Image and vision computing

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Covert communicationDigit steganography

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The experimental results show that the proposed method increases the number of embedded secret bits

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image quality, we usually have to scarify the embedding capacity,and vice versa.

Nowadays, many steganographic methods have been proposedto hide secret messages into an image. A commonly used methodis the least signicant bit (LSB) replacement, which is the simplesthiding technique by using some least bits of cover pixels to embedsecret data [46,10]. Mielikainens LSB matching revisited method

high embedding efciency and secrecy with low distortion, a largern leads to a smaller embedding rate according to the equationR = (log2(2n + 1))/n. In other words, the EMD embedding methodhas its maximum embedding rate which is approximate 1.161 bitsper pixel when n = 2.

This paper improves the EMD embedding method, especially inembedding capacity. In our proposed method, each secret digit in a(2m + 1)-ary notational system is carried by a pair of cover pixels.The data hider can segment the pair of cover pixels into two parts:one is used to embed the secret data and the other is used as anindicator for the decoder to extract the secret data. The embedding

* Corresponding author. Tel.: +886 4 23323000 4293; fax: +886 4 23742337.E-mail addresses: [email protected] (C.-F. Lee), [email protected], m9503085@

Image and Vision Computing 26 (2008) 16701676

Contents lists availab

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elsfcu.edu.tw (C.-C. Chang).a great deal of attentions from both the academic and industrialcommunities [111]. An original image, also called a cover image,is used to embed the secret data. The stego-image is a version ofthe cover image where secret messages are embedded. By meansof creating stego-images that are perceptually identical to the cov-er images with small embedding distortion, the imperceptibilityfor protecting the sensitive and condential information can bemaintained without being detected or extracted. Two important is-sues for current data hiding techniques are to preserve the imper-ceptibility and the embedding capacity at the same time. However,this is an irreconcilable conict: if we want to preserve high stego-

M N bits. Dene the embedding rate R as the rate of the length ofembedded messages to the maximum capacity M N. If the rate Rismore thanone, it represents the steganographic embeddingmeth-od with high embedding capacity [8,9,11].

Recently, Zhang and Wang [9] proposed a steganography totransform the binary secret data into a stream of secret digits ina (2n + 1)-ary notational system. Zhang and Wangs embeddingmethod uses n cover pixels to carry one secret digit in a (2n + 1)-ary notational system. The embedding rate, R = (log2(2n + 1))/n, isdened for calculating the number of secret bits that can be carriedby a cover pixel. Though Zhang and Wangs method could achieveData hidingEmbedding capacity

1. Introduction

Message transmission over the Inmost everywhere. Some problems maws of communication channel. Didata security technique, has been dev0262-8856/$ - see front matter 2008 Elsevier B.V. Adoi:10.1016/j.imavis.2008.05.005more than 1.7 times compared with the EMD embedding method. Even with such high embedding capac-ity, the average PSNR of 44.3 dB shows that the visual quality does not decline to an unacceptable degree.

2008 Elsevier B.V. All rights reserved.

is quite common in al-ise due to the securityeganography, a kind ofquickly and it receives

[7] can resist immune against the steganographic attacks becauseit has not the asymmetric property of LSB replacement methods.LSBmatching revisitedmethodalso achieves the samequality of ste-go-images aswell as LSB replacement does. However, it does not en-hance theembeddingcapacity. Fora cover image IwithM N pixels,the maximum data hiding capacity of LSB steganography isKeywords:ding by exploiting modication direction, IEEE Communication Letters 10 (2006) (113), pp.781783],because the embedding rate of EMD embedding method is R = (log2(2n + 1))/n, when m > 2 and n = 2.An improvement of EMD embedding mesegmentation strategy

Chin-Feng Lee a,*, Chin-Chen Chang b,c, Kuo-Hua WanaDepartment of Information Management, Chaoyang University of Technology, 168 JifonbDepartment of Information Engineering and Computer Science, Feng Chia University, 1cDepartment of Computer Science and Information Engineering, National Chung Cheng

a r t i c l e i n f o

Article history:Received 22 November 2007Received in revised form 1 April 2008Accepted 5 May 2008

a b s t r a c t

In this paper, a novel data hpaper keeps (16 pm) MSBcations on an m-dimensionThe embedding rate of proembedding method propos

Image and Vis

journal homepage: www.ll rights reserved.od for large payloads by pixel

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. Road, Wufong Township, Taichung County 41349, Taiwan, ROCenhwa Rd., Seatwen, Taichung 40724, Taiwan, ROCersity, 160 San-Hsing, Ming-Hsiung, Chiayi 621, Taiwan, ROC

ng method by using pixel segmentation strategy is proposed. The proposedf a pixel-pair unchanged and alters pm LSBs to indicate the virtual modi-pseudo-random vectors for carrying the secret data, where m 2pm1 1.ed method is R = (log2(2m + 1))/2, which is greater than that of the EMDby Zhang and Wang [X. Zhang, S. Wang, Efcient steganographic embed-

le at ScienceDirect

n Computing

evier .com/locate / imavis

rate of our method is steadily increased as m gets larger withoutlosing the stego-image quality and security. Experimental resultsshow that our proposed method still keeps pretty good quality ofthe stego-image, while the embedding capacity is exactly enlarged.

The rest of this paper is organized as follows. In Section 2, wereview previous approaches of embedding in grayscale images.Then, in Section 3, we introduce the proposed embedding andextracting procedures for grayscale images. We make comparisonsof embedding rate and stego-image quality between our methodand Zhang and Wangs method in Section 4. Finally, we conclude

because at most one cover pixel needs to be increased or decreasedby one for a pixel-group of cover pixels. Though, the EMD embed-ding method gets high quality of stego-image, there is still muchroom to further improve the embedding capacity, because theembedding rate R = (log2(2n + 1))/n for the best case of n = 2 is only1.2 secret bits per cover pixel.

3. Our proposed method

S4 i.e., pm = (8 PV1) + (8 PV2) = 16 (PV1 + PV2). After the pixel

C.-F. Lee et al. / Image and Vision Computing 26 (2008) 16701676 1671this in Section 5.

2. The EMD embedding method

An embedding method to exploit the modication directions fordata hiding (also called the EMD embedding method for short) wasproposed by Zhang and Wang [9]. The EMD embedding methodpseudo-randomly permutes all pixels in a cover image with asecret key to partition the pixels into a series of groups. A pixel-group contains n grayscale pixels and is denoted as (g1,g2, . . . ,gn).The secret message to be embedded needs to be converted into asequence of secret digits of a (2n + 1)-ary notational system, whereeach secret digit falls within [0,2n]. Eq. (1) depicts that a secretmessage of binary stream can be segmented into many pieces withL bits, and the decimal value of each secret piece is represented byK digits in the (2n + 1)-ary notational system, where

L bK log22n 1c: 1In the EMD embedding method, the data hiders can choose one of(2n + 1)-ary notational systems and determine the length K of seg-mented bits to convert the secret message into a sequence of secretdigits. This feature can increase the security if the attacker does notknow the value of K and n. Zhang and Wang dened an embeddingfunction f as weighted sum function modulo (2n + 1) for each pixel-group:

f g1; g2; . . . ; gn g1 1 g2 2 . . . gn nmod2n 1:2

If a secret digit to be embedded into a given cover pixel-group(g1,g2, . . . ,gn) is not equal to the value calculated from the embed-ding function, only one of the cover pixels has to be modied byeither increasing or decreasing one; otherwise, no modicationneeds to be done. That is why the EMD embedding methods distor-tion induced in the stego-image is not great.

In the extracting procedure, if the stego pixel-group isg01; g02; . . . ; g0n, then the secret digit can be extracted by the follow-ing extraction function.

f g01; g02; . . . ; g0n g01 1 g02 2 . . . g0n nmod2n 1:3

The EMD embedding method provides a pretty high stego-imagequality with the PSNR value greater than 51 dB in average. This isFig. 1. Pixel-pair segmentation. (a) A grasegmentation is done, S1 and S3 are combined to be an area of avector of coordinates (VCA) as shown in Fig. 1(b) which can befurther processed to form a group of integer coordinates for logi-cally embedding data. Moreover, S2 and S4 are combined to be acoordinate vector modication area (VMA) as shown in Fig. 1(c).

Example 3.1. For a given pair of cover pixels C = (125, 101)10, werst transform C into its corresponding binary stream (01111101,01100101)2. Assume a key is used to obtain PV1 = 7 and PV2 = 6, i.e.,pm = 3, then the bits of C in VCA are (0111110 011001)2 and the bitsof C in VMA are (101)2.

3.2. Embedding procedure

As we know, the distortion of grayscale image increases greatlyif we change the most signicant bits (MSBs) instead of the leastsignicant bits (LSBs). In addition, the modication of the most sig-nicant bits is much easier to be detected. Therefore, in the pro-posed method, only pm least signicant bits distributed over theVMA of the given pair of cover pixels are possibly altered. In otherwords, we do not physically modify the (16 pm) most signicantbits to achieve the embedding of secret messages. In this way, goodstego-image quality can be preserved and the embedding ratio ishigh.

In fact, the (16 pm) bits of VCA are merely used as a seed ofrandom function fr which can be predetermined and known byboth data hiders and extractors. The outcome generated by theIn this section, we rstly introduce the developed pixel-pairsegmentation strategy. Then, the proposed data embedding andextracting procedures are presented to improve information hidingratio than that of Zhang and Wangs method.

3.1. Pixel-pair segmentation

The message embedding is performed onto a pair of cover pix-els. With two grayscale pixels, 16 bits can be segmented into fourpieces (see Fig. 1(a)), which are denoted as S1, S2, S3, and S4, respec-tively. S1 refers to the piece which has PV1 most signicant bits ofthe rst cover pixels, S2 refers to the piece which has (8 PV1) leastsignicant bits of the rst cover pixels, S3 refers to the piece whichhas PV2 most signicant bits of the second cover pixels, and S4refers to the piece which has (8 PV2) least signicant bits of thesecond cover pixels. Let pm is the length of S2 concatenating withyscale pixel-pair; (b) VCA; (c) VMA.

to Eq. (5), the F value of hyper-cube corresponding to (7,13,9)10 is4. Meanwhile, the values of hyper-cubes corresponding to the sixneighbors of (7,13,9)10 are all within [0,6] as shown in Fig. 2.

Example 3.3. Lets continue Example 3.2. We have gotten thehyper-cube value (say F = 4) by given the vector of coordinates(7,13,9)10, where m = 3. If a secret digit falling in [0,7] is going tobe embedded, the coordinates should be logically modied tobe one of the (2m + 1) outcomes, totally depending on thevalue of the embedded secret digit s. The seven outcomes are(g1,g2,g3), (g1 1,g2,g3), (g1 + 1,g2,g3), (g1,g2 1,g3), (g1,g2 + 1,g3),(g1,g2,g3 1), and (g1,g2,g3 + 1), respectively, discussed as follows.

Computing 26 (2008) 16701676series of pixel-pairs.Step 3: For each pair of cover pixels, say C, we further proceed to

divide the pixel-pair C into two areas, VCA and VMA asshown in Fig. 1.

Step 4: Use the (16 pm) bits in VCA as a seed of random func-tion to generate a vector of coordinates denoted as(g1,g2, . . . ,gm), where gi can be any positive integer, fori = 1, 2, . . . , m, where m 2pm1 1.

Step 5: Convert a binary secret message into a sequence ofsecret digits in the (2m + 1)-ary notational system.

Step 6: Apply the embedding function which can be calculatedin Eq. (4) to embed every secret digit in the (2m + 1)-ary notational system.

F f g1; g2; . . . ; gm Xmi1

gi i" #

mod2m 1: 4

Since the vector of coordinates (g1,g2, . . . ,gm) corresponds to a unithyper-cube in an m-dimensional integer space, the hyper-cubecan be labeled with its F value. Obviously, the F value of anyhyper-cube and its 2m neighbors are integers within [0,2m], andthey are mutually different.

There are (2m + 1) possible cases when embedding a secret digits. If s is equal to F, no modication for the vector of coordinates isneeded. Otherwise, one of the m coordinates, i.e., gi needs to belogically modied. From Eq. (5), d can be obtained rst.

d s F mod 2m 1: 5Then, when d is greater than m, the value of g(2m1)d has to belogically decreased by one; otherwise, the value of gd has to belogically increased by one. That is, when we embed a secretdigit in the (2m + 1)-ary notational system, one logical outcomeof (g1,g2, . . . ,gm), (g1 1,g2, . . . ,gm), (g1 + 1,g2, . . . ,gm), (g1,g2 1,. . . ,gm), (g1,g2 + 1, . . . ,gm), . . . , (g1,g2, . . . ,gm 1), and (g1,g2, . . . ,gm + 1) is obtained after applying the embedding function inEq. (5).

Example 3.2. According to Example 3.1, when pm = 3, m is three.random function is a vector of coordinates with m positive inte-gers, which can be denoted as (g1,g2, . . . ,gm) and can be expressedas a unit of hyper-cube in an m-dimensional space. Here, m isdetermined by the value of pm such that m 2pm1 1. The hy-per-cube related to the vector of coordinates (g1, g2, . . . ,gm) is in-spired from the hyper-cube of a pixel-group introduced by Zhangand Wang. The difference between the vector of coordinates (g1,g2, . . . ,gm) proposed here and the pixel-group proposed by Zhangand Wang is that the vector of coordinates is projected from the16 pm bits of VCA for imitating the embedding way proposedby Zhang et al. That is,m integers of vector coordinates are not cov-er pixels. Therefore, no physical modication is performed on thecoordinate values. Also, no bits of VCA are modied during theembedding procedure. The embedded secret message has to beconverted into a sequence of secret digits of the (2m + 1)-ary nota-tional system, where each secret digit falls within [0,2m]. We mod-ify the pm bits of VMA to indicate which integer of g1, g2, . . . , and gmwill be logically increased/decreased one when a secret digit isgoing to be embedded.

The embedding steps are presented as follows.

Step 1: Determine the pm value as introduced in the procedureof pixel-pair segmentation.

Step 2: Pseudo-randomly permute all grayscale cover pixelswith a secret key, and divide these cover pixels into a

1672 C.-F. Lee et al. / Image and VisionAssume that the bit stream (0111110 011001)2 is an inputargument of a predetermined random function fr and the randomfunction fr will return a vector of coordinates, (7,13,9)10. AccordingCase 1: if we want to embed (0)7, we rst calculate d = s Fmod(2m + 1) = 0 4 mod 7 = 3, which is not greater than m,where m = 3. Therefore, we add one to g3 such that thevector of coordinates (7,13,9)10 can be replaced by(7,13,10)10.

Case 2: if we want to embed (1)7, we calculate d = s F mod(2m + 1) = 1 4 mod 7 = 4, and get d is greater than m.Therefore, we decrease g2m+1d by 1 to obtain (7,13,8)10.

Case 3: if we want to embed (2)7, we do the calculation asd = s F mod (2m + 1) = 2 4 mod 7 = 5, and see d isgreater thanm. Therefore, we decrease g2m+1d by 1 suchthat g2 = 12 and the vector of coordinates is (7,12,9)10.

Case 4: if we want to embed (3)7, d is calculated as d = s Fmod(2m + 1) = 3 4 mod 7 = 6, which is greater than m.Therefore, we decrease g2m+1d by 1 such that g1 = 6and the vector of coordinates is (6,13,9)10.

Case 5: To embed (4)7 in (7,13,9)10, according to Fig. 2, if wewant to embed (3)7 in (7,13,9)10, no modication isneeded.

Case 6: if we want to embed (5)7, we have d = s F mod(2m + 1) = 5 4 mod 7 = 1, which is not greater thanm. Therefore, we add one to g1 such that the vector ofcoordinates (7,13,9)10 can be replaced by (8,13,9)10.

Case 7: if we want to embed (6)7, we calculate d = s F mod(2m 1) = 0 4 mod 7 = 2, which is not greater thanm. Therefore, we add one to g2 such that the vector ofcoordinates (7,13,9)10 can be replaced by (7,14,9)10.

As mentioned in Section 3.1, the most (16 pm) signicant bitsof VCA can be used as a seed of random function and promise no bitmodication will be occur during the whole process. In the laststep of embedding procedure, we physically modify the pm bitsof VMA to indicate how the vector of coordinates are changedaccording to Eq. (4). We use the most (pm 1) bits of VMA to whichgi of the coordinate vector (g1,g2, . . . ,gm) should be logically modi-ed. The last one bit of VMA is used to be a sign indicator. If the bitFig. 2. the hyper-cube values of the vector of coordinates (7,13,9)10 and its sixneighbors.

VMA to express the logical modication of the vector of

In order to compare the performance of the EMD embeddingand the proposed methods, we use the embedding rate denedas R = S/H W to calculate the number of secret bits carried byone cover pixel, i.e., bits per pixel (bpp), where S refers to the num-ber of bits of the secret data, and H W is the total number of cov-er pixels.

By Zhang and Wangs method, S = (H W log2(2n + 1))/n.Therefore, the embedding rate R of the EMD embedding methodis (log2(2n + 1))/n, where n = 2, which has the best embedding rateR of (log25)/2, when n is set to be 2. In our proposed method,S = (H W log2(2m + 1))/2 that implies R = log2(2m + 1)/2 = log2(pm 1)/2 and the best embedding rate is log215/2, whichis almost twice than that of Zhang and Wangs method. Table 1compares the embedding rate for the EMD embedding and the pro-posed methods.

The proposed paper keeps (16 pm) MSBs of a pixel-pair un-changed and alters pm LSBs to indicate the virtual modicationson m-dimensional pseudo-random vectors for carrying the secretdata. Compared with the LSB replacement, the proposed methoduses pm LSBs to theoretically carry log2(pm 1)/2 secret bits, whichis slightly less than the number of secret bits embedded in the LSB

n Computing 26 (2008) 16701676 1673applying Eq. (6) to the vector (7,14,9)10, we can extract thesecret digit (s = 6).

4. Experimental results

For evaluating the embedding capacity as well as visual stego-image quality, we implemented the most common LSB replace-Case 6: If the modication we have to do is g3 1, it means thatthe three bits in VMA is (110)2.

Case 7: If we do no modication on the vector of coordinates(7,13,9)10, it means that the three bits in VMA can beeither (000)2 or (001)2.

3.3. Data extraction

The same as the embedding procedure, the extractingprocedure has to segment a given pair of stego-pixels intotwo parts: the vector coordinate area (VCA) composed of(16 pm) bits, and the vector modication area (VMA) com-posed of pm bits.

Use the (16 pm) bits in VCA as a seed of a predetermined ran-dom function fr to generate a vector of coordinates denoted asg01; g02; . . . ; g0m, where g0i can be any positive integer, for i = 1,2, . . . ,m and m 2pm1 1. Apply the following extraction functionas shown in Eq. (6) to the vector of coordinates g01; g02; . . . ; g0m so asto extract the embedded secret digit s in the (2m + 1)-ary nota-tional system.

s f g01; g02; . . . ; g0m g01 1 g02 2 . . . g0m m mod 2m 1: 6

Example 3.5. For a given pair of stego-pixels which is(126,101)10 = (01111110, 01100101)2, pm = 3, m = 3, and thevector of coordinates g01; g02; g03 (7,13,9)10, which is theoutcome of a predetermined random function fr by using thebinary stream (011111 0110010)2 as the input argument of fr.For the three bits, i.e., (10 1)2, of VMA which obviously comesfrom the given pair of stego-pixels, the most two signicantbits, i.e., (10)2, indicate that g02 6 g2, and g0i gi for i = 1, 3.Similarly, since the last signicant bit of VMA is (1)2, it indicatesthat g02 g2 1.The outcome means that the vector of coordi-nates has been changed from (7,13,9)10 to (7,14,9)10. Aftercoordinates (7,13,9)10. The seven cases are described in detail asfollows.

Case 1: If the modication we have to do is g1 + 1, it means thatthe three bits in VMA is (011)2.

Case 2: If the modication we have to do is g1 1, it means thatthe three bits in VMA is (010)2.

Case 3: If the modication we have to do is g2 + 1, it means thatthe three bits in VMA is (101)2.

Case 4: If the modication we have to do is g2 1, it means thatthe three bits in VMA is (100)2.

Case 5: If the modication we have to do is g3 + 1, it means thatthe three bits in VMA is (111)2.of sign indicator is 0, then the ith g value should be decreased byone; otherwise, the value gi should be increased by one.

Example 3.4. Let us continue Example 3.3 with pm = 3, m = 3.There are (2*3 + 1) cases for physically modifying the three bits of

C.-F. Lee et al. / Image and Visioment, Zhan andWangs method and the proposed method by usingC language on the Intel Core 2 Duo 5600 CPU computer with 1GBRAM.replacement. Given a cover pixel-pair, Table 2 compares theembedding capacity for exploiting two and three LSB planes,respectively, to carry the number of secret bits per cover pixel.The last row of Table 2 shows the average secret bits that are ex-actly embedded into a cover pixel.

Peak signal-to-noise rate (denoted as PSNR) is a common mea-surement for evaluating the performance of embedding methods.In the experiment, we use PSNR value as a criterion to estimatethe stego-image quality. We test the proposed algorithm andZhang and Wangs method on various grayscale images namedLena, Baboon, Tiffany, F16, Pepper, Goldhill, Boat,Babara, and Zelda. These test images have the same size, thatis 512 512.

The EMD embedding method has the maximum embeddingrate about 1.16 bits per pixel, meaning that R = (log5)/2 bits/pixel,and the average PSNR value of stego-images is about 51 dB with262,144 embedded bits. At the embedding rate R = (log15)/2 withthe embedding capacity of 441,913463,528 bits, we present thePSNR values of our proposed method for these nine stego-imagesin Fig. 3. The average PSNR value is about 44.3 dB. Asm 2pm1 1, m is determined by the value of pm. When the

Table 1The embedding rate (bpp) comparison between the EMD and the proposed methods

The number of cover pixelsfor carrying one secret digit

2 3 4

EMD embedding log2(5)/2 log2(7)/3 log2(9)4Proposed method with 2LSBs log2(15)/2 log2(63)/3 log2(255)/4Proposed method with 3LSBs log2(63)/2 log2(511)/3 log2(4095)/4

Table 2Given a cover pixel-pair, the embedding secret bits per cover pixel (bpp) forexploiting two and three LSB planes, respectively

The number of LSB planes usedto carry secret bits

2 LSB planes 3 LSB planes

LSB replacement 2 3Proposed method (theoretical

results)log2(15)/2 = 1.953 log2(63)/2 = 2.9886

Proposed method (the averagesecret bits actually

1.733 2.746embedded in a cover pixelaccording to the experimentalresults)

Fig. 3. Results of stego-images with R = (log15)/2.

0

10

20

30

40

50

60

Lena

Babo

onTif

finy

F16

Pepp

er

Goldh

ill

Barba

raBo

atZe

lda

Zheng et.alR=(log5)/2

Proposed SchemeR=(log15)/2

Proposed SchemeR=(log31)/2

Fig. 4. The PSNR values of proposed methods and Zhang et al.s method by embedding secret data with 262,144 bits and full embedding.

1674 C.-F. Lee et al. / Image and Vision Computing 26 (2008) 16701676

embedding rate R is (log15)/2, the PSNR value of stego-image isabout 44.3 dB in average; when the embedding rate R is raised to(log31)/2, the PSNR value will reduce to the average of 38 dB(Fig. 4). Although the PSNR values of stego-image are lower thanthose of the EMD embedding method, our proposed method hashigher embedding rate and more embedded bits as well. In otherwords, our proposed method can tune down the pm value to im-prove the embedding rate. In the proposed method, a trade-off be-tween the embedding capacity and the stego-image quality may berealized by adjusting the pm value.

The difference image histograms for the detection of LSBreplacement and proposed methods are shown in Fig. 5. Fig. 5(a)is the image histogram for the original Lena image of size512 512. Fig. 5(b) and (c) represent the stego-image histogramsproduced using the LSB replacement and the proposed methodsby exploiting two LSB planes to carry secret data. Similarly, Fig.5(d) and (e) represent the stego-image histograms produced usingthe LSB replacement and the proposed methods by exploiting threeLSB planes to carry secret messages. In terms of the statistical anal-ysis, Fig. 5(b) through (e) illustrate the comparable behaviors for

C.-F. Lee et al. / Image and Vision Computing 26 (2008) 16701676 1675Fig. 5. The difference image histograms for the detection of LSB replacement and proposed methods.

both the LSB replacement and the proposed methods; their stego-image histograms are different from the original one and can benoticeable when the data hiding are performed on three LSBplanes. However, the LSB replacement is less secure, because it iseasy to sequentially collect secret message in terms of pm LSB bits,thereby easily leaving recognizable ngerprints. In contrast, theproposed method uses a random generator fr to project an m-dimensional pseudo-random vector onto a virtual hyperspacerstly and then deals with the virtual modications to hide secretmessages by exploiting the EMD embedding. The random genera-tor fr as well as the value of m act as secure keys. Without knowingthe keys, the attacker has no awareness of the secret message.Therefore, the proposed method can achieve some degree ofsecurity.

5. Conclusions

The embedding capacity and the quality of stego-image are twoimportant issues for data hiding methods. Our proposed methodhas the embedding rate R = (log2(2m + 1))/2 which is greater thanthat R = (log2 (2n + 1))/n of the EMD embedding method proposedby Zhang et al., when m > 2 and n=_2. The experimental resultsshow that the proposed method is able to embed more information

than the EMD embedding method can do and still keeps good ste-go-image quality at an acceptable level.

References

[1] Hide and Seek. Available from: .[2] S. Katzenbeisser, F.A.P. Petitcolas, Information Hiding Techniques for

Steganography and Digital Watermarking, Artech House, Boston, 2000.[3] H. Wang, S. Wang, Cyber warfare: steganography vs. steganalysis,

Communications of the ACM 47 (10) (2004) 7682.[4] S. Dumitrescu, X. Wu, Z. Wang, Detection of LSB steganography via sample pair

analysis, IEEE Transactions on Signal Processing 51 (7) (2003) 19952007.[5] A. Ker, Improved detection of LSB steganography in grayscale images, in: J.

Fridrich (Ed.), Proceedings of the Sixth International Workshop on InformationHiding, vol. 3200, Springer, Toronto, Canada, May 2004, pp. 97115.

[6] A. Ker, Quantitative evaluation of pairs and RS steganalysis, in: Edward J. DelpIII, Ping W. Wong (Eds.), Proceedings of SPIE Security, Steganography, andWatermarking of Multimedia Contents VI, SPIE, vol. 5306, California, USA,January 2004, pp. 8397.

[7] J. Mielikainen, LSB matching revisited, IEEE Signal Processing Letters 13 (5)(2006) 285287.

[8] C.C. Thien, J.C. Lin, A simple and high-hiding capacity method for hiding digit-by-digit data in images based on modulus function, Pattern Recognition 36(12) (2003) 28752881.

[9] X. Zhang, S. Wang, Efcient steganographic embedding by exploitingmodication direction, IEEE Communications Letters 10 (113) (2006) 781783.

[10] C.K. Chan, L.M. Cheng, Hiding data in images by simple LSB substitution,Pattern Recognition 37 (3) (2004) 469474.

[11] T. Zhang, X. Ping, A new approach to reliable detection of LSB steganography innatural images, Signal Processing 83 (10) (2003) 20852093.

1676 C.-F. Lee et al. / Image and Vision Computing 26 (2008) 16701676

An improvement of EMD embedding method for large payloads by pixel segmentation strategyIntroductionThe EMD embedding methodOur proposed methodPixel-pair segmentationEmbedding procedureData extraction

Experimental resultsConclusionsReferences