J Forensic Sci, 2014 doi: 10.1111/1556-4029.12618 Available online at: onlinelibrary.wiley.com
TECHNICAL NOTE DIGITAL & MULTIMEDIA SCIENCES
Yanjun Cao,1 Ph.D.; Tiegang Gao,2 Ph.D.; Guorui Sheng,1 Ph.D.; Li Fan,1 Ph.D.; and Lin Gao,1 Ph.D.
A New Anti-forensic Scheme— Hiding the Single JPEG Compression Trace for Digital Image
ABSTRACT: To prevent image forgeries, a number of forensic techniques for digital image have been developed that can detect an image’s origin, trace its processing history, and can also locate the position of tampering. Especially, the statistical footprint left by JPEG compression operation can be a valuable source of information for the forensic analyst, and some image forensic algorithm have been raised based on the image statistics in the DCT domain. Recently, it has been shown that footprints can be removed by adding a suitable anti-forensic dithering signal to the image in the DCT domain, this results in invalid for some image forensic algorithms. In this paper, a novel anti-forensic algorithm is proposed, which is capable of concealing the quantization artifacts that left in the single JPEG compressed image. In the scheme, a chaos-based dither is added to an image’s DCT coefficients to remove such artifacts. Effectiveness of both the scheme and the loss of image quality are evaluated through the experiments. The simulation results show that the proposed anti-forensic scheme can verify the reliability of the JPEG forensic tools. KEYWORDS: forensic science, anti-forensic, digital image forgery, single JPEG compression, digital fingerprint, chaotic signal With the popularity of low-cost and higher resolution digital cameras, digital images are playing an important role than ever before, a variety of digital products can be visited through internet no matter when and where. However, due to the powerful image editing software (e.g., Photoshop, Illustrator, 3D max), digital images can be easily manipulated and altered without leaving visible clues; thus, it poses a serious social problem such as much of their content can be trusted, whether it can be used as a witness in a courtroom, insurance claims, and scientific fraud. As a mature standard, JPEG compression has been widely used in digital image coding, and in some application cases, many multimedia metadata are compressed in this format. Therefore, the intrinsic footprints left by the JPEG compression may give useful information for the inspector to trace the previous JPEG history, and some forensic techniques have been utilized to successfully distinguish an image’s JPEG operation with the help of the statistical feature. When a digital image is compressed into the JPEG format, the image histogram of the DCT coefficients will leave a visible characteristic known as quantization artifacts; by means of this property, Popescu et al. gave the evidence of whether an image underwent double JPEG compression (1,2) and Lukas et al. can even estimate the primary quantization matrix (3,4). What is more, by employing the quantization artifacts during JPEG processing, Li and Sun extracted block artifact grids (BAG) (5,6), and the mismatch between these grids can be taken as a
1 College of Information Technical Science, Nankai University, No 94, Weijin Road, Tianjin, Nankai District, 300071, China. 2 College of Software, Nankai University, No 94, Weijin Road, Tianjin, Nankai District, 300071, China. Received 30 Dec. 2012; and in revised form 11 June 2013; accepted 4 July 2013.
© 2014 American Academy of Forensic Sciences
trial of tampering. Obviously, if the image is directly carried out the JPEG compression, the compression history can be obtained by some existing forensic schemes. However, sometimes the compression trace of image needs to be concealed for some political or other purpose, so some algorithms that can hide mark of image compression must be considered; this is called anti-forensic scheme. Image anti-forensic scheme aims at covering history of distorting for the image and making some forensic algorithm against image tampering ineffective. At presents, some researchers have realized the importance of anti-forensic and some schemes have been proposed. For example, Kirchner et al. (7) proposed a method using a series of processing to make the resampling (e.g., rotation and scaling) undetectable; Zhao et al. (8) designed an operator to conceal the peak– gap artifacts that left in the histogram of the contrast-enhanced image, on the other hand, Stamm et al. (9,10) hided the DCT coefficient quantization artifacts through adding anti-forensic dither; their methods can test the robustness of some JPEG forensic tools, but, with this scheme, in the high frequency subbands, it is more likely that all coefficients are quantized to zero; this may result in that the parameter estimator has no solution, and consequently, it leaves clues to the forensic investigator, based on this situation, an improved scheme that uses imputation to deal with cases that lack an estimator was proposed (11). At present, there is only a little work for image anti-forensic to make the existing image forensics algorithms more reliable and robust; the research work on anti-forensic needs to be widely explored and tested. In this paper, a novel image anti-forensic scheme is proposed the pseudo-code of the anti-forensic Algorithm is shown in Appendix. The scheme can attack against the state-of-the-art BAG-based forensic methods, which have been proposed by Li 1
2
JOURNAL OF FORENSIC SCIENCES
and Ye (5,6). Different from Stamm’s work (9,10), in the proposed scheme, a chaos-based dither technique is introduced into the work, and chaotic noise is mapped into an image’s DCT quantization coefficients for the target of removing such artifacts. To the best of our knowledge, this is the first time that chaos-based dither technology is used in the anti-forensic research area. Different from Stamm’s anti-forensic scheme, the proposed anti-forensic method can give parameter estimate even if the JPEG quality factor is smaller, and so the performance is better with the lower JPEG quality factor than that of the Stamm’s. A large number of experiments show that the proposed scheme can remove the compression artifacts, and it also can befool some forensic algorithms. The rest of the paper is organized as follows: JPEG compression background and method is briefly reviewed, followed by the proposed anti-forensic scheme, and then the experimental results and the corresponding analysis are given. Finally, some conclusion remarks for the future work are given. Brief Review of the JPEG Compression JPEG is one of the most popular standards for the effective compression of the still digital images; when an image with the size of IM 9 N is compressed in JPEG format, it must undergo two phases: • Encoding 1
2 3
For the purpose of encoding, the image is first segmented into a series of nonoverlapping sub-blocks with the size of 8 9 8 pixels, denoting each sub-block as M N k : Bi;j 1 i; j 8; 1 k 8 8 The 2D-DCT transform is applied to each sub-block Bki;j . Each transformed DCT coefficient Ci,j is quantized by its corresponding quantizer Qi,j within a quantization table Q, and it
• 1
2
3
should be noted that, different digital device may have distinct quantization table. Consequently, after the previous processing, each DCT coefficient Ci,j is quantized to the approximate value ^ i;j ¼ roundðCi;j =Qi;j Þ; ð1 i 8; 1 j 8Þ, then those C quantized DCT coefficients are entropy encoded and form the final JPEG file. Decoding For the decoder, when he receives the JPEG file, first, he operates the procedure by decoding the JPEG bit stream to the original sequence. The inverse quantization is carried out for each quantized DCT coefficient by simply multiplying its corresponding quantizer Qi,j, denoting the dequantized coefficient as 0 ^ i;j Qi;j : ¼C Ci;j The 2D-IDCT transform is performed on each DCT coefficient sub-block and the results are rounded and truncated to the integer interval [0, 255].
It can be seen from the JPEG compression and decompression process that there left a significant footprint in the decompressed image. One is the rounding artifact, the other is the truncating artifact, as the rounding operation occurs in each 8 9 8 block and the error brought by truncating highly depends on the image content; the rounding error is the attention in the proposed scheme. After quantization and dequantization, each DCT coefficient will be an integer multiple of the quantizer Qi,j, this can be obtained from the analysis of Eq. (1), which is given in the following. ^ i;j Qi;j C0 ¼ C i;j
ð1Þ
zfflfflfflfflfflfflffl}|fflfflfflfflfflfflffl{ Ci;j ¼ roundð Þ Qi;j Qi;j |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}
ð1Þ
ð2Þ
In Eq. (1), after step (1), the intermediate result Ci,j/Qi,j is rounded to the integer value, and the multiplication between
FIG. 1––The histograms of the DCT coefficients for different sub-bands. (a): The histograms of the uncompressed image’s DCT Coefficients for 63 AC subbands. (b): The histogram taken from the (2, 3) sub-band. (c): The same image after JPEG compression, and (d): The anti-forensically altered version by using our proposed method.
CAO ET AL.
two integers will also generate integer value, just as step (2) 0 will cluster shows; hence, the dequantized coefficients Ci;j around the integral multiple of Qi,j and leave visible big gaps in the histogram, which can be seen in Fig. 1. Figure 1a is the histograms of the uncompressed image’s DCT coefficients for 63 AC sub-bands; all these DCT coefficients are unquantized, as can be seen in Fig. 1a; if the image did not undergo JPEG compression, there will not be distinct artifacts in the histogram of the DCT coefficients. On the contrary, due to the lossy JPEG compression, visible big gaps are left, that can be used by the forensic tools. In the proposed scheme, chaotic signal noise is used to fill these gaps; thus, the distribution of the anti-forensically reconstructed DCT coefficients can accord with the uncompressed one, and it can be shown in Fig. 1c and Fig. 1d, where Fig. 1c and Fig. 1d are the histograms before and after applying chaos-based anti-forensic scheme. Anti-forensic Scheme To conceal the DCT coefficient quantization artifacts, suitable noise needs to be injected into the quantized DCT coefficients, so that the gaps of the DCT coefficient histogram can be removed. However, when the signal noise is added, there is a thorny issue—how much noise should be added? If the additive noise is excessive, the image will induce visual distortion, and on the contrary, the gap traces left in the quantized DCT coefficients cannot be erased. So the distribution of the additive noise must be modeled from the quantized DCT coefficients, then using the chaos optimization and combining with the chaos-based dither, and the scheme can generate the suitable noise. The detailed anti-forensic scheme is shown in Fig. 2. The Model of DCT Coefficients The distribution of the DCT coefficients has been thoroughly studied and researched in the past decade, and Gamma, Laplacian, or Gaussian distribution for AC coefficients are typical model; among them, the Laplacian distribution is the most suitable model for the AC coefficients (12,13), while there is no general model for the DC coefficients. In the proposed scheme, the AC coefficients is used as Laplacian distribution, and for the DC coefficients, chaos is used to generate the desired distribution. Generally speaking, the Laplacian PDF (Probability Distribution Function) of the unquantized AC coefficients is defined as
FIG. 2––The anti-forensic scheme.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
f ðxÞ ¼
k 2
expðkxÞ if x \ 0 expðkxÞ if x 0
3 ð2Þ
After quantization, the AC components of the DCT coefficients may be distributed to the different discrete interval, but the AC DCT coefficients scattered in each interval still obey the Laplacian distribution, therefore, estimating the parameter k accurately is the key problem. Since during the JPEG compression, to achieve the desired compression ratio, different quantization step length maybe used for different sub-bands; generally, the larger step length is used for the high frequency while smaller step length is used for the low frequency; thus, the variance of the DCT coefficients in different sub-bands will be different; using this property, formula (14) is used to estimate the parameter k. pffiffiffi 2 ð3Þ k¼ r where r stands for the variance of the dequantized coefficients. As no general model can be used for the DC coefficients, another way was used to generate the desired noise, which is extensively discussed in next Section. Noise Adding As was analyzed in the previous sections, the noise added to each AC coefficient must obey the Laplacian distribution, so we can generate the approximate noise by simply using Eq. (2). However, during the lossy quantization, most of the DCT coefficients in the high frequency sub-bands are quantized to zero; thus, the scale parameter k in Eq. (3) cannot be estimated accurately to compensate for this bias, and the chaotic logistic map (15) is used to generate the chaotic signal, which has the following advantages:
•
•
From the viewpoint of anti-forensic the successes of the noise adding operation directly will result in the failure of the forensic algorithms. Using proper parameter ki,j, the logistic map can generate the approximate optimal noise for all the sub-bands. Logistic map is sensitive to the initial conditions; using this property, ki,j can be used as the initial parameter and can obtain various signal noise. Generally, different sub-band has different ki,j 2 [0, 1], so this can guarantee the added noise is dissimilar for all the sub-bands, moreover, compared with the pseudorandom noise, if ki,j can be saved, the added noise from the anti-forensically modified image can also be removed and the original JPEG image can be restored in some special case.
In this way, by adding these signals together with the previous noise, the algorithm can remove the quantization artifacts perfectly. The details of implementation are as follows: Step 1: For a given JPEG compressed grayscale image f with M 9 N pixels, it is first divided it into B nonoverlapping sub-blocks with the size 8 9 8 pixels, and then the 2D-DCT transform is applied to each sub-block. After that, a DCT coefficients matrix can be obtained, denote it as M; each element of M is a 8 9 8 DCT coefficient submatrix, which corresponds to each sub-block. As the original encoder is unknown, the original AC coefficients are unavailable, and the quantization table Q must be estimated (3–4); in the scheme, MATLAB JPEG TOOLBOX (16) is used to obtain the quantization table Q, and then the dequantized DCT coefficients k ð1 k BÞ can be easily derived using the same quantizaCi;j
4
JOURNAL OF FORENSIC SCIENCES
tion table Q to requantize the DCT coefficient submatrices. Thus, the dequantized DCT coefficient matrix M0 can be k is the (i, j)—th sub-band of the k—th obtained, where Ci;j M sub-block, B ¼ 8 N8 ; 1 i 8; 1 j 8. 0
88 matrix zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ 1 B0 1 ... c11;j B c1;1 BB 1 B B c2;1 ... c12;j C C B@ A B ............... B 1 1 B c ... c i;1 i;j M0 ¼ B B .. B . B0 k 1 B c1;1 ... ck1;j B B B ck ... ck2;j C B B 2;1 C @@ A ............... ... cki;j cki;1
0 ...
.. . ...
1
1
... C CC ... CC @ AC ............... C C l l ... ci;j ci;1 C C C C .. C . C 0 B 1 ... cB1;j C c1;1 C C B cB ... cB2;j C B 2;1 CC @ AA ............... cBi;1 ... cBi;j cl1;1 B cl B 2;1
cl1;j cl2;j
ð4Þ Step 2: After 2D-DCT and quantization steps, each sub-block is transformed to a 8 9 8 DCT coefficient matrix; obviously, there are 64 DCT coefficients; among them, the (1, 1) position is the DC sub-band, others are the AC sub-bands. So, for the dequantized DCT coefficient matrix M0 , there are a total of B DC coefficients and B0 (B0 = 63 9 B) AC coefficients, which can be seen from Eq. (4). For the convenience of adding noise to these dequantized DCT coefficients, we extract each sub-band from M0 and reark , range those DCT coefficients to a matrix, denoted as Mi;j 0
c1i;j B lþ1 B ci;j k Mi;j ¼B B .. @ . cqi;j
c2i;j clþ2 i;j .. . cqþ1 i;j
. . . cli;j . . . clþp i;j .. .. . . . . . cki;j
1 C C C C A
ð5Þ
Z
¼
x
(1 1
1 2 expðki;j xÞ 12 expðki;j xÞ
n1i;j B lþ1 B ni;j k Ni;j ¼B B .. @ . nqi;j
n2i;j nlþ2 i;j .. . qþ1 ni;j
ð8Þ
where (0 ≤ R ≤ 4), and the number of iterations is controlled by the parameter e (e = N1/Nnum Qi,j). Generally, in an natural image, for different sub-bands, the estimated scale parameter ki,j 2 (0, 1) are distinct, as chaotic logistic map is sensitive to initial conditions; using this property, the estimated ki,j is used as the initial parameter of Eq. (8), and then set an appropriate control parameter R; Eq. (8) can generate the desired chaotic noise for all the sub-bands. In short, for all the (i, j)—th (2 ≤ i ≤ 8, 2 ≤ j ≤ 8) AC sub-bands, AC coeffik0 can be obtained through cients Mi;j 8 k > < Mi;j þ kmin Rð1 kmin Þ k0 k k þ Ni;j Xnþ1 Mi;j ¼ Mi;j > : Mk þ Nk þ X nþ1 i;j i;j
if Nzero ¼ Nnum if Nzero =Nnum s if Nzero =Nnum [ s
ð9Þ
In Eq. (9), kmin is the smallest estimated scale parameter. As there is not an accurate model for the DC coefficient distribution, we can simply iterate the chaotic logistic map to obtain k , where the additive noiseN1;1 k N1;1 ¼ k1;1 R 1 k1;1
ð10Þ
0
k k k M1;1 ¼ M1;1 þ N1;1
ð11Þ
Using the above strategy, the proposed scheme can guarantee that the quantization artifacts can be removed and only leave small visual distortions to the modified image. Experiments and Results
f ðuÞdu if x \ 0 if x 0
ð6Þ
where the scale parameter ki,j was estimated using Eq. (3). Then k can be generated, where using Eq. (6), the needed noise Ni;j 0
Xnþ1 ¼ Xn Rð1 Xn Þ
Therefore, the modified DC coefficients can be represented as
where 1 < l < l + p < q < k ≤ B. By the same way, the additive k can be constructed for the DC and AC subnoise matrix Ni;j band, respectively. Take the (i, j)—th AC sub-band, for example, according to k can Eq. (2), the Cumulative Distribution Function (CDF) of Ni;j be defined as Eq. (6), FðxÞ ¼
k using higher frequencies. Therefore, the distribution of Ni;j Eq. (6) is not accurate. To combat this, donate Nzero as the number DCT coefficients that are quantized to zero, and N1 is used as the number of nonzero and Nnum is used as the total number of DCT coefficients in the (i, j)—th sub-band. If Nzero/Nnum > s, where s is a user defined parameter, the chaotic logistic map is used to generate the suitable chaotic noise, and then add these k to the certain sub-band. The standard logistic map noise and Ni;j is given by Eq. (8).
1 . . . nli;j C . . . nlþp i;j C C .. C .. . A . . . . nki;j
ð7Þ
However, as the previous discussions, some high frequency sub-bands were quantized with larger quantizaton step lengths; thus, most of the DCT coefficients were quantized to zero, this implies that the variance of each DCT coefficient decreases at
To testify the efficiency of the proposed algorithm, 150 images from the Uncompressed Color Image Database (17) are used to compress using a quality factor of {55, 65, 75, 85, 90}, respectively. Thus, there are totally 750 JPEG compressed images. Then, the proposed algorithm is used on these compressed images. In the experiments, the proposed method is compared with Stamm’s anti-forensic work (9,10), and two forensic methods (5–6) are also used to test. The testing parameter is set to: s = 0.9 and R = 4 for the logistic map. Unless specified, otherwise, the results reported in the following experiments are with the default parameters. Figure 3 shows an illustration of the anti-forensic operation. In Fig. 3, Fig. 3a–c are the DCT coefficient histograms that came from the (3, 2) sub-band, where Fig. 3a is the DCT coefficient histogram of the uncompressed image; Fig. 3b is its JPEG compressed version that was quantized with the quality factor 90 and Fig. 3c is the histogram of the modified DCT coefficients based on the proposed scheme. Figure 3d–f are another illustration,
CAO ET AL.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
5
FIG. 3––The histograms of the DCT coefficients taken from the (3, 2), (3, 3) and (2, 3) sub-band. Each row, left: uncompressed, center: the same image after JPEG compression, and right: the anti-forensically modified version of the JPEG compressed image.
where the image is compressed by a quality factor 75, and the DCT coefficients are extracted from the (3, 3) sub-band. Figure 3e shows that, there left big gaps in the histogram of the quantized DCT coefficients; however, Fig. 3f shows that these gaps can be removed through performing the proposed method. Figure 3g–i are the anti-forensic results from another perspective, where the image is compressed using a lower quality factor 65, and the DCT coefficients are extracted from the (2, 3) sub-band. As can be seen from Fig. 3h, with the decrease of the image quality factor, most of the DCT coefficients were quantized to zero; thus, it needs adding much more noise; however, by applying the proposed approach, the scheme can approximately reconstruct the quantized DCT coefficients, this can be seen from Fig. 3i. Table 1 is the result of image quality compared with Stamm’s anti-forensic work (9,10), and it can be seen from Table 1, with TABLE 1––The image quality comparison with Stamm’s work (9,10).
Q 55 65 75 85 90
Our Method PSNR (average) 36.75 38.34 39.15 40.84 41.10
db db db db db
Stamm’s Work (9,10) PSNR (average) 38.49 40.27 41.66 42.68 43.35
db db db db db
the decrease of the image quality factors, the value of PSNR between the original image and the anti-forensically modified image is declined for both of the methods. When the image is compressed with lower quality factor (Q = 65), the anti-forensically modified image using the proposed method still have a great visual effect, this can be seen in Fig. 4. Figure 4 shows the JPEG compression and anti-forensically modified images; among these, Fig. 4a, 4c, 4e, 4g, 4i are compressed by a quality factor 90, 85, 75, 70, and 65, respectively. Figure 4b, 4d, 4f, 4h, 4j are the modified images using the proposed anti-forensic technique. Through the comparison, it can be noticed that only a little visual distortion is introduced. What’s more, the PSNR between the original JPEG compressed image and its anti-forensically altered image is PSNR = 42.24 db, PSNR = 41.73 db, PSNR = 40.7 db, PSNR = 38.98 db, and PSNR = 37.25 db, and it is shown in Fig. 4a,b, Fig. 4c,d, Fig. 4e,f, Fig. 4g,h, and Fig. 4i,j respectively. The results imply that, the noise added to the DCT coefficients only bring negligible visual distortion to the image quality. Furthermore, for the proposed method, to test its ability of deceiving other forensic tools, those 750 JPEG compressed images were used to carry test. For each JPEG compressed image, it is randomly tampered an area, and then is recompressed using the same image quality factor. After that, the proposed anti-forensic technique and Stamm’s anti-forensic method
6
JOURNAL OF FORENSIC SCIENCES
FIG. 4––The JPEG compressed images and its corresponding anti-forensically modified version. (a, c, e, g and i), are the JPEG compressed images, (b, d, f, h and j) are the anti-forensically modified images.
TABLE 2––The performance comparison with Stamm’s work (9,10). Q
Our Accuracy (%)
Stamm’s Accuracy (%)
55 65 75 85 90
86.31 87.10 92.55 92.82 93.89
80.69 82.45 91.12 93.78 94.80
(9,10) were used to these tampered images. For those anti-forensically altered images, the forensic methods (5) and (6) are applied to locate the tampering areas. The test results are listed in Table 2.
Table 2 is the performance comparisons between the proposed anti-forensic method and Stamm’s anti-forensic methods (9,10). Here, the anti-forensic accuracy is the ratio that the forensic method (5) and (6) cannot classify the image as tampered one. Through the experiments, about 98.67% of the 750 tampered images cannot be located the doctored regions, and only 1.3% of these images can be located the tampered areas correctly, even though the image quality is poor (Q = 55). Moreover, in most cases, the proposed scheme has higher detection accuracy than Stamm’s methods, and with the decrease of the image quality factor, the detection accuracy of Stamm’s dropped quickly, as the lower the compression quality is, the more coefficients were quantized to zero. This is just the drawback for Stamm’s
CAO ET AL.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
7
FIG. 5––The detection results by using the forensic algorithm (5) and (6). For (b–e), the first column is the tamped image, second is the detection results by using (5) and (6), third and forth is the anti-forensically modified image, and its detection result by using (5) and (6), respectively.
8
JOURNAL OF FORENSIC SCIENCES
FIG. 6––Pseudo-code of the anti-forensic algorithm.
CAO ET AL.
anti-forensic methods, because their method cannot add any noise to these coefficients, which were quantized to zero; hence, the block artifacts left in the JPEG compressed image cannot be removed. For example, the detection accuracy ratio is 86.31% versus 80.69% for two methods with low quality factor Q = 55. This indicates that, the proposed anti-forensic scheme is more effective than Stamm’s methods and can fool the forensic algorithms that based on extracting the BAG feature, some experimental results were shown in Fig. 5. Figure 5 is an illustration before and after applying anti-forensic method of the paper. In Fig. 5, Fig. 5a is the original image, Fig. 5b–e are the tampered images and the detection results using the algorithm in (5) and (6). In Fig. 5b, one region from a natural image was copied and pasted it to Fig. 5a; as can be seen in Fig. 5b, there are two tampered areas in the first image, the second image is the detection result using the method in (5–6), the third image is the antiforensically altered image by applying the proposed anti-forensic scheme, and the last image is the detection result using the same forensic algorithm in (5–6); obviously, after the anti-forensic operation was performed, the methods mentioned above cannot find the doctored regions. Figure 5c–e all shows the similar behavior. In Fig. 5c, a flower from one natural landscape image was copied and pasted to Fig. 5a, and then shrink and rotate it by angle of 20% nd 90°; through the detection results of Fig. 5c–e, it can found that, no matter the tampered area underwent scaling or rotation, the methods in (5) and (6) can still locate the tampered regions perfectly; however, when the proposed anti-forensic scheme was applied, these methods became invalid. Conclusions In this paper, a novel image anti-forensic scheme is proposed, in the scheme, for the target of erasing the DCT quantization artifacts that left in the single JPEG compressed image; a chaosbased dither technique is introduced to generate the desired chaotic noise, and these noise are injected into the quantized DCT coefficients such that the distribution of the modified coefficients is consistent with the unquantized DCT coefficients. Experimental results and analysis show that, for a given JPEG compression image, using the proposed method, the DCT quantization artifacts can be removed and this only results in small visual distortions; what is more, the proposed anti-forensic scheme can also verify the validity of the forensic algorithm, and this also can find the vulnerabilities of some existing and upcoming forensic algorithms, the proposed scheme may also be extended to hide the double JPEG compression trace. With the development of new anti-forensic scheme, people also probe the algorithm for countering anti-forensics; future work on the anti-forensic of JPEG compression needs not only to find way to keep the distribution of frequency sub-bands analogous to the authentic one, but also not to reveal any doctored trace at different quality factors (18). Some deep theory analysis and experiments will be carried out with the proposed scheme, and the scheme will also be improved with the help of steganographic algorithm for JPEG images. Acknowledgment A portion of this work was supported by the National Science Fund of China (60873117), Key Program of Natural Science Fund of Tianjin (Grant #11JCZDJC16000), China.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
9
References 1. Donald B. Statistical tools for digital image forensics [Ph.D. thesis]. Hanover, NH: Dartmouth College, 2004. 2. Popescu AC, Farid H. Statistical tools for digital forensics. In: Fridrich JJ, editor. Information Hiding, 6th International Workshop (IH); 2004 May 23–25; Toronto, Canada. Berlin, Germany: Springer Berlin Heidelberg, 2005;128–47. 3. Fan Z, de Queiroz R. Identification of bitmap compression history: Jpeg detection and quantizer estimation. IEEE Trans Image Process 2003;12 (2):230–5. 4. Lukas J, Fridrich J. Estimation of primary quantization matrix in double compressed jpeg images. Proceedings of Digital Forensic Research Workshop; 2003 Aug 6–8; Cleveland, OH. Trumansburg, NY: DFRWS, 2003;5–8. 5. Li W, Yuan Y, Yu N. Passive detection of doctored jpeg image via block artifact grid extraction. Signal Process 2009;89(9):1821–9. 6. Ye S, Sun Q, Chang E. Detecting digital image forgeries by measuring inconsistencies of blocking artifact. 2007 IEEE International Conference on Mutimedia and Expo; 2007 July 2–5; Beijing, China. Piscataway, NJ: IEEE, 2007;12–5. 7. Kirchner M, Bohme R. Hiding traces of resampling in digital images. IEEE T INF FOREN SEC 2008;3(4):582–92. 8. Cao G, Zhao Y, Ni R, Tian H. Anti-forensics of contrast enhancement in digital images. Proceedings of the 12th ACM Workshop on Multimedia and Security; 2010 Sep 9–10; Rome, Italy. New York, NY: ACM, 2010;25–34. 9. Stamm M, Liu K. Anti-forensics of digital image compression. IEEE T INF FOREN SEC 2011;6(3):1050–65. 10. Stamm M, Tjoa S, Lin W, Liu K. Anti-forensics of jpeg compression. 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP); 2010 Mar 14-19; Dallas, TX. Piscataway, NJ: IEEE, 2010;1694–7. 11. Lai SY, Bohme R. Countering counter-forensics: the case of JPEG compression. Information Hiding 2011, 13th International Conference (IH 2011); 2011 May 18–20; Prague, Czech Republic. Berlin, Germany: Springer Berlin Heidelberg, 2011;285–98. 12. Lam E, Goodman J. A mathematical analysis of the dct coefficient distributions for images. IEEE Trans Image Process 2000;9(10):1661–6. 13. Dwivedi V. JPEG image compression and decompression with modeling of DCT coefficients on the Texas instrument video processing board TMS320DM6437 [PhD thesis]. Sacramento, CA: California State University, 2010. 14. de Queiroz RL. Processing jpeg-compressed images and documents. IEEE Trans Image Process 1998;7(12):1661–72. 15. Gao T, Chen Z. Image encryption based on a new total shuffling algorithm. Chaos, Solitons Fractals 2008;38(1):213–20. 16. Sallee P. Matlab JPEG toolbox; http://www.philsallee.com/jpegtbx/index. html. 17. Schaefer G, Stich M. Ucid-an uncompressed color image database. In: Yeung MM, Lienhart RW, Li CS, editors. Proceedings of SPIE Volume 5307, Storage and Retrieval Methods and Applications for Multimedia 2004; 2004 Jan 20-22; San Jose, CA. Bellingham, WA: SPIE, 2004;472–80. 18. Valenzise G, Tagliasacchi M, Tubaro S. The cost of JPEG compression anti-forensics. 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 2011 May 22–27; Prague, CZ. Piscataway, NJ: IEEE, 2011;1884–7. Additional information and reprint requests: Tiegang Gao, Ph.D. College of Software Nankai University No 94, Weijin Road, Nankai District Tianjin China, 300071 E-mail: [email protected]
Appendix Pseudocode of the Anti-forensic Algorithm In this section, we give the pseudocode of the anti-forensic algorithm; for more details, please see Fig. 6.
TECHNICAL NOTE DIGITAL & MULTIMEDIA SCIENCES
Yanjun Cao,1 Ph.D.; Tiegang Gao,2 Ph.D.; Guorui Sheng,1 Ph.D.; Li Fan,1 Ph.D.; and Lin Gao,1 Ph.D.
A New Anti-forensic Scheme— Hiding the Single JPEG Compression Trace for Digital Image
ABSTRACT: To prevent image forgeries, a number of forensic techniques for digital image have been developed that can detect an image’s origin, trace its processing history, and can also locate the position of tampering. Especially, the statistical footprint left by JPEG compression operation can be a valuable source of information for the forensic analyst, and some image forensic algorithm have been raised based on the image statistics in the DCT domain. Recently, it has been shown that footprints can be removed by adding a suitable anti-forensic dithering signal to the image in the DCT domain, this results in invalid for some image forensic algorithms. In this paper, a novel anti-forensic algorithm is proposed, which is capable of concealing the quantization artifacts that left in the single JPEG compressed image. In the scheme, a chaos-based dither is added to an image’s DCT coefficients to remove such artifacts. Effectiveness of both the scheme and the loss of image quality are evaluated through the experiments. The simulation results show that the proposed anti-forensic scheme can verify the reliability of the JPEG forensic tools. KEYWORDS: forensic science, anti-forensic, digital image forgery, single JPEG compression, digital fingerprint, chaotic signal With the popularity of low-cost and higher resolution digital cameras, digital images are playing an important role than ever before, a variety of digital products can be visited through internet no matter when and where. However, due to the powerful image editing software (e.g., Photoshop, Illustrator, 3D max), digital images can be easily manipulated and altered without leaving visible clues; thus, it poses a serious social problem such as much of their content can be trusted, whether it can be used as a witness in a courtroom, insurance claims, and scientific fraud. As a mature standard, JPEG compression has been widely used in digital image coding, and in some application cases, many multimedia metadata are compressed in this format. Therefore, the intrinsic footprints left by the JPEG compression may give useful information for the inspector to trace the previous JPEG history, and some forensic techniques have been utilized to successfully distinguish an image’s JPEG operation with the help of the statistical feature. When a digital image is compressed into the JPEG format, the image histogram of the DCT coefficients will leave a visible characteristic known as quantization artifacts; by means of this property, Popescu et al. gave the evidence of whether an image underwent double JPEG compression (1,2) and Lukas et al. can even estimate the primary quantization matrix (3,4). What is more, by employing the quantization artifacts during JPEG processing, Li and Sun extracted block artifact grids (BAG) (5,6), and the mismatch between these grids can be taken as a
1 College of Information Technical Science, Nankai University, No 94, Weijin Road, Tianjin, Nankai District, 300071, China. 2 College of Software, Nankai University, No 94, Weijin Road, Tianjin, Nankai District, 300071, China. Received 30 Dec. 2012; and in revised form 11 June 2013; accepted 4 July 2013.
© 2014 American Academy of Forensic Sciences
trial of tampering. Obviously, if the image is directly carried out the JPEG compression, the compression history can be obtained by some existing forensic schemes. However, sometimes the compression trace of image needs to be concealed for some political or other purpose, so some algorithms that can hide mark of image compression must be considered; this is called anti-forensic scheme. Image anti-forensic scheme aims at covering history of distorting for the image and making some forensic algorithm against image tampering ineffective. At presents, some researchers have realized the importance of anti-forensic and some schemes have been proposed. For example, Kirchner et al. (7) proposed a method using a series of processing to make the resampling (e.g., rotation and scaling) undetectable; Zhao et al. (8) designed an operator to conceal the peak– gap artifacts that left in the histogram of the contrast-enhanced image, on the other hand, Stamm et al. (9,10) hided the DCT coefficient quantization artifacts through adding anti-forensic dither; their methods can test the robustness of some JPEG forensic tools, but, with this scheme, in the high frequency subbands, it is more likely that all coefficients are quantized to zero; this may result in that the parameter estimator has no solution, and consequently, it leaves clues to the forensic investigator, based on this situation, an improved scheme that uses imputation to deal with cases that lack an estimator was proposed (11). At present, there is only a little work for image anti-forensic to make the existing image forensics algorithms more reliable and robust; the research work on anti-forensic needs to be widely explored and tested. In this paper, a novel image anti-forensic scheme is proposed the pseudo-code of the anti-forensic Algorithm is shown in Appendix. The scheme can attack against the state-of-the-art BAG-based forensic methods, which have been proposed by Li 1
2
JOURNAL OF FORENSIC SCIENCES
and Ye (5,6). Different from Stamm’s work (9,10), in the proposed scheme, a chaos-based dither technique is introduced into the work, and chaotic noise is mapped into an image’s DCT quantization coefficients for the target of removing such artifacts. To the best of our knowledge, this is the first time that chaos-based dither technology is used in the anti-forensic research area. Different from Stamm’s anti-forensic scheme, the proposed anti-forensic method can give parameter estimate even if the JPEG quality factor is smaller, and so the performance is better with the lower JPEG quality factor than that of the Stamm’s. A large number of experiments show that the proposed scheme can remove the compression artifacts, and it also can befool some forensic algorithms. The rest of the paper is organized as follows: JPEG compression background and method is briefly reviewed, followed by the proposed anti-forensic scheme, and then the experimental results and the corresponding analysis are given. Finally, some conclusion remarks for the future work are given. Brief Review of the JPEG Compression JPEG is one of the most popular standards for the effective compression of the still digital images; when an image with the size of IM 9 N is compressed in JPEG format, it must undergo two phases: • Encoding 1
2 3
For the purpose of encoding, the image is first segmented into a series of nonoverlapping sub-blocks with the size of 8 9 8 pixels, denoting each sub-block as M N k : Bi;j 1 i; j 8; 1 k 8 8 The 2D-DCT transform is applied to each sub-block Bki;j . Each transformed DCT coefficient Ci,j is quantized by its corresponding quantizer Qi,j within a quantization table Q, and it
• 1
2
3
should be noted that, different digital device may have distinct quantization table. Consequently, after the previous processing, each DCT coefficient Ci,j is quantized to the approximate value ^ i;j ¼ roundðCi;j =Qi;j Þ; ð1 i 8; 1 j 8Þ, then those C quantized DCT coefficients are entropy encoded and form the final JPEG file. Decoding For the decoder, when he receives the JPEG file, first, he operates the procedure by decoding the JPEG bit stream to the original sequence. The inverse quantization is carried out for each quantized DCT coefficient by simply multiplying its corresponding quantizer Qi,j, denoting the dequantized coefficient as 0 ^ i;j Qi;j : ¼C Ci;j The 2D-IDCT transform is performed on each DCT coefficient sub-block and the results are rounded and truncated to the integer interval [0, 255].
It can be seen from the JPEG compression and decompression process that there left a significant footprint in the decompressed image. One is the rounding artifact, the other is the truncating artifact, as the rounding operation occurs in each 8 9 8 block and the error brought by truncating highly depends on the image content; the rounding error is the attention in the proposed scheme. After quantization and dequantization, each DCT coefficient will be an integer multiple of the quantizer Qi,j, this can be obtained from the analysis of Eq. (1), which is given in the following. ^ i;j Qi;j C0 ¼ C i;j
ð1Þ
zfflfflfflfflfflfflffl}|fflfflfflfflfflfflffl{ Ci;j ¼ roundð Þ Qi;j Qi;j |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}
ð1Þ
ð2Þ
In Eq. (1), after step (1), the intermediate result Ci,j/Qi,j is rounded to the integer value, and the multiplication between
FIG. 1––The histograms of the DCT coefficients for different sub-bands. (a): The histograms of the uncompressed image’s DCT Coefficients for 63 AC subbands. (b): The histogram taken from the (2, 3) sub-band. (c): The same image after JPEG compression, and (d): The anti-forensically altered version by using our proposed method.
CAO ET AL.
two integers will also generate integer value, just as step (2) 0 will cluster shows; hence, the dequantized coefficients Ci;j around the integral multiple of Qi,j and leave visible big gaps in the histogram, which can be seen in Fig. 1. Figure 1a is the histograms of the uncompressed image’s DCT coefficients for 63 AC sub-bands; all these DCT coefficients are unquantized, as can be seen in Fig. 1a; if the image did not undergo JPEG compression, there will not be distinct artifacts in the histogram of the DCT coefficients. On the contrary, due to the lossy JPEG compression, visible big gaps are left, that can be used by the forensic tools. In the proposed scheme, chaotic signal noise is used to fill these gaps; thus, the distribution of the anti-forensically reconstructed DCT coefficients can accord with the uncompressed one, and it can be shown in Fig. 1c and Fig. 1d, where Fig. 1c and Fig. 1d are the histograms before and after applying chaos-based anti-forensic scheme. Anti-forensic Scheme To conceal the DCT coefficient quantization artifacts, suitable noise needs to be injected into the quantized DCT coefficients, so that the gaps of the DCT coefficient histogram can be removed. However, when the signal noise is added, there is a thorny issue—how much noise should be added? If the additive noise is excessive, the image will induce visual distortion, and on the contrary, the gap traces left in the quantized DCT coefficients cannot be erased. So the distribution of the additive noise must be modeled from the quantized DCT coefficients, then using the chaos optimization and combining with the chaos-based dither, and the scheme can generate the suitable noise. The detailed anti-forensic scheme is shown in Fig. 2. The Model of DCT Coefficients The distribution of the DCT coefficients has been thoroughly studied and researched in the past decade, and Gamma, Laplacian, or Gaussian distribution for AC coefficients are typical model; among them, the Laplacian distribution is the most suitable model for the AC coefficients (12,13), while there is no general model for the DC coefficients. In the proposed scheme, the AC coefficients is used as Laplacian distribution, and for the DC coefficients, chaos is used to generate the desired distribution. Generally speaking, the Laplacian PDF (Probability Distribution Function) of the unquantized AC coefficients is defined as
FIG. 2––The anti-forensic scheme.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
f ðxÞ ¼
k 2
expðkxÞ if x \ 0 expðkxÞ if x 0
3 ð2Þ
After quantization, the AC components of the DCT coefficients may be distributed to the different discrete interval, but the AC DCT coefficients scattered in each interval still obey the Laplacian distribution, therefore, estimating the parameter k accurately is the key problem. Since during the JPEG compression, to achieve the desired compression ratio, different quantization step length maybe used for different sub-bands; generally, the larger step length is used for the high frequency while smaller step length is used for the low frequency; thus, the variance of the DCT coefficients in different sub-bands will be different; using this property, formula (14) is used to estimate the parameter k. pffiffiffi 2 ð3Þ k¼ r where r stands for the variance of the dequantized coefficients. As no general model can be used for the DC coefficients, another way was used to generate the desired noise, which is extensively discussed in next Section. Noise Adding As was analyzed in the previous sections, the noise added to each AC coefficient must obey the Laplacian distribution, so we can generate the approximate noise by simply using Eq. (2). However, during the lossy quantization, most of the DCT coefficients in the high frequency sub-bands are quantized to zero; thus, the scale parameter k in Eq. (3) cannot be estimated accurately to compensate for this bias, and the chaotic logistic map (15) is used to generate the chaotic signal, which has the following advantages:
•
•
From the viewpoint of anti-forensic the successes of the noise adding operation directly will result in the failure of the forensic algorithms. Using proper parameter ki,j, the logistic map can generate the approximate optimal noise for all the sub-bands. Logistic map is sensitive to the initial conditions; using this property, ki,j can be used as the initial parameter and can obtain various signal noise. Generally, different sub-band has different ki,j 2 [0, 1], so this can guarantee the added noise is dissimilar for all the sub-bands, moreover, compared with the pseudorandom noise, if ki,j can be saved, the added noise from the anti-forensically modified image can also be removed and the original JPEG image can be restored in some special case.
In this way, by adding these signals together with the previous noise, the algorithm can remove the quantization artifacts perfectly. The details of implementation are as follows: Step 1: For a given JPEG compressed grayscale image f with M 9 N pixels, it is first divided it into B nonoverlapping sub-blocks with the size 8 9 8 pixels, and then the 2D-DCT transform is applied to each sub-block. After that, a DCT coefficients matrix can be obtained, denote it as M; each element of M is a 8 9 8 DCT coefficient submatrix, which corresponds to each sub-block. As the original encoder is unknown, the original AC coefficients are unavailable, and the quantization table Q must be estimated (3–4); in the scheme, MATLAB JPEG TOOLBOX (16) is used to obtain the quantization table Q, and then the dequantized DCT coefficients k ð1 k BÞ can be easily derived using the same quantizaCi;j
4
JOURNAL OF FORENSIC SCIENCES
tion table Q to requantize the DCT coefficient submatrices. Thus, the dequantized DCT coefficient matrix M0 can be k is the (i, j)—th sub-band of the k—th obtained, where Ci;j M sub-block, B ¼ 8 N8 ; 1 i 8; 1 j 8. 0
88 matrix zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ 1 B0 1 ... c11;j B c1;1 BB 1 B B c2;1 ... c12;j C C B@ A B ............... B 1 1 B c ... c i;1 i;j M0 ¼ B B .. B . B0 k 1 B c1;1 ... ck1;j B B B ck ... ck2;j C B B 2;1 C @@ A ............... ... cki;j cki;1
0 ...
.. . ...
1
1
... C CC ... CC @ AC ............... C C l l ... ci;j ci;1 C C C C .. C . C 0 B 1 ... cB1;j C c1;1 C C B cB ... cB2;j C B 2;1 CC @ AA ............... cBi;1 ... cBi;j cl1;1 B cl B 2;1
cl1;j cl2;j
ð4Þ Step 2: After 2D-DCT and quantization steps, each sub-block is transformed to a 8 9 8 DCT coefficient matrix; obviously, there are 64 DCT coefficients; among them, the (1, 1) position is the DC sub-band, others are the AC sub-bands. So, for the dequantized DCT coefficient matrix M0 , there are a total of B DC coefficients and B0 (B0 = 63 9 B) AC coefficients, which can be seen from Eq. (4). For the convenience of adding noise to these dequantized DCT coefficients, we extract each sub-band from M0 and reark , range those DCT coefficients to a matrix, denoted as Mi;j 0
c1i;j B lþ1 B ci;j k Mi;j ¼B B .. @ . cqi;j
c2i;j clþ2 i;j .. . cqþ1 i;j
. . . cli;j . . . clþp i;j .. .. . . . . . cki;j
1 C C C C A
ð5Þ
Z
¼
x
(1 1
1 2 expðki;j xÞ 12 expðki;j xÞ
n1i;j B lþ1 B ni;j k Ni;j ¼B B .. @ . nqi;j
n2i;j nlþ2 i;j .. . qþ1 ni;j
ð8Þ
where (0 ≤ R ≤ 4), and the number of iterations is controlled by the parameter e (e = N1/Nnum Qi,j). Generally, in an natural image, for different sub-bands, the estimated scale parameter ki,j 2 (0, 1) are distinct, as chaotic logistic map is sensitive to initial conditions; using this property, the estimated ki,j is used as the initial parameter of Eq. (8), and then set an appropriate control parameter R; Eq. (8) can generate the desired chaotic noise for all the sub-bands. In short, for all the (i, j)—th (2 ≤ i ≤ 8, 2 ≤ j ≤ 8) AC sub-bands, AC coeffik0 can be obtained through cients Mi;j 8 k > < Mi;j þ kmin Rð1 kmin Þ k0 k k þ Ni;j Xnþ1 Mi;j ¼ Mi;j > : Mk þ Nk þ X nþ1 i;j i;j
if Nzero ¼ Nnum if Nzero =Nnum s if Nzero =Nnum [ s
ð9Þ
In Eq. (9), kmin is the smallest estimated scale parameter. As there is not an accurate model for the DC coefficient distribution, we can simply iterate the chaotic logistic map to obtain k , where the additive noiseN1;1 k N1;1 ¼ k1;1 R 1 k1;1
ð10Þ
0
k k k M1;1 ¼ M1;1 þ N1;1
ð11Þ
Using the above strategy, the proposed scheme can guarantee that the quantization artifacts can be removed and only leave small visual distortions to the modified image. Experiments and Results
f ðuÞdu if x \ 0 if x 0
ð6Þ
where the scale parameter ki,j was estimated using Eq. (3). Then k can be generated, where using Eq. (6), the needed noise Ni;j 0
Xnþ1 ¼ Xn Rð1 Xn Þ
Therefore, the modified DC coefficients can be represented as
where 1 < l < l + p < q < k ≤ B. By the same way, the additive k can be constructed for the DC and AC subnoise matrix Ni;j band, respectively. Take the (i, j)—th AC sub-band, for example, according to k can Eq. (2), the Cumulative Distribution Function (CDF) of Ni;j be defined as Eq. (6), FðxÞ ¼
k using higher frequencies. Therefore, the distribution of Ni;j Eq. (6) is not accurate. To combat this, donate Nzero as the number DCT coefficients that are quantized to zero, and N1 is used as the number of nonzero and Nnum is used as the total number of DCT coefficients in the (i, j)—th sub-band. If Nzero/Nnum > s, where s is a user defined parameter, the chaotic logistic map is used to generate the suitable chaotic noise, and then add these k to the certain sub-band. The standard logistic map noise and Ni;j is given by Eq. (8).
1 . . . nli;j C . . . nlþp i;j C C .. C .. . A . . . . nki;j
ð7Þ
However, as the previous discussions, some high frequency sub-bands were quantized with larger quantizaton step lengths; thus, most of the DCT coefficients were quantized to zero, this implies that the variance of each DCT coefficient decreases at
To testify the efficiency of the proposed algorithm, 150 images from the Uncompressed Color Image Database (17) are used to compress using a quality factor of {55, 65, 75, 85, 90}, respectively. Thus, there are totally 750 JPEG compressed images. Then, the proposed algorithm is used on these compressed images. In the experiments, the proposed method is compared with Stamm’s anti-forensic work (9,10), and two forensic methods (5–6) are also used to test. The testing parameter is set to: s = 0.9 and R = 4 for the logistic map. Unless specified, otherwise, the results reported in the following experiments are with the default parameters. Figure 3 shows an illustration of the anti-forensic operation. In Fig. 3, Fig. 3a–c are the DCT coefficient histograms that came from the (3, 2) sub-band, where Fig. 3a is the DCT coefficient histogram of the uncompressed image; Fig. 3b is its JPEG compressed version that was quantized with the quality factor 90 and Fig. 3c is the histogram of the modified DCT coefficients based on the proposed scheme. Figure 3d–f are another illustration,
CAO ET AL.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
5
FIG. 3––The histograms of the DCT coefficients taken from the (3, 2), (3, 3) and (2, 3) sub-band. Each row, left: uncompressed, center: the same image after JPEG compression, and right: the anti-forensically modified version of the JPEG compressed image.
where the image is compressed by a quality factor 75, and the DCT coefficients are extracted from the (3, 3) sub-band. Figure 3e shows that, there left big gaps in the histogram of the quantized DCT coefficients; however, Fig. 3f shows that these gaps can be removed through performing the proposed method. Figure 3g–i are the anti-forensic results from another perspective, where the image is compressed using a lower quality factor 65, and the DCT coefficients are extracted from the (2, 3) sub-band. As can be seen from Fig. 3h, with the decrease of the image quality factor, most of the DCT coefficients were quantized to zero; thus, it needs adding much more noise; however, by applying the proposed approach, the scheme can approximately reconstruct the quantized DCT coefficients, this can be seen from Fig. 3i. Table 1 is the result of image quality compared with Stamm’s anti-forensic work (9,10), and it can be seen from Table 1, with TABLE 1––The image quality comparison with Stamm’s work (9,10).
Q 55 65 75 85 90
Our Method PSNR (average) 36.75 38.34 39.15 40.84 41.10
db db db db db
Stamm’s Work (9,10) PSNR (average) 38.49 40.27 41.66 42.68 43.35
db db db db db
the decrease of the image quality factors, the value of PSNR between the original image and the anti-forensically modified image is declined for both of the methods. When the image is compressed with lower quality factor (Q = 65), the anti-forensically modified image using the proposed method still have a great visual effect, this can be seen in Fig. 4. Figure 4 shows the JPEG compression and anti-forensically modified images; among these, Fig. 4a, 4c, 4e, 4g, 4i are compressed by a quality factor 90, 85, 75, 70, and 65, respectively. Figure 4b, 4d, 4f, 4h, 4j are the modified images using the proposed anti-forensic technique. Through the comparison, it can be noticed that only a little visual distortion is introduced. What’s more, the PSNR between the original JPEG compressed image and its anti-forensically altered image is PSNR = 42.24 db, PSNR = 41.73 db, PSNR = 40.7 db, PSNR = 38.98 db, and PSNR = 37.25 db, and it is shown in Fig. 4a,b, Fig. 4c,d, Fig. 4e,f, Fig. 4g,h, and Fig. 4i,j respectively. The results imply that, the noise added to the DCT coefficients only bring negligible visual distortion to the image quality. Furthermore, for the proposed method, to test its ability of deceiving other forensic tools, those 750 JPEG compressed images were used to carry test. For each JPEG compressed image, it is randomly tampered an area, and then is recompressed using the same image quality factor. After that, the proposed anti-forensic technique and Stamm’s anti-forensic method
6
JOURNAL OF FORENSIC SCIENCES
FIG. 4––The JPEG compressed images and its corresponding anti-forensically modified version. (a, c, e, g and i), are the JPEG compressed images, (b, d, f, h and j) are the anti-forensically modified images.
TABLE 2––The performance comparison with Stamm’s work (9,10). Q
Our Accuracy (%)
Stamm’s Accuracy (%)
55 65 75 85 90
86.31 87.10 92.55 92.82 93.89
80.69 82.45 91.12 93.78 94.80
(9,10) were used to these tampered images. For those anti-forensically altered images, the forensic methods (5) and (6) are applied to locate the tampering areas. The test results are listed in Table 2.
Table 2 is the performance comparisons between the proposed anti-forensic method and Stamm’s anti-forensic methods (9,10). Here, the anti-forensic accuracy is the ratio that the forensic method (5) and (6) cannot classify the image as tampered one. Through the experiments, about 98.67% of the 750 tampered images cannot be located the doctored regions, and only 1.3% of these images can be located the tampered areas correctly, even though the image quality is poor (Q = 55). Moreover, in most cases, the proposed scheme has higher detection accuracy than Stamm’s methods, and with the decrease of the image quality factor, the detection accuracy of Stamm’s dropped quickly, as the lower the compression quality is, the more coefficients were quantized to zero. This is just the drawback for Stamm’s
CAO ET AL.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
7
FIG. 5––The detection results by using the forensic algorithm (5) and (6). For (b–e), the first column is the tamped image, second is the detection results by using (5) and (6), third and forth is the anti-forensically modified image, and its detection result by using (5) and (6), respectively.
8
JOURNAL OF FORENSIC SCIENCES
FIG. 6––Pseudo-code of the anti-forensic algorithm.
CAO ET AL.
anti-forensic methods, because their method cannot add any noise to these coefficients, which were quantized to zero; hence, the block artifacts left in the JPEG compressed image cannot be removed. For example, the detection accuracy ratio is 86.31% versus 80.69% for two methods with low quality factor Q = 55. This indicates that, the proposed anti-forensic scheme is more effective than Stamm’s methods and can fool the forensic algorithms that based on extracting the BAG feature, some experimental results were shown in Fig. 5. Figure 5 is an illustration before and after applying anti-forensic method of the paper. In Fig. 5, Fig. 5a is the original image, Fig. 5b–e are the tampered images and the detection results using the algorithm in (5) and (6). In Fig. 5b, one region from a natural image was copied and pasted it to Fig. 5a; as can be seen in Fig. 5b, there are two tampered areas in the first image, the second image is the detection result using the method in (5–6), the third image is the antiforensically altered image by applying the proposed anti-forensic scheme, and the last image is the detection result using the same forensic algorithm in (5–6); obviously, after the anti-forensic operation was performed, the methods mentioned above cannot find the doctored regions. Figure 5c–e all shows the similar behavior. In Fig. 5c, a flower from one natural landscape image was copied and pasted to Fig. 5a, and then shrink and rotate it by angle of 20% nd 90°; through the detection results of Fig. 5c–e, it can found that, no matter the tampered area underwent scaling or rotation, the methods in (5) and (6) can still locate the tampered regions perfectly; however, when the proposed anti-forensic scheme was applied, these methods became invalid. Conclusions In this paper, a novel image anti-forensic scheme is proposed, in the scheme, for the target of erasing the DCT quantization artifacts that left in the single JPEG compressed image; a chaosbased dither technique is introduced to generate the desired chaotic noise, and these noise are injected into the quantized DCT coefficients such that the distribution of the modified coefficients is consistent with the unquantized DCT coefficients. Experimental results and analysis show that, for a given JPEG compression image, using the proposed method, the DCT quantization artifacts can be removed and this only results in small visual distortions; what is more, the proposed anti-forensic scheme can also verify the validity of the forensic algorithm, and this also can find the vulnerabilities of some existing and upcoming forensic algorithms, the proposed scheme may also be extended to hide the double JPEG compression trace. With the development of new anti-forensic scheme, people also probe the algorithm for countering anti-forensics; future work on the anti-forensic of JPEG compression needs not only to find way to keep the distribution of frequency sub-bands analogous to the authentic one, but also not to reveal any doctored trace at different quality factors (18). Some deep theory analysis and experiments will be carried out with the proposed scheme, and the scheme will also be improved with the help of steganographic algorithm for JPEG images. Acknowledgment A portion of this work was supported by the National Science Fund of China (60873117), Key Program of Natural Science Fund of Tianjin (Grant #11JCZDJC16000), China.
.
A SCHEME FOR HIDING THE JPEG COMPRESSION TRACE
9
References 1. Donald B. Statistical tools for digital image forensics [Ph.D. thesis]. Hanover, NH: Dartmouth College, 2004. 2. Popescu AC, Farid H. Statistical tools for digital forensics. In: Fridrich JJ, editor. Information Hiding, 6th International Workshop (IH); 2004 May 23–25; Toronto, Canada. Berlin, Germany: Springer Berlin Heidelberg, 2005;128–47. 3. Fan Z, de Queiroz R. Identification of bitmap compression history: Jpeg detection and quantizer estimation. IEEE Trans Image Process 2003;12 (2):230–5. 4. Lukas J, Fridrich J. Estimation of primary quantization matrix in double compressed jpeg images. Proceedings of Digital Forensic Research Workshop; 2003 Aug 6–8; Cleveland, OH. Trumansburg, NY: DFRWS, 2003;5–8. 5. Li W, Yuan Y, Yu N. Passive detection of doctored jpeg image via block artifact grid extraction. Signal Process 2009;89(9):1821–9. 6. Ye S, Sun Q, Chang E. Detecting digital image forgeries by measuring inconsistencies of blocking artifact. 2007 IEEE International Conference on Mutimedia and Expo; 2007 July 2–5; Beijing, China. Piscataway, NJ: IEEE, 2007;12–5. 7. Kirchner M, Bohme R. Hiding traces of resampling in digital images. IEEE T INF FOREN SEC 2008;3(4):582–92. 8. Cao G, Zhao Y, Ni R, Tian H. Anti-forensics of contrast enhancement in digital images. Proceedings of the 12th ACM Workshop on Multimedia and Security; 2010 Sep 9–10; Rome, Italy. New York, NY: ACM, 2010;25–34. 9. Stamm M, Liu K. Anti-forensics of digital image compression. IEEE T INF FOREN SEC 2011;6(3):1050–65. 10. Stamm M, Tjoa S, Lin W, Liu K. Anti-forensics of jpeg compression. 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP); 2010 Mar 14-19; Dallas, TX. Piscataway, NJ: IEEE, 2010;1694–7. 11. Lai SY, Bohme R. Countering counter-forensics: the case of JPEG compression. Information Hiding 2011, 13th International Conference (IH 2011); 2011 May 18–20; Prague, Czech Republic. Berlin, Germany: Springer Berlin Heidelberg, 2011;285–98. 12. Lam E, Goodman J. A mathematical analysis of the dct coefficient distributions for images. IEEE Trans Image Process 2000;9(10):1661–6. 13. Dwivedi V. JPEG image compression and decompression with modeling of DCT coefficients on the Texas instrument video processing board TMS320DM6437 [PhD thesis]. Sacramento, CA: California State University, 2010. 14. de Queiroz RL. Processing jpeg-compressed images and documents. IEEE Trans Image Process 1998;7(12):1661–72. 15. Gao T, Chen Z. Image encryption based on a new total shuffling algorithm. Chaos, Solitons Fractals 2008;38(1):213–20. 16. Sallee P. Matlab JPEG toolbox; http://www.philsallee.com/jpegtbx/index. html. 17. Schaefer G, Stich M. Ucid-an uncompressed color image database. In: Yeung MM, Lienhart RW, Li CS, editors. Proceedings of SPIE Volume 5307, Storage and Retrieval Methods and Applications for Multimedia 2004; 2004 Jan 20-22; San Jose, CA. Bellingham, WA: SPIE, 2004;472–80. 18. Valenzise G, Tagliasacchi M, Tubaro S. The cost of JPEG compression anti-forensics. 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 2011 May 22–27; Prague, CZ. Piscataway, NJ: IEEE, 2011;1884–7. Additional information and reprint requests: Tiegang Gao, Ph.D. College of Software Nankai University No 94, Weijin Road, Nankai District Tianjin China, 300071 E-mail: [email protected]
Appendix Pseudocode of the Anti-forensic Algorithm In this section, we give the pseudocode of the anti-forensic algorithm; for more details, please see Fig. 6.
