461 blocks of 4 4 pixels are affected. These four tampered images when the p values are set to 1–4 are shown in Fig. 8. The pixel difference images and the block difference images for the tamper test are listed in Fig. 9. From the results, some white spots within the tampered object are found in each pixel difference image. It indicates that some modified pixels within the butterfly have the same gray levels as the original pixels in the embedded image. The total numbers of different pixels and different blocks in the tamper test when the p values are set to 1–4 are listed in Table 2. It is shown that 456 image blocks are tampered for these p values.

The detected results of the proposed tamper detection procedure are listed in Fig. 10. The roughly detected images and the refined images are listed. No white spots are found within the modified areas in these final refined images. Compared to the tampered area as shown in Fig. 7(b), the tampered area of each refined image is clearly detected. However, some modified blocks in the boundary of the tampered area cannot be detected by using the proposed tamper detection procedure. The total numbers of the tampered blocks in the roughly detected images and the final refined images by using the proposed scheme are listed in Table 3. The numbers of the tampered blocks in the roughly detected

Table 3 Total numbers of the tampered image blocks in the roughly detected images and the final refined images.

Table 4 Analysis of the tamper test (unit: pixel).

p

Roughly detected image

Final refined image

Factors

p¼1

p¼ 2

p¼3

p ¼4

p¼1 p¼2 p¼3 p¼4

208 286 286 287

382 409 409 409

TP TN FP FN

370 91 12 15,911

398 63 11 15,912

398 63 11 15,912

398 63 11 15,912

Fig. 11. Results of the false detection for the tamper test. (a) False detection image (p ¼ 1); (b) false detection image (p ¼ 2); (c) false detection image (p ¼3); and (d) false detection image (p¼ 4).

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images are equal to 208, 286, 286, and 287 when the p values are 1, 2, 3, and 4, respectively. There are 382, 409, 409, and 409 tampered blocks in the refined images when the p values are 1, 2, 3, and 4, respectively. Results of the false detected images of the proposed tamper detection procedure are listed in Fig. 11. The false Table 5 Total number of image blocks with different embeddable bits in the tamper test. t

p ¼1

p¼2

p¼3

p¼4

t¼ 0 t¼ 1 t¼ 2 t¼ 3 t¼ 4 t¼ 5 t¼ 6 t¼ 7 t¼ 8 t¼ 9 t¼ 10 t¼ 11 t¼ 12 t¼ 13 t¼ 14 t¼ 15

5729 4219 2800 1723 938 511 259 119 52 13 3 17 0 0 0 1

3126 3202 2635 2074 1566 1205 935 676 459 252 121 90 27 8 4 4

3124 3202 2637 2073 1567 1205 935 676 459 252 121 90 27 8 4 4

3123 3201 2638 2074 1567 1205 935 676 459 252 121 90 27 8 4 4

detected image blocks are found in the boundary of the tampered area in each refined image. In addition, the analysis of the detecting accuracy for the tamper tests is listed in Table 4. The results of true positive (TP), true negative (TN), false positive (FP), and false negative are provided for these tests. There are 16,384 image blocks for each 512 512 image when the block size is set to 4 4. Recall that 456 blocks are affected when a butterfly is added into the embedded images in the tamper test. According to the results, 91, 63, 63, and 63 true negative blocks are detected for the first tamper test when the p values are 1, 2, 3, and 4, respectively. In addition, 12, 11, 11, and 11 false positive blocks are detected for the first tamper test when the p values are 1, 2, 3, and 4, respectively. Results of the total numbers of the image blocks with different embeddable bits are listed in Table 5. The numbers of the blocks without any embeddable bits in the roughly detected images are equal to 5729, 3216, 3124, and 3123 when the p values are 1, 2, 3, and 4, respectively. There are 34.967%, 19.629%, 19.067%, and 19.067% blocks of 4 4 pixels with no embeddable positions when the p values are 1, 2, 3, and 4, respectively. To understand the distribution of the embeddable locations in the proposed scheme, locations of the un-embeddable blocks in the test image “Lenna” are listed in Fig. 12. The

Fig. 12. Locations of the un-embeddable blocks in the test image “Lenna”. (a) p ¼1; (b) p ¼ 2; (c) p ¼ 3; and (d) p ¼ 4.


number of un-embeddable blocks decreases as the p value increases in the proposed scheme. 4. Conclusions A novel reversible tamper detection scheme is proposed in the paper. A block-based authentication code generation procedure is designed in the proposed scheme because the hiding capacity of the reversible data hiding approach is limited. The authentication codes are then embedded into the residual values block by block by using the prediction-based histogram shifting process. Multiple pairs of peak and zero points can be selected to embed the authentication codes in the proposed scheme. From the experimental results, good image qualities of the embedded images are obtained in the proposed scheme. Average embedded image qualities of 51.475 dB and 48.830 dB are achieved with the block size 4 4 when the p values are set to 1 and 2, respectively. In addition, clear tampered shapes can be detected for the tampered images by using the proposed scheme. According to the false detected images of the proposed scheme, only few false detected blocks appear in the boundary of the tampered area. Traditional irreversible image authentication schemes can only be employed to detect the tampered images of the general-purposed images. The proposed scheme provides the data reversibility and can be employed to protect the image integrity of the general-purposed images as well as the special-purposed images. In other words, the proposed image authentication scheme can be used to detect the tampered areas for the remote sensing images, the medical images, the military images, and so on.

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