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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 Steganalysis of Reversible Vertical Horizontal Data Hiding Technique Thom Ho Thi Huong, Canh Ho Van Tien Trinh Nhat Faculty of Information Technology, Dept. of Professional Technique, College of Technology, Haiphong Private University, Ministry of Public Security, Vietnam National University, Haiphong, Vietnam Hanoi, Vietnam Hanoi, Vietnam thomhth@hpu.edu.vn hovancanh@gmail.com tientn@vnu.edu.vn Abstract—This paper proposes a steganalysis scheme for to attack a specific steganography technique such as a detecting the reversible vertical horizontal (RVH) data hiding [1]. steganalytic method was presented in [2] for detecting stego- The RVH scheme was introduced in the IJCSIS International images using the method proposed in [3]. Journal Vol. 7, No. 3, March 2010. In the RVH data hiding, the message bits are embedded into cover-image by two embedding In this paper, we proposed a steganalytic scheme to detect phases: the horizontal embedding procedure HEm and the the RVH watermarking scheme introduced in brief in the vertical embedding procedure VEm. The pixel pairs belonging to abstract. Our experimental results show the feasibility of the the horizontally embeddable and vertically embeddable pixel pair proposed method. It is useful in detecting malicious activities domain are transformed to mark message bits. Through analysis, on stego-images and also suggests a design consideration for we detect out that, the two histograms of LSB scanning future development of steganographic techniques. The rest of horizontally and vertically vary from a stego-image to the cover this paper is organized as follows. In the next section, we image. Based on this observation, we design a specific steganlytic present again the RVH scheme in brief. Section III describes method for attacking the RVH steganography. Experimental the proposed steganalytic method. Experimental results are results show the detection accuracies of the steganography with given in section IV, and conclusions are made finally in various embedding rates are acceptable. The proposed technique Section V. can be applied in detecting the misuse of steganographic technology in malicious activities. II. REVIEW OF THE RVH DATA HIDING SCHEME Keywords-Steganography, steganalysis, watermarking, cover image, In the steganographic method proposed in [1] used the stego image, payload, reversible data hiding. multiple embedding strategies to improve the image quality and the embedding capacity. Basically, this method embeds I. INTRODUCTION each message bit b of the secret bit stream into each grayscale Steganography is [1, 3, 4, 5] is the art and science of cover pixel pair of a grayscale cover image in raster scan order. concealed communication. The basic concept is to hide the This scheme includes two main stages, namely, the horizontal very existence of the secret message. Digital object such as a embedding procedure HEm and the vertical embedding text, image, video, or audio segment can be used as the cover procedure VEm. For the HEm procedure, the input image is data. To obtain acceptable hiding payload and keep fidelity of horizontally scanned in raster scan order (i.e., from left to right the stego-image, the LSB replacement techniques [2,4 or other and top to bottom) to gather two neighboring pixels x and y references] are popular and widely studied in the literature. into a cover pixel pair (x, y). If y is an odd value, then the cover These methods usually hide more data in image areas with pixel pair (x, y) is defined as a horizontally embeddable pixel higher spatial variations. Reversible steganography [1,3-5] is pair. Otherwise, the cover pixel pair (x, y) is defined as a one of the interesting branches of steganographic technology in horizontally non-embeddable pixel pair. For the VEm which the original cover image can be reconstructed without procedure, the input image is vertically scanned in raster scan any loss. order to group two neighboring pixels u and v into a pixel pair (u, v). If v is an even value, then the pixel pair (u, v) is defined Steganalysis is the counterpart of steganography, the goal as a vertically embeddable pixel pair. Otherwise, the pixel pair of the steganalysis is to detect the hidden message, (u, v) is defined as a vertically non-embeddable pixel. equivalently, to discriminate the stego object from the non- stego-object. The steganalysis techniques proposed in the The secret bit sequence S is divided into two subsequence literature can be classified into two categories: the universal S1 and S2. The bit stream B1 is created by concatenating the steganalysis which is designed to detect the hidden message secret subsequence S1 and the auxiliary data bit stream A1 embedded with various data embedding algorithms such as a (i.e., B1=S1||A1). Similarly, the bit stream B2= S2||A2. The technique proposed in [6] is used to attack the LSB generation of A1 and A2 will be described latter. The overview steganography, and the specific steganalysis which is designed of the RVH embedding process is shown in Fig. 1. 7 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 equal to S1 (i.e., B1=S1). During the execution of the HEm procedure, for the first LC1 pixels in O, when each pixel has been processed for embedding, its LSB is taken as an auxiliary data bit of A1 and appended to the end of B1. That is, B1 is gradually grown until the LC1 auxiliary data bits in A1 are concatenated into B1. Finally, the to_be_embedded bit stream is B1=S1||A1, which is completely embedded into O. Similar to the generation of A1, the auxiliary data stream A2 is actually the LSBs of the first LC2 (LC2 is the length of the compressed location map CM2 ended with the unique end of map indicator EOM2) pixels in the image V and generated as follows. B2 initially equals the secret bit sequence S2. Fig. 1. Embedding phase of RVH steganographic system [1] During the execution of the procedure VEm, for the first LC2 pixels in the image U, when each pixel has been processed for Firstly, the bit sequence B1 is horizontally embedded into embedding, its LSB is taken as an auxiliary data bit of A2 and O by using the HEm procedure to obtain the output image T append to the end of B2 until the LC2 auxiliary data bits in A2 sized H x W pixels. Secondly, the compressed location map are concatenated into B2. Finally, the information bit sequence CM1 whose length is LC1 (will be described later), is is B2=S2||A2, which is fully marked into the image U. embedded in to T by using the least significant bit (LSB) replacement technique to obtain the output image U with size For the purposes of extracting B1 and recovering O, a of H x W pixels. Thirdly, the bit sequence B2 is vertically location map HL sized H x (W/2) is needed to record the embedded into U by using the VEm procedure to get the output positions of the horizontally embeddable pixel pair (x, y) in O. image V with size of H x W pixels. Fourthly, the compressed The location map HL is a one-bit bitmap. All the entries of HL location map CM2 whose length is LC2 is embedded into V by are initialized to 0. If cover pixel pair (x, y) is the horizontally using the LSB replacement technique to get the final stego embeddable pixel pair, then the corresponding entry of HL is image with size of H x W pixels. set to be 1. Next, the location map HL is losslessly compressed by using the JBIG2 codec (Howard et al, 1998 [8]) or an Each bit b in stream B1 is horizontally embedded into each arithmetic coding toolkit (Carpenter, 2002 [7]) to obtain the horizontally embeddable pixel pair (x, y) at a time by using the compressed location map CM1 whose length is LC1. The horizontal embedding rule HR defined below until the whole compressed location map CM1 is embedded into the image T bit stream B1 is completely marked into O to obtain the output by using the LSB replacement technique as mentioned above. image T. Similarly, for the purposes of extracting B2 and recovering the Each bit b in B2 is vertically embedded into each vertically image U, we also need a location map VL sized (H/2) x W to embeddable pixel pair (u, v) at a time by using the vertical mark the position of the vertically embeddable pixel pairs (u, v) embedding rule VR defines below until the entire bit sequence in U. Then, VL is also losslessly compressed by using the B2 is concealed into U to get the output image V. JBIG2 codec or an arithmetic coding toolkit to obtain the compressed location map CM2 whose length is LC2. Next, the The horizontal embedding rule HR: For each pair (x, y), we map CM2 is concealed into the image V by using the LSB apply the following embedding rules: steganography as mentioned above. HR1: If the to_be_embedded bit b=1, then the stego The final output of the embedding phase is the final stego pixel pair is unchanged by (x0, y0) = (x, y). image X with size of H x W pixels. HR2: If the to_be_embedded bit b=0, then the stego III. THE PROPOSED STEGANALYTIC SCHEME FOR THE RVH pixel pair is changed by (x0, y0) = (x, y-1). STEGANOGRAPHY The vertical embedding rule VR: For each pair (u,v), we After embedding a large message sequence M (its ratio is apply the following embedding rules: about 90% of maximum embeddable capacity of image) into VR1: If the to_be_embedded bit b=0, then the stego the original image Baboon sized 512x512 pixels (show Fig. 2) pixel pair is unchanged by (u0, y0) = (u,v). using the RVH scheme to obtain the stego-image Baboon, we calculate histogram of the two images (cover Baboon image VR2: If the to_be_embedded bit b=1, then the stego and stego Baboon image), resulted in Fig. 3. It’s very hard to pixel pair is changed by (u0, y0) = (u, v+1). detect any difference between the two images. It is noted that the rule HR and VR don’t cause the However, when we separably calculate two histograms on underflow and overflow problem. That is the changed pixel all pixel odd columns and all pixel even rows of the cover pairs are assured to fall in the allowable range [0,255]. Baboon image, shown in Fig. 4. Similarly, calculate two histograms on all pixel odd columns and all pixel even rows of The auxiliary data bit sequence A1 is actually the LSBs of the stego Baboon image, resulted in Fig. 5. It’s easy to the first LC1 (LC1 is the length of the compressed location difference between pair histogram in Fig.4 (a) and Fig. 5 (a), in map CM1 ended with the unique end of map indicator EOM1) Fig. 4 (b) and Fig. 5 (b). The informality appears in Fig 5 (a) pixels in the image T and generated as follows. Initially, B1 is 8 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 and (b) due to embedding process of RVH scheme following description in detail below. 2000 1800 1600 1400 1200 1000 800 600 400 200 0 0 50 100 150 200 250 300 (a) 2500 2000 Fig. 2. The Baboon image sized 512x512 pixels 4000 1500 3500 3000 1000 2500 2000 500 1500 1000 0 0 50 100 150 200 250 300 500 (b) 0 Fig. 5. Histogram of the stego Baboon images: (a) histogram on all pixel odd 0 50 100 150 200 250 300 (a) columns, (b) histogram on all pixel even columns 4000 3500 3000 According to the horizontal embedding procedure HEm, 2500 from an input image O, the pixels of the image O are 2000 horizontally grouped into pixel pairs (x, y), these pairs are 1500 partitioned into two sets, one set is E1 and other set is , the 1000 set E1 contains pixels pair which are horizontally embeddable 500 pixel pairs, while the set consists of those pixel pairs which 0 are horizontally non-embeddable pixel pairs. 0 50 100 150 200 250 300 (b) Now, we examine the migration of LSB histogram of the Fig. 3. Histogram of the tested two images: (a) the cover Baboon image, (b) the stego Baboon image image O and the image T obtained after embedding secret bit 2000 B1. Without loss of generality, let (x, y) and ( be the 1800 1600 corresponding pixel pairs in the image O and the stego-image 1400 T, respectively. In the horizontal embedding procedure HEm, 1200 pixel pairs (x, y) E1, i.e. the LSB of pixel y be bit 1, are 1000 selected to embed message bits. Here, We don’t examine 800 600 change of LSB histogram of pixels x on pixel even-columns 400 because they are still remained value after embedding message 200 bits. In the image T, the LSB of is changed to either 0 or 1, 0 0 50 100 150 200 250 300 (a) and each of them appears in the same probability. It is 2000 obviously that the probability of bit 0 and bit 1 are 0.5 and 0.5, 1800 respectively. For pixel pairs (x, y) , i.e. the LSB of pixel y 1600 be bit 0, after embedding secret bits, is unchanged. So the 1400 probability of bit 0 and 1 are 1 and 0, respectively. 1200 1000 Next, the compressed location map CM1 (CM1 is a binary 800 stream, whose length is LC1) are marked into the image T by 600 the LSB replacement technique to obtained image U. That 400 200 changes a part of probability of LSB of bit 1 and bit 0 on all 0 pixel even-columns in the image T. Assume that the bits are 0 50 100 150 200 250 300 (b) randomly distributed, so the probability of bit 0 and bit 1 are Fig. 4. Histogram of the cover Baboon images: (a) histogram on all pixel odd Pmap1(0) = Pmap1(1). columns, (b) histogram on all pixel even columns 9 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 Base on above discussions, the probabilities of bit 0 and bit used to embed message, i.e. the embedding ration of P R- 1 of all pixels on even-column in the image U can be H=0.45 0.9=0.405. From (1), we have PLSB-H(0) calculated. Assume the probability of pixel pairs belonging to =0.405 (0.5 0.45+0.55) + 0.595 0.5 = 0.611375 and PLSB- E1 and the probability of pixel pairs belonging to be H(1)=0.405 (0.5 0.45)+0.595 0.5 = 0.388625. Next, and , respectively. After marking the location map CM1, calculated the probability of bit 0 and the probability of bit 1 of PE1 and are changed to P’E1 and . Let PR-H is the the output image X. We know that the probability of E2 equals embedding ratio defined by dividing the number pairs actually to the probability of the LSB of bit 0 of all pixels on even – used to hide data by the total number of pairs the image O. The rows, i. e. PE2 = PLSB(0)/2 + PLSB_H(0)/2 = (0.5+0.611375)/2 = probability of bit b={0,1} of LSB of the image U can be 0.5556875 and =0.4443125. After covering a part of the calculated using the following equation LSB of image V by the location map CM2 with a probability 0.05 (assumed), the two probability PE2 and change to (1) P’E2=0.5056875 and = 0.4943125, respectively. For the vertical embedding procedure VEm, vertically scan The embedding ratio of 90 % of the embeddable pairs are the output image U in raster scan order to group pixel pairs (u, used to embed message, i.e. the embedding ration of P R- v), we classify the pairs into two sets, one is E2 and other is V=0.5056875 0.9=0.45511875. So probability of LSB of bit 0 , the set E2 contains all pixel pairs which are vertically and bit 1 of the output image X from (2) we obtain PLSB- embeddable pixel pairs, the set consisting pixel pairs are V(0)=0.45511875 (0.5 0.5056875) + 0.54488125 0.5 vertically non-embeddable pixel pairs. Let (u, v) and ( be 0.3875, PLSB_V(1)0.61248. pixel pairs of the image U (before using the procedure Vem) Now, we check again the probability of LSB of bit 1 and the and the stego-image V (after embedding secret message using probability of LSB of bit 0 of all pixels on pixel even-columns, the procedure Vem). In the procedure VEm, only pixel pairs (u, PLSB_even_column(0)=PLSB_H(0)/2 + PLSB_V(0)/2 =(0.611375+ v) E2, i.e. the LSB of v is bit 0, are embedded message bits. 0.3875)/2=0.4994375, PLSB_even_column(1) = (PLSB_H(1) + After embedding message bits, the LSB of the pixels PLSB_V(0))/2=(0.388625+0.61248)/2=0.5005525. We found out (obtained from E2) is either 0 or 1. So, the probabilities of bit 0 that the probability of bit 0 PLSV_even_column(0) and probability of and bit 1 of ( are equals to 0.5. For pixel pairs (u, v) , bit 1 PLSB_even_column(1) are the same, that is after completing the i.e. the LSB of pixel v be bit 1, after embedding secret bits, is vertical procedure VEm, it make the value of these unchanged. So the probability of bit 0 and 1 are 0 and 1, probabilities be balanced. However, the probability of LSB of respectively. bit 0 and bit 1 of all pixels on pixel odd-columns don’t equal based on the following calculating: Next, the compressed location map CM2 are marked into the PLSB_odd_column(0)=(PLSB_org_odd_column(0)/2+PLSB_V(0)/2)=(0.5/2 + image V by the LSB replacement technique to obtained image 0.3875/2)=0.44375, PLSB_odd_column(1)=(PLSB_org_odd_column(1)/2 + X. That changes a part of probability of LSB of bit 1 and bit 0 PLSB_V(1)/2)=(0.5/2+0.61248/2)=0.55624. Where on all pixel even-rows in the image V. Assume the bits of the PLSB_org_odd_column(0) and PLSB_org_odd_column(1) be the probabilities map CM2 are randomly distributed, so the probability of bit 0 of the LSB of bit 0 and bit 1 of all pixels on the pixel odd- and bit 1 are Pmap2(0) = Pmap2(1). column of the image X. A half of them isn’t changed during From above discussions, the probabilities of bit 0 and bit 1 process of the RVH scheme, so PLSB_org_odd_column(0)/2 and in the LSB of image X after using the vertical embedding PLSB_org_odd_column(1)/2 equal to 0.5/2 and 0.5/2, respectively. We procedure VEm can be calculated. Assume the probability of can see obvious difference of the occurrences of bit 1 and bit 0 pixel pairs belonging to E2 and the probability of pixel pairs in the LSB on all pixel odd_columns and all pixel belonging to be and , respectively. After marking even_column of the stego-image of the RVH scheme with the location map CM2, PE2 and are changed to P’E2 and respect to a standard natural image. Based on the problem, the . Let PR-V be the embedding ratio defined by dividing the following rule is given to discriminate a stego-image of the number pairs actually used to hide data by the total number of RVH steganography from a nature image. pairs the image V. The probability of bit b={0,1} of LSB of the image V can be calculated using the following equation W(X) = (3) (2) From equation (3), an image is detected be stego-image marked by the RVH scheme if one of the measured values For a natural image, assume that the LSB is randomly |PLSB(0) – PLSB(1)| on all pixel odd columns (or pixel even distributed, then the expected probability of bit 0 and the columns) or pixel even rows (or pixel odd rows) is greater than probability bit 1 of all pixel on pixel even-columns are the threshold T (0 ≤ T ≤ 1). The threshold T is used to control the same, i.e. PLSB(0) = PLSB(1)=0.5. So probability PE1=0.5, decision boundary of nature images and stego images, its value =0.5. After covering a part of the LSB of image T by the depends on specific applications. location map CM1 with a probability 0.05 (assumed), the two probability PE1 and change to P’E1=0.45 and =0.55, IV. EXPERIMENTAL RESULT respectively. Consider the Baboon stego-image from the To show the reliability of the proposed method, we take Baboon cover image, the probability of the embeddable pairs 500 image from USC-SIPI Image Database [9] and content (i.e. those pixel pairs belonging to the procedure HEm) of an based image retrieval (CBIR) image database [10] and convert input image T is P’E1, and 90 % of the embeddable pairs are them into 8-bit grayscale images. The images are used to test 10 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 proposed classification. The hidden messages used in our test are made by the pseudo random number generator. We embed 0.4 different amount of message using the RVH scheme, and measure the migration of LSB histogram in the stego images. 0.35 Five embedding ratios 0%, 25%, 50%, 75% and 100% are used 0.3 in the test, and the obtained |PLSB(0)-PLSB(1)| values on all pixel even-rows of the stego-images are depicted in Fig. 6 – 10, |Plsb(0) - Plsb(1)| 0.25 respectively. We also measure the accuracy of the proposed method in detecting the RVH scheme in different embedding 0.2 ratio and likelihood threshold value T, shown in table 1. 0.15 0.25 0.1 0.05 0.2 0 0 50 100 150 200 250 300 350 400 450 500 |Plsb(0) - Plsb(1)| 0.15 Number of images Fig. 9. The distribution of |PLSB(0) – PLSB(1)| value of the 500 stego images on 0.1 all pixel even-rows with embedding ratio 75% 0.5 0.05 0.45 0.4 0 0 50 100 150 200 250 300 350 400 450 500 0.35 Number of images |Plsb(0) - Plsb(1)| 0.3 Fig. 6. The distribution of |PLSB(0) – PLSB(1)| value of the 500 cover images on all pixel even-rows 0.25 0.2 0.35 0.15 0.3 0.1 0.25 0.05 |Plsb(0) - Plsb(1)| 0 0.2 0 50 100 150 200 250 300 350 400 450 500 Number of images 0.15 Fig. 10. The distribution of |PLSB(0) – PLSB(1)| value of the 500 stego images on all pixel even-rows with embedding ratio 100% 0.1 TABLE I. THE DETECTION ACCURACY OF THE PROPOSED METHOD WITH 0.05 VARIOUS EMBEDDING RATIOS AND THRESHOLD VALUES 0 Embedding 0 50 100 150 200 250 300 350 400 450 500 Number of images Ratio (%) 0 25 50 75 100 Fig. 7. The distribution of |PLSB(0) – PLSB(1)| value of the 500 stego images on Threshold T all pixel even-rows with embedding ratio 25% Cover 70.6 % 2% 0.6% 0% 0% 0.01 Stego 29.4 % 98% 99.4 % 100% 100 % 0.35 Cover 80.6 % 5.8 % 0.6 % 0% 0 0.02 Stego 19.4 % 94.2 % 99.4 % 100% 100 % 0.3 Cover 84.4 % 7.4 % 2.2 % 0 0 0.03 Stego 15.6 % 92.6 % 97.8 % 100% 100% 0.25 Cover 86.8 % 11 % 2.4 % 0 0 0.04 Stego 13.2 % 89 % 97.6 % 100% 100% |Plsb(0)-Plsb(1)| 0.2 Cover 89 % 13.8 % 3.6 % 0.2 % 0 0.05 86.2% 96.4 % 99.8% 100% 0.15 Stego 11 % 0.1 From Fig. 6 , we can see that most of the value of |PLSB(0) – 0.05 PLSB(1)| approach zero for natural images, while the higher 0 value of |PLSB(0) – PLSB(1)| is obtained with embedding ratio 0 50 100 150 200 250 300 350 400 450 500 Number of images 25%, 50%, 75% and 100% shown from Fig. 7 to Fig. 10. From table 1, we see that when the likelihood threshold value T is set Fig. 8. The distribution of |PLSB(0) – PLSB(1)| value of the 500 stego images on all pixel even-rows with embedding ratio 50% 11 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 0.035, we can obtain an acceptable result in detecting stego [7] Carpenter, B., 2002. Compression via Arithmetic Coding images used the RVH steganography. http://www.colloquial.com/ArithmeticCoding/ [8] P.G. Howard, F. Kossentini, B. Martins, S. Forchhammer, W. J. V. CONCLUSION Rucklidge, 1998. The emerging JBIG2 standard. IEEE Transactions on Circuits and Systems for Video Technology 8 (7), pp. 838-848. The paper presents a method to break the RVH [9] USC-SIPI Image Database, steganography based on the observation of the distribution of “http://sipi.usc.edu/services/database/Database.htm” 0 and 1 bits of the LSBs on pixel odd-columns (pixel even- [10] CBIR Image Database, University of Washington, columns) or pixel even-rows (pixel odd-rows) of the RVH http://www.cs.washington.edu/research/imagedatabase/groundtruth/.. stego-images. The experimental results are shown that the proposed method can detect stego - images reliably with AUTHORS PROFILE embedding ratio being greater 25%. On the other hand, we show a problem of security of the RVH scheme in the data Ho Thi Huong Thom received the B.S. degree of embedding process. Information Technology department from Haiphong Private University and the M.S. degree in Information ACKNOWLEDGMENT Systems from College of Technology, Vietnam National Our special thanks to Haiphong Private University (HPU) University in Vietnam, in 2001 and 2005, respectively. for their financial support to our research and College of She has started her career as Lecturer in Department of Information Technology, Vietnam National University, Hanoi for their Technology in Haiphong Private University, Vietnam and served for 9 years. support to good working environment. We would like to Currently, she is pursuing Doctor of Information Systems from College of extend our thanks to my guide, our friends and family Technology, Vietnam National University, Hanoi, Vietnam. Her research members without whose inspiration and support our efforts interests includes Image processing, Information Security, Information Hiding. would not have come to success. REFERENCES Ho Van Canh received the B.S. degree in Mathematics from Hanoi City University in Vietnam in 1973, the Dr. [1] P. Mohan Kumar, K. L. Shunmuganathan, A reversible high embedding Sci. degree in Faculty of statistology from KOMENSKY capacity data hiding technique for hiding secret data in images, International Journal of Computer Science and Information Security, University in Czechoslovakia in 1987. Currently, he has Vol.7, No. 3, March 2010, pp. 109-115. been working as a cryptologist in Dept. of Professional [2] Yeh-Shun Chen, Ran-Zan Wang, Yeuan-Kuen Lee, Shih-Yu Huang, Technique, Ministry of Public Security, Vietnam. His Steganalysis of reversible contrast mapping water marking, Proceedings of the world congress on Engineering 2008 Vol I, WCE2008, July 2-4, research interests include cryptography, information security, information 2008, London, U.K., pp. 555-557. hiding. [3] D. Coltuc and J. M. Chassery, “ Very fast watermarking by reversible contrast mapping,” IEEE Signal Processing Lett., vol. 14, no. 4, pp. 255– 258, Apr. 2007. Trinh Nhat Tien received the B.S degree from University [4] J. Tian, “ Reversible Data embedding using a difference expansion,” of Prague in Czechoslovakia in 1974, and the Dr. degree IEEE Trans. Circuits Syst. Video technol., vol. 13, no. 8, pp. 890– 896, Aug. 2003. from University of Prague, Czechoslovakia and University [5] Z. Ni, Y. Q. Shi, N. Ansari, and W. Su, “ Reversible Data Hiding,”IEEE of Hanoi, Vietnam in 1984. He has started as Lecturer in Trans. Circuits Syst. Video technol., vol. 16, no. 3, pp. 354– 362, Mar. Department of Information Technology of College of 2006. [6] J. Fridrich, M. Goljan, and R. Du, “ Reliable detection of LSB Technology, Vietnam National University, Hanoi, Vietnam since 1974. His steganography in color and grayscale images,”Proceedings of the ACM research interests include algorithm, complexity of algorithm, information International Multimedia Conference and Exhibition, pp. 27– 30, 2001. security. 12 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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