Detection of LSB Matching Steganography using the Envelope of Histogram

Transcription

1 646 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY 29 Detetion of LSB Mathing Steganography using the Envelope of Histogram Jun Zhang Shool of Information Siene Guangdong University of Business Studies,Guangzhou,P.R. China Yuping Hu and Zhibin Yuan Department of Software Enginerring Guangdong University of Business Studies,Guangzhou,P.R. China Abstrat As well-known, it is hard to detet LSB mathing steganography when over images are sans of photographs, whih usually have high-frequeny noise. This paper proposes a novel steganalysis method for this issue by making use of the following two fats: One is the loal maxima of an image histogram derease and the loal minima inrease after LSB mathing steganography. As a result, the area between upper envelope and lower envelope of the histogram of a stego image will be smaller than that of a over image. The other is LSB mathing embedding in the spatial domain of an image orresponds to low-pass filtering of the histogram. So, there are some differenes in the high order statistial moments of high frequenies of the histogram. Based on these fats, this paper onstruts a novel feature vetor to distinguish between stego and over images. Experimental results show the proposed sheme has better performane than some state-of-the-art steganalyzers in the literature. Index Terms Steganalysis, LSB mathing, Image I. INTRODUCTION Steganography has reeived onsiderable interest during the last few years, espeially after anedotal reports alleged that this tehnology was used by terrorist. Steganography seeks to provide a overt ommuniation hannel between two parties. It is ommonly framed as the prisoners problem [1-2]: Two prisoners, Alie and Bob, are permitted to ommuniate between one another, while under the surveillane of a Warden. The Warden, Eve, is free to examine all transmitted ontents between Alie and Bob and must deide whether suh transmissions inlude a overt message. If there is a overt message, then the ommuniation between the prisoners will be prevented. The ontent that doesn t ontain the overt message is referred to as the over ontent, whih might be an image, video, audio or text. Otherwise it is referred to as the stego ontent. The goal of Alie and Bob is to develop steganographi algorithms so that a overt message is undetetable by Eve. Nowadays, a wide variety of steganographi algorithms have been proposed. They an be ategorized in two groups: Spatial domain tehniques like least signifiant bit (LSB replaement, LSB mathing [3], Pixel Value Differening [4] and Stohasti Modulation [5]; Transform domain tehniques like Outguess [6], F5 [7], Pathwork [8]. In the other side, steganalysis attempts to defeat the goal of steganography. It aims to expose the presene of the hidden message, equivalently, to disriminate the stego ontent from the over ontent. Steganalysis are ommonly ategorized as either targeted or blind. Targeted steganalysis seeks to detet the use of a known steganographi algorithm. It an reveal the overt message or even estimate the embedding ratio with the knowledge of the steganographi algorithm [9-14]. Blind steganalysis seeks to detet a range of steganographi algorithms, possibly inluding previously unknown algorithms. Blind steganalysis first extrat some features from ontents, or more speifially, images, then selet or design a lassifier, and train the lassifier using the features extrated from training image sets, and lastly, lassify the features for an identifying given images [15-22]. Usually, it is likely that steganalysis methods that target a speifi embedding sheme an give more aurate and reliable results than blind steganalysis ones. However, blind approahes are more pratial beause of their flexibility and ability to be quikly adjusted to new or ompletely unknown steganographi methods. Perhaps surprisingly, detetion of LSB mathing steganography has proved onsiderably more diffiult than for LSB replaement. LSB replaement method simply replaes the LSB bitplane of a over image with the orresponding bits of a hidden message. This an be done for all pixels in the image or only for a pseudorandomly hosen portion, when the embedding rate is less than one, i.e. the length of the hidden message is less than the number of pixels in the image. Currently, a number of papers have reported very suessful steganalysis of LSB replaement [9-1]. This suess is redited to the fat that LSB replaement is inherently asymmetri, i.e. an even valued pixel will either retain its value or be inremented 29 ACADEMY PUBLISHER

2 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY by one. However, it will never be deremented. The onverse is true for odd-valued pixels. Rather than simple replae the LSB with the desired message bit, LSB mathing sheme randomly inrements or derements the orresponding pixel value when the desired message bit is different from the LSB. Due to remove the asymmetry of odd and even pixels, detetion of LSB mathing is known to be muh more diffiult than deteting LSB replaement. There are some detetors for LSB mathing steganography in the literature. Unfortunately, their performanes are often low when over images have highfrequeny noise, suh as high resolution sans of photographs. This paper addresses this issue. Setion II first reviews three state-of-the-art steganalyzers used to detet LSB mathing steganography, whih are algorithms of Harmsen et al. [23],Ker [24] and Goljan et al.[25]. They an be roughly onsidered as sharing a ommon arhiteture, namely (i feature extration in some domain and (ii Fisher Linear Disriminant (FLD analysis to obtain a 2-lass lassifier. Setion III examines the effet of LSB mathing steganography on the intensity histogram. We show that the loal maxima of the histogram of images will derease and the loal minima will inrease after LSB mathing embedding. This property an be used to define a feature to detet LSB mathing steganography. The feature is the area between upper envelope and lower envelope of the histogram. Moreover, sine LSB mathing embedding in the spatial domain of an image orresponds to low-pass filtering of the histogram, there must be some differenes in the high order statistial moments of high frequenies of the histogram. Aording to these fats, we onstrut a novel feature vetor to distinguish between stego and over images. Setion IV explains the details of the proposed steganalyzer. In setion V, we give experimental results and ompare the performane with the three state-of-theart steganalyzers. The paper is onluded in Setion VI. II. RELATED WORK Steganalysis an be modeled as a lassify problem as shown in Fig.1. Input a test image, extrat some features X form it, then a lassify funtion F is used to identify it. If F(X is more than a threshold T then the test image belongs to over lass otherwise it belongs to stego lass. The performane of steganalysis depends on two fators: one is whih features of images are seleted. The other is whih lassify funtions are used. The latter is well studied in the fields of pattern reognize and mahine learning, whih usually a test image extrated features: X No lassifier: F Y=F(X>T? Yes Figure 1. The ommon arhiteture of steganalyzer stego imag over image is Fisher Linear Disriminant(FLD, Support Vetor Mahine (SVM or Neural Network (NN. The former is the key issue in steganalysis. That means: a steganalyzer must find out some features of images that are sensitive to embedding modifiations so that it an distinguish between over and stego images. In this setion, we will briefly review the three state-of-the-art steganalyzers for LSB mathing steganography and fous on how to selet features in these methods. A. Center of Mass of the Histogram Charateristi Funtion One of the first steganalyzers was proposed by Harmsen and Pearlman [23]. They model LSB mathing steganography as independent additive noise. Due to the fat that noise adding in the spatial domain orresponds to low-pass filtering of the histogram, the histogram of stego images has less power in high frequenies than the histogram of over images. So, the enter of mass of the Histogram Charateristi Funtion H, whih is obtained by Fourier transform of the histogram h, will derease after LSB mathing embedding. Then, it was used as a feature for distinguishing between over and stego images. This sheme is alled a Histogram Charateristi Funtion steganalysis (HCF. The enter of mass of HCF is alulated as follows: C ( H 127 i= = 127 i H i= H ( i ( i This tehnique has quite good performane for deteting LSB mathing steganography in RGB olor images. However, it performs very poorly in graysale images indeed. B. Center of mass of the Adjaeny Histogram Charateristi Funtion Ker suggested that HCF sheme has bad performane in graysale images sine it is a lak of sparsity in the histogram [24]. He then proposed to use a twodimensional adjaeny histogram, expressing how often eah pixel intensity is observed horizontally next to eah other. Beause adjaent pixels tend to have lose intensities, this histogram is sparse off the diagonal. He showed that LSB mathing steganography also redues to low-pass filtering the adjaeny histogram and defined a enter of mass of the adjaeny histogram harateristi funtion as follows: ( H 127 ( i + H i= (1 i= C = (2 127 H 29 ACADEMY PUBLISHER

3 648 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY 29 In addition, to redue the variability of this feature aross images, Ker reommended omputing the same enter of mass using a downsampled version of the image. For disussing next, the former is referred to as AD-HCF and the latter is referred to as CAD-HCF. C. Wavelet Absolute Moment Holotyak and Fridrih [18] desribed a blind steganalysis approah based on lassifying higher-order statistial features derived from an estimation of the stego signal in the wavelet domain. Goljan [25] presented an improved version of Holotyak s method by using absolute moments of the noise residual. The proposed approah is flexible and enable reliable detetion of presene of seret messages embedded using a wide range of steganographi methods that inlude LSB mathing, LSB replaement, Stohasti Modulation, and others. This steganalyzer is referred to as WAM. The algorithm of WAM is desribed as follows: Step 1: Input a test image I Step 2: I is transformed by disrete wavelet transforms (DWT. The results inlude 4 subimages, whih are denoted as LL, LH, HL, HH Step 3: The three high frequeny subimages are denoised by wavelet filter, and the results are denoted as ' ' ' LH, HL, HH respetively. Step 4: Compute the residual subimages: Δ LH = LH LH ' ' ', ΔHL = HL HL, ΔHH = HH HH Step 5: Calulate high-order absolute moments of the residual subimages: Δ ( i LH mean Δ LH, ( i HL mean Δ HL Δ ( i, i=1 9. HH mean Δ HH Δ, Finally, they use all these 27 data as a feature vetor to distinguish between over and stego images. WAM steganalysis performs very well for over images that were previously ompressed using JPEG, but its auray is very low in over images sanned from photographs. ( p LSB is the least signifiant bit of p. The pixels of a over image are seleted (pseudo randomly using a shared stego key for embedding. Rather than simply replaing the LSB with the desired message bit (LSB replaement sheme, the orresponding pixel value is randomly inremented or deremented in LSB mathing steganography. However, if pixels are and 255, we fore them to be 1 and 244, respetively. So, without the asymmetry of LSB replaement, it is muh more diffiult to detet the LSB mathing steganography than LSB replaement. p ps = p p + 1 if b LSB( p if b = LSB( p 1 if b LSB( p & r > (3 & r < B. Effets of LSB Mathing steganography on Histogram The histogram of the over image is alulated by using following formula: h ( n = { p = n} (4 Where n is graysale level in the range 255. The histogram stands for the number of pixels with graysale level n. Assume that a maximal-length hidden message (1 bit per pixel of the over image is embedded and message bit b is also an i.i.d. random variable with uniform distribution on {,1}. We now disuss the effets on histogram of the over image by LSB mathing steganography. Let us begin with an example of LSB mathing steganography. Fig.2 shows a over image, whih is the photography of artwork with size Fig.3 shows the histogram of the over image and stego image in whih message bits are embedded by LSB mathing method. As we an see the histogram of the stego image is more smooth than that of the over image. III. ANALYSIS FOR LSB MATCHING STEGANOGRAPHY A. LSB mathing steganography We assume that images are graysale ones, whih means their pixels will be in the range 255. The pixels at loation of over image and stego image are denoted as p and p s, respetively. In LSB mathing steganography, one message bit is embedded at pixel by applying the following formula (3. p Where r is an i.i.d. random variable with uniform distribution on 1, + 1, b is the message bit, and { } Figure 2. The over image 29 ACADEMY PUBLISHER

4 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY Moreover, the loal maximums beome smaller and the loal minimums beome larger. This is true by following theoretial analysis indeed. h( Definition 1. In a histogram funtion, is a loal maximum point if the two inequalities h( n h( n 1 and h ( n h( n + 1 are true and one of inequalities is strit. h( Definition 2. In a histogram funtion, is a loal minimum point if the two inequalities h( n h( n 1 and h ( n h( n + 1 are true and one of inequalities is strit. Lemma 1. If n is a loal maximum point of histogram then hs ( n < h ( n. Here, the h ( and h s ( stand for histograms of the over and stego image, respetively Figure 3. The top one is the histogram of the over image shown in Fig.2 and the bootom is that of the stego image n n Proof. We assume r, message bit b and LSB( p in formula (3 are random variables with uniform distribution independently. Then, a pixel p s of the stego image is obtained by following probability: P ( p s = p + 1 = P( ( b LSB ( p ( r = 1 = P( b LSB ( p P( r = 1 = 1 / 2 1 / 2 = 1 / 4 Similarly, P ( p s = p 1 = 1/ 4 and P ( p s = p = 1/ 2. Denote the number of pixels that their graysale level are from n up to n + 1, and n down to n 1 after LSB embedding as Δ( n n + 1 and Δ( n n 1, respetively. Then, Δ ( n n + 1 = h( n P( ps = p + 1 = h( n / 4. Similarly, Δ ( n n 1 = h( n / 4. So, h s ( n = h ( n Δ( n n + 1 Δ( n n 1 + Δ( n 1 n + Δ( n + 1 n = h ( n h ( n /4 h ( n /4 + h ( n 1 /4 + h ( n + = h ( n ( h ( n h ( n 1 + ( h ( n h ( n + 1 /4 < h ( n Symmetrially, we an dedue the following lemma 2. 1 /4 Lemma 2. If n is a loal minimum point of histogram then hs ( n > h ( n. The lemmas show the fat that after LSB mathing the loal maxima of an image histogram derease and the loal minima inrease. So, we an expet the area between the upper envelope and lower envelope of the histogram of the over image will be larger than that of the histogram of the stego image. As a result, we use it as one of features to distinguish between over and stego images. The area an be alulated by the following proedure: Identify all the loal extrema, then onnet them by a ubi spline line to form the upper envelope u (. Repeat the proedure for the loal minima to produe the lower envelope l (, as shown in Fig.3. The area is defined as the absolute of the differene between the upper envelope and lower envelope.that is, 255 n= ( n l( n S = u (5 Fig.3 learly shows the area of the histogram of the over image is larger than that of the stego image. Their areas are and 41288, respetively. Furthermore, we demonstrate this fat mentioned above by a set of images, whih ontains 1 never ompression 29 ACADEMY PUBLISHER

5 65 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY 29 9 x Figure 4. The aeras of envelope of histogram of over and stego images. The symbols and o stand for S of over images and of Ss stego images, respetively. images like Fig.2. The results are shown in Fig.4, in whih the symbols and o stand for of over images and S s of stego images, respetively. As we an see, almost lager than S s are. So we an use the area of envelope of histogram as a disriminator to separate over images from stego images. Finally, we investigate another feature for steganlaysis. LSB mathing sheme an be modeled as independent additive noise, it leads to low pass filtering on the intensity histogram. As a result, the histogram of the stego image has less power in high frequenies than the histogram of the over image [23]. We gain the high frequenies of the histogram by disrete wavelet transform shown in Fig.5. The top one is the high frequeny oeffiients of the histogram of the over image and the bottom is that of the stego image. As we an see, there are some differenes in the high order statistial moments of high frequenies of the histograms. For example, the standard deviations of the top and bottom one are , 5.55, respetively. That means the standard deviation of histogram of the stego image is smaller than that of the over image. This is almost true for eah image aording to our experiments. So, we an use the standard deviation as another feature to distinguish between stego and over images. Combined with the feature mentioned above, we an expet to improve auray of detetion. S IV. STEGANALYSIS ALGORITHM S As disussed above, we present two features for steganalysis. Moreover, we introdue another feature based on the loal extremum of histogram in our previous work [26]. Making use of these three features, we propose the following steganalysis algorithm. Step 1. Given a test image, alulate the histogram of the image by formula (4. Step 2. Compute all loal maximums and minimums of Figure 5. The top one is the high frequeny oeffiients of histogram of the over image and the bootom is that of the stego image the histogram. Step 3. Work out the area between the upper envelope and lower envelope of the histogram by formula (5, denoted as. f 1 Step 4. Transform the histogram by DWT, and then alulate the high order statistial moments of the high frequenies. In our experiments we just selet the standard deviation, denoted as. f 2 Step 5. Calulate the sum of absolute differenes between eah loal extremum n and its neighbors in the histogram. That is, f 3 ( h( n h( n 1 + h( n h( n 1 = + n f f 2 3 Step 6. Combine 1, and to form the threedimensional feature vetor. Then, the Fisher linear f (6 29 ACADEMY PUBLISHER

6 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY disriminator (FLD is introdued to lassify over and stego images. The FLD is a simple lassifiation method whih finds an optimal linear projetion of the features. Advantages of the FLD method inlude reasonably fast training, very fast use, and no training parameters to selet. In the FLD, the feature spae is projeted on a onedimensional spae, where various deision rules an be applied for determining the lassifiation thresholds. Finally, we use reeiver operating harateristi urves (ROC to evaluate the performane of our method and ompare it with other methods. ROC an show how the false positives and true positives vary as the detetion threshold is adjusted [27]. V. EXPERIMENTAL RESULTS It is an established fat nowadays that detetion of LSB mathing steganography is signifiantly more diffiult for never ompressed images, graysale images, and sans of photographs, and notably easier for images that were previously proessed using JPEG or for olor images. So our tests will fous on the following dataset, whih inludes never ompressed saned images. The dataset is derived from the Corel Image Database, whih inludes 2 olor images sanned from photographs of artworks. The original images are 24-bit, pixels, never ompressed and they usually have high level of noise. In our experiments, we rop the original olor images into pixels and overt them to graysales. Here, ropping was preferred over resizing, in order to avoid introduing artifats due to resampling with interpolation. For this dataset, the following proedure was performed for the steganalyzer to alulate its ROC [28]: 1 Apply LSB embedding steganography with embedding rate p to all images in the dataset D to obtain the dateset of stego images D ; 2 Separate both dataset into a training set { D ( I, D ( I } and a test set { D ( I, D ( I }, where I ' is a subset of the image indexes and I is its omplement. The size of the training set was set to be equal to 5% of the dataset size; 3 For the steganalyzer under test, ompute the assoiated feature vetor for all images in the training set and perform FLD analysis to obtained the trained projetion vetor v ; 4 For the steganalyzer under test, ompute the assoiated feature vetor for all images in the test set, and projet the feature vetor onto v ; 5 Compare the resulting salar values to a threshold τ and reord the probabilities of false positives and true positives for different values of the threshold in order to obtain the Reeiver Operating Charateristi urve of the steganalyzer. Firstly, we evaluate the performane of our method under embedding rate p =.3, p =. 5, p =. 7 and Probability of detetion p=1 p=.7.1 p=.5 p= Probability of false positive Figure 6. ROCs for the proposed method with various embedding rate Probability of detetion HCF AD-HCF CAD-HCF WAM Our method Probability of false positive Figure 7. ROCs for the five steganalyzers under embedding rate.5. p = 1. The experimental results are shown in Fig.6. As we an see, when the embedding rate inreases the performane will improve. For example, at false positive rate 5% the detetion rates are 9%, 98%, 1% and 1% for the embedding rates.3,.5,.7 and 1. Then, fixing the embedding rate p =.5 we ompare our method with the Histogram Charateristi Funtion steganalysis (HCF [23], the adjaeny HCF-COM version (AD-HCF and the alibrated adjaeny HCF- COM version (CAD-HCF of Ker s method [24], and Goljan s method (WAM [25]. Fig.7 shows the ROCs for the five steganalyzers. We an see: (1 The performane of our method is the best one. For example, at false positive rate 3% the detetion rates of our method, HCF,AD-HCF, CAD-HCF and WAM are 96%,86%, 87%, 73%, 32%,respetively. (2 WAM method has the worst detetion rates for this sanned image set. This is due to the fat that the high level of noise of sanned images interferes with the additive stego signal. So it appears to be very diffiult for 29 ACADEMY PUBLISHER

7 652 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY 29 WAM method to distinguish between the stego signal and noise naturally present in images. (3 The performane of AD-HCF is almost the same as that of HCF in this dataset. (4 The alibrated detetor (CAD-HCF performs worse than the standard detetor ( AD-HCF. That means the alibration tehnique fails when a hidden message only 5% of the maximum is embedded. VI. CONCLUSION The detetion of LSB mathing steganography remains unresolved, espeially for the unompressed graysale images with high level of noise, suh as sans of photographs. In this paper, we present a novel steganalysis sheme for this issue. By analyzing the embedding algorithm of LSB mathing steganography, we prove the fat that the loal maximum of histogram of a over image derease and loal minimum inrease after message bits are embedded. Moreover, due to the fat that the histogram of the stego image has less power in high frequenies than that of the histogram of the over image, there are some differenes in the high order statistial moments of high frequenies. Based on these fats, we onstrut a new feature vetor and use the FLD to distinguish between the over and stego images. The experimental results show the proposed sheme is superior to the HCF and WAM methods in the dataset of sans of photographs. It is well-known that the performane of urrent state-ofthe-art steganalyzers for detetion of LSB mathing steganography is highly sensitive to the datasets from different soures. No detetors have yet proven universally reliable. Further work is needed to understand this variability and to haraterize it for partiular algorithms, and also to develop a hybrid method that ombines all advantages of the related methods. ACKNOWLEDGMENT This work was supported by National Natural Siene Foundation of China under Grant No , Guangdong Natural Siene Foundation (N: and Natural Siene Foundation of Department of Eduation of Guangdong Provine (N:5Z13 REFERENCES [1] G. J. Simmons, The prisoners problem and the subliminal hannel, in Advanes in Cryptology: Proeedings of CRYPTO 83. Plenum Pub Corp, pp , 1984 [2] I. J. Cox, Ton Kalker, Georg Pakura and Mahia Sheel, Information transmission and steganography, Leture Notes in Computer Siene, vol. 371, pp.15-29, 25 [3] Q. Liu, A. Sung, J. Xu, and B. Ribeiro, Image omplexity and feature extration for steganalysis of LSB, in ICPR6, pp. II:267 27, 26 [4] N. Wu and M. Hwang, Data hiding: urrent status and key issues, International Journal of Network Seurity, vol. 4, no. 1, pp. 1 9, 27 [5] J. Fidih and M. Goljan, Digital image steganography using stohasti modulation, SPIE Eletroni Imaging, pp , 23 [6] N. Provos, Defending against statistial steganalysis, Usenix Seurity Symp., pp , 21 [7] A. Westfeld, F5 - a steganographi algorithm,, Springer- Verlag Berlin Hd, pp , 21 [8] R. Anderson and F. Petiolas, On the limits of steganography, IEEE Journal of Seleted Areas in Comuniation, pp , 1998 [9] J. Fridrih, M. Goljan, R. Du, Reliable detetion of LSB steganography in olor and graysale images, in: Proeedings of ACM Workshop Multimedia Seurity, pp. 27 3, 21 [1] S. Dumitresu, X. Wu, Z. Wang, Detetion of LSB steganography via sample pair analysis, IEEE Trans. Signal Proess, 51 (7, pp , 23 [11] T. Zhang, X.J. Ping, A new approah to reliable detetion of LSB steganography in natural image, Signal Proess. 83 (1, pp ,23 [12] J. Fridrih, Feature-based steganalysis for JPEG images and its impliations for future design of steganographi shemes, in: Proeedings of sixth Information Hiding Workshop, Leture Notes in Computer Siene, vol. 32, pp , 24 [13] J. Fridrih, M. Goljan, D. Hogea, Steganalysis of JPEG images: breaking the F5 algorithm, in: Proeedings of fifth International Workshop on Information Hiding, Leture Notes in Computer Siene, vol. 2578, Springer, Berlin, pp , 22. [14] Andrew D. Ker, Quantitive evaluation of pairs and RS steganalysis., Pro.SPIE Seurity, Steganography,Watermarking Multimedia Contents, vol.536, E. J. Delp III and P. W. Wong, Eds., pp , 24 [15] I. Avibas, N. Memon, B. Sankur, Steganalysis of watermarking tehniques using image quality metris, in: Proeedings of the SPIE, Seurity and Watermarking of Multimedia Contents II, vol. 4314, pp , 2 [16] H. Farid, Deteting hidden messages using higher-order statistial models, in: Proeedings of IEEE International Conferene on Image proessing, vol. 2, pp , 22 [17] S. Lyu, H. Farid, Steganalysis using olor wavelet statistis and onelass support vetor mahines, in: Proeedings of the SPIE, Seurity, Steganography, and Watermarking of Multimedia Contents VI, vol. 536, pp , 24 [18] T. Holotyak, J. Fridrih, S. Voloshynovskiy:, Blind Statistial Steganalysis of Additive Steganography Using Wavelet Higher Order Statistis, The 9th IFIP TC-6 TC- 11 Conferene on Communiations and Multimedia Seurity. Leture Notes in Computer Siene, vol. 3677, pp ,25 [19] J. Fridrih, David Soukal, Miroslav Goljan, Maximum likelihood estimation of length of seret message embedded using steganography in spatial domain, Pro.SPIE,5681,pp ,25 [2] Y.Q. Shi, G.R. Xuan, C.Y. Yang et al., Effetive steganalysis based on statistial moments of wavelet harateristi funtion, in: Proeedings of IEEE International Conferene on Information Tehnology: Coding and Computing, pp , 25 [21] G.R. Xuan, Y.Q. Shi, J.J. Gao et al., Steganalysis based on multiple features formed by statistial moments of wavelet harateristi funtions, in: Proeedings of seventh International Information Hiding Workshop, 29 ACADEMY PUBLISHER

8 JOURNAL OF COMPUTERS, VOL. 4, NO. 7, JULY Leture Notes in Computer Siene, vol. 3727, Springer, Berlin, pp , 25 [22] Y. Wang, P. Moulin, Optimized feature extration for learning-based image steganalysis, IEEE Trans. Inf. Forensis Seur. 2 (1,pp ,27 [23] J. Harmsen, W. Pearlman, Higher-order statistial steganalysis of palette images, Pro. SPIE Seurity Watermarking Multimedia Contents, vol. 52, E. J. Delp III and P.W.Wong, Eds., pp , 23 [24] Andrew D. Ker, Steganalysis of LSB Mathing in Graysale Images, IEEE Signal Proessing Letters, Vol. 12, No. 6, pp , 25 [25] M. Goljan, J. Fridrih, and T. Holotyak, New blind steganalysis and its impliations, in Seurity, Steganography, and Watermarking of Multimedia Contents VIII, ser. Proeedings of SPIE, vol. 672, pp.1 13, 26 [26] Jun Zhang, I. J. Cox, G. Doerr, Steganalysis for LSB mathing in images with high-frequeny noise, Pro. IEEE Workshop on Multimedia Signal Proessing, pp , 27 [27] R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classifiation, 2nd ed. Wiley-Intersiene, 21 [28] G. Canelli, G. Doerr, M. Barni, and I. J. Cox, A omparative study of ±1 steganalyzers, Pro. IEEE International Workshop on Multimedia Signal Proessing, pp , 28 Jun Zhang was born in Sihuan, China in He reeived his Ph.D degree in omputer siene from Huazhong Universityof Siene & Tehnology, China in 23 and his M.S. degree in Mathematis from Lanzhou University in He had been a visiting postdotoral Researher in University College London, UK under Prof. Ingemar Cox s supervision. Now, he is the retor of Information Siene Shool, Guangdong University of Business Studies. His researh interest is information seurity suh as data hiding, watermarking and privay protetion. In this field, He has published more than 3 papers. Moreover he had been in harge of some projets sponsored by National Natural Siene Foundation of China and Guangdong Natural Siene Foundation. He served as many workshop hairs, advisory ommittee or program ommittee member of various international IEEE. Yuping Hu was born in He reeived his B.S. degree in elestial survey from Chinese Aademy of Siene, China, in 1996 and his Ph.D. degree in omputer siene from Huazhong University of Siene and Tehnology, Wuhan, China in 25. He is urrently pursuing the postdotoral researh in omputer appliations from Central South University, Changsha, China. Dr.Hu is a professor in the Shool of Information siene, Guangdong University of Business Studies, Guangzhou, China. His urrent researh interests inlude digital watermarking, image proessing, multimedia and network seurity. Zhibin Yuan was born in He reeived his Ph.D degree in omputer siene from Huazhong University of Siene & Tehnology, China in 27 and his M.S. degree in omputer siene from Huazhong University of Siene & Tehnology in 21. Dr.Yuan is a Leturer in the Shool of Information siene, Guangdong University of Business Studies, Guangzhou, China. His urrent researh interests inlude formal methods, model heking, and privay protetion. 29 ACADEMY PUBLISHER