Distortion Function Designing for JPEG Steganography with Uncompressed Side-image

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1 Dstorton Functon Desgnng for JPEG Steganography wth Uncompressed Sde-mage Fangjun Huang School of Informaton Scence and Technology, Sun Yat-Sen Unversty, GD 56, Chna Jwu Huang School of Informaton Scence and Technology, Sun Yat-Sen Unversty, GD 56, Chna Weq Luo School of Software, Sun Yat-Sen Unversty, GD 56, Chna Yun-Qng Sh Department of Electrcal and Computer Engneerng, New Jersey Insttute of Technology, NJ 72, USA ABSTRACT In ths paper, we present a new framework for desgnng dstorton functons of jont photographc experts group (JPEG) steganography wth uncompressed sde-mage. In our framework, the dscrete cosne transform (DCT) coeffcents, ncludng all drect current (DC) coeffcents and alternatng current (AC) coeffcents, are dvded nto two groups: frst-prorty group (FPG) and second-prorty group (SPG). Dfferent strateges are establshed to assocate the dstorton values to the coeffcents n FPG and SPG, respectvely. In ths paper, three scenaros for dvdng the coeffcents nto FPG and SPG are exemplfed, whch can be utlzed to form a seres of new dstorton functons. Expermental results demonstrate that whle applyng these generated dstorton functons to JPEG steganography, the ntrnsc statstcal characterstcs of the carrer mage wll be preserved better than the pror-art, and consequently the securty performance of the correspondng JPEG steganography can be mproved sgnfcantly. Categores and Subject Descrptors I.4 [Image Processng and computer vson] Keywords JPEG, steganography, steganalyzer, dstorton functon. INTRODUCTION The key concept behnd the securty of steganographc systems s the statstcal un-detectablty. It may be nfluenced by many factors [], such as the choce of cover object, the type of modfcaton operaton on cover elements, the number of embeddng changes (related to the payload), and the dstorton functons used to dentfy ndvdual elements of cover that could be modfed durng embeddng. Assume that the frst three factors mentoned above are the same, desgnng the dstorton functon wll be an mportant approach to mnmzng the mpact caused by embeddng, and thus mprove the securty performance of steganography. Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. IH&MMSec 3, June 7 9, 23, Montpeller, France. Copyrght ACM /3/6...$5.. To mnmze the mpact caused by data embeddng, the sender should choose to modfy those elements (pxels/coeffcents) n such a way that the caused detectable dstorton s as small as possble. Embeddng the secret message bts under the gudance of mnmzng dstorton functon can mprove the securty performance of steganography and has been known for a long tme. In [2], Frdrch et al. presented the perturbed quantzaton (PQ) steganography. As a specfc case, they ponted out that the sender can constran the embeddng changes to those DCT coeffcents that experence the largest quantzaton error,.e., the coeffcents wth the quantzaton error of ± ( s a small postve number). Such knd of coeffcents, when rounded to the other value, may leave the smallest embeddng dstorton. In [3], another two adaptve versons of PQ,.e., texture-adaptve PQ (PQt) and energy-adaptve PQ (PQe) have been presented. Through consderng the local block content such as texture complexty and energy capacty, JPEG steganography wth hgher securty performance can be obtaned. In [4-6], the authors have combned quantzaton step wth quantzaton error n ther dstorton functon to mprove the securty performance of JPEG steganography. Besdes the quantzaton step, Wang and N [7] presented a new JPEG dstorton functon wth consderaton of the block entropy, and the expermental results demonstrate that ths new dstorton functon may lead to less detectablty of steganalyzers. Recently, Huang et al. [8] presented another dstorton functon for JPEG steganography, whch s called new PQ (NPQ). Three factors are consdered,.e., the quantzaton error, the quantzaton step and the magntude of quantzed DCT coeffcents to be modfed. Va nonlnearly combnng these three dfferent factors, the new dstorton functon, NPQ, can mprove the securty performance of JPEG steganography sgnfcantly as demonstrated n [8]. All the aforementoned dstorton functons are employed to fnd the DCT coeffcents that may result n less detectable dstorton after modfcaton. Generally, they are appled together wth the utlzaton of matrx encodng (embeddng) technology [9, ]. For example, n [2] Frdrch et al. have exemplfed how to mplement PQ dstorton functon n JPEG steganography wth the help of Wet paper codes [, 2]. In [3], Km et al. provded a smple and practcal scheme to apply PQ dstorton functon wth matrx encodng, whch s based on modfed bnary Hammng codes [4]. Ths new matrx encodng strategy allows more than one embeddng change n each coeffcent block. Va a bruteforce search, the modfcatons are made on those coeffcents that may ntroduce mnmal detectable dstorton, and thus mprovng 69

2 the securty performance of the correspondng JPEG steganography. Accordng to the number of allowable changng bts n each coeffcent block, these modfed matrx encodng (MME) schemes are called MME2, MME3, etc. Smlar approach can also be made based on BCH (Bose, Chaudhur and Hocquenghem) codes [4] to mprove the embeddng effcency of matrx encodng as descrbed n [4, 6, 5, 6]. However, snce the decodng of BCH codes s much more complcated than Hammng codes, some specfc technques need to be adopted by the sender to reduce the tme complexty and storage complexty n the embeddng process. In [5], Fller et al. provded the syndrome-trells codes (STCs), whch can be utlzed for embeddng whle mnmzng an arbtrary addtve dstorton functon wth a performance near the theoretcal bound. Ths new methodology can drectly mprove the securty performance of many exstng steganographc schemes, allowng them to communcate larger payloads at the same embeddng dstorton or to decrease the dstorton for a gven payload. In ths paper, we present a new framework for desgnng dstorton functons wth uncompressed sde-mage, whch can be appled to JPEG steganography usng any of the above mentoned matrx encodng strateges. In our framework, the DCT coeffcents, ncludng the drect current (DC) coeffcents and all the alternatng current (AC) coeffcents of JPEG mage are dvded nto two groups: frst-prorty group (FPG) and secondprorty group (SPG). Dfferent strateges wll be establshed to assocate the dstorton values to the coeffcents n FPG and SPG, respectvely. Generally, the coeffcents that may result n less detectable dstorton n the embeddng process are grouped nto FPG and the rest are nto SPG. Note that n our framework, all DCT coeffcents are utlzed for matrx encodng, and we beleve that any DCT coeffcent can be modfed n the embeddng process. In an extreme case, we can change any sngle coeffcent n a gven JPEG mage and the ntroduced dstorton wll not be perceved by today s most powerful JPEG steganalyzers. Thus n our framework, no coeffcent s consdered as un-changeable, and any DCT coeffcent can be modfed f needed n the embeddng process. That s also the man dfference between the dstorton functons generated from our framework and those prevously presented n the lterature. In ths paper, three dfferent scenaros for dvdng the coeffcents nto FPG and SPG are exemplfed, whch can be utlzed to form a seres of new dstorton functons. Va applyng these generated dstorton functons n JPEG steganography wth matrx encodng, the modfcatons wll manly be made on those coeffcents that may result n less detectable dstorton n the embeddng process. Thus JPEG steganography wth hgher securty performance can be obtaned. The rest of ths paper s organzed as follows. In Secton II, the proposed new framework s ntroduced. Expermental results and analyss are llustrated n Secton III, and the concluson s drawn n Secton IV. 2. PROPOSED FRAMEWORK Suppose the raw, uncompressed sde-mage s avalable to the sender. The DCT coeffcents that have been dvded by quantzaton steps and not yet rounded are called un-rounded DCT coeffcents, and those that have been dvded by the quantzaton steps and rounded are called quantzed DCT coeffcents, respectvely. To facltate the explanaton, the exstng dstorton functons such as PQ [2] and are referred to as ordnary dstorton functons, and those to be proposed below n ths paper are referred to as advanced dstorton functons. To make ths paper self-contaned, we wll ntroduce the PQ and NPQ dstorton functons frstly. 2. PQ and NPQ Wthout loss of generalty, the quantzed coeffcents and unrounded DCT coeffcents utlzed for data hdng are represented by C = c, c,, c ) and C = ( c', c',, c' ), ( 2 N ' 2 N respectvely, where N represents the number of DCT coeffcents n the quantzed and un-rounded coeffcent sequence. The relatonshp between c ( N) and c' ( N) s as follows. c = round( c' ) () where round(x) s a functon that rounds the element x to the nearest nteger. Note that n Equaton (), c represents the quantzed DCT coeffcent that s obtaned n JPEG compresson wthout secret message embeddng. Suppose that whle embeddng the secret message the modfcaton needs to be made on c, and the coeffcent after beng modfed s represented by s. The PQ dstorton functon s represented as follows. d PQ c = c c' s c' (2) where x s a functon that returns the absolute value of the correspondng element x. For any coeffcent c, the PQ dstorton PQ value d c can be computed accordng to Equaton (2). As ponted out n [2, 3], whle embeddng the secret message bts, the sender should select those coeffcents wth mnmal PQ dstorton values for modfcaton. NPQ can be regarded as an mproved verson of PQ consderng the quantzaton step and the magntude of the quantzed DCT coeffcents to be modfed. Suppose the quantzaton step assocated wth the coeffcent c s q. Accordng to [8], the NPQ dstorton functon s represented as follows. d NPQ PQ λ λ2 c = dc ( q ) ( μ+ c ) (3) where λ and λ 2 are two parameters that are used to control the q and c, respectvely. As recommended mpacts caused by n [8], the two control parameters λ and λ 2 can be selected n the rage of (, ]. The parameter μ s utlzed to avod the zero dvsors n Equaton (3). When NPQ s only utlzed to compute the dstorton value correspondng to the non-zero DCT coeffcents, μ s selected as. Otherwse, the parameter μ can be selected as a small number, e.g., the number of. For any NPQ coeffcent c, the NPQ dstorton value d c can be computed accordng to Equaton (3). As ponted out n [8], whle embeddng the secret message bts, the sender can select those coeffcents 7

3 wth mnmal NPQ dstorton values for modfcaton to obtan JPEG steganography wth hgh securty performance. 2.2 The Proposed Dstorton functon As mentoned above, n our new framework the DCT coeffcents are dvded nto two groups: FPG and SPG. The coeffcents n FPG and SPG are assocated wth dstorton values calculated va usng dfferent strateges. Frstly, the mpact caused by the modfcatons of coeffcents n FPG and SPG are measured usng some ordnary dstorton functons. Secondly, those obtaned dstorton values assocated wth the coeffcents n SPG are multpled by a penalty factor, whch s a bg value. Thus the dstorton values assocated wth the coeffcents n FPG may be much less than that n SPG n general n our advanced dstorton functon. When conductng matrx encodng wth some syndrome codes as n [4-8, 3, 6], several alternatve solutons may be produced and those coeffcents n FPG that may result n less dstorton n the embeddng process wll take precedence for modfcaton. Even f all the alternatve solutons are restrcted to those coeffcents n SPG, the coeffcents n SPG assocated wth smaller ordnary dstorton values wll stll take precedence for modfcaton. That s, the advanced dstorton functons generated from our framework can orentate us to make as less dstorton as possble n embeddng the secret message bts, and thus the securty performance of JPEG steganography wll be mproved. The proposed advanced dstorton functon s defned n Equaton (4). d ADV = d ORD ( + ρ) (4) c In Equaton (4), the c d represents the mpact caused by ORD c modfcaton operaton on coeffcent c, whch s computed accordng to the ordnary (abbrevated as ORD ) dstorton functons such as PQ, NPQ and some others. The penalty factor ρ s selected as a bg value (e.g., 6 ) f the coeffcent c SPG, otherwse t s selected as. Accordng to Equaton (4), for any coeffcent c n the nput mage, the advanced (abbrevated as ADV ) dstorton value d ADV can be easly computed. Va applyng the advanced dstorton functons generated from our framework to JPEG steganography, no specal processng needs to be made on those DCT coeffcents wth the values of + and - as that n [7, 8, 3]. Note that n [7, 8, 3], the dstorton functons have only been appled on the non-zero AC DCT coeffcents. If the coeffcent wth value of + or - s flpped to, the recpent wll not be able to accurately locate the correspondng non-zero coeffcents utlzed for matrx encodng n the transmttng end, and the embedded secret message bts may not be extracted successfully. Thus specal modfcaton operaton should be made by the sender on those coeffcents wth the quantzed values of + and -. For example, n [7, 8, 3] the coeffcents wth the quantzed values of + and - can only be flpped to +2 and -2, respectvely. Snce the dstorton functons generated from framework are appled on all the DCT coeffcents,.e., all the DCT coeffcents are utlzed for matrx encodng, no such specal modfcaton operaton needs to be made whle c applyng our advanced dstorton functons to JPEG steganography. For any coeffcent c ( N) to be modfed, the operaton s conducted as follows. c +, = c, f ( c f ( c c' ) s (5) c' ) > where s s the coeffcent after havng been modfed. Furthermore, snce all the DCT coeffcents (ncludng DC coeffcents and numerous zero AC coeffcents besdes the nonzero AC coeffcents) are ncluded n our framework whle applyng those advanced dstorton functons to JPEG steganography, the embeddng effcency (the number of bts embedded per embeddng change [7]) of matrx encodng wll be mproved sgnfcantly. For example, f we select MME2 embeddng strategy for matrx encodng, wth the usage of k [ 2 -, k] ( k ) modfed bnary Hammng codes, k secret message bts can be embedded nto 2 k - quantzed DCT coeffcents by changng at most two of them. That s, the larger the k, more effcently the matrx encodng wll be accomplshed. Accordng to [8, 9, 3], the parameter k of Hammng codes s determned by the number of secret message bts (represented by n) and the number of DCT coeffcents (represented by N) utlzed for matrx encodng. In general we wll select the mum k that qualfes the nequalty k 2 - k > n N. It s obvously that wth embeddng the same number of secret message bts, the algorthms utlzng more DCT coeffcents for data hdng wll result n a more effcent matrx encodng. Note that n order to exchange the secret message bts successfully, both the sender and recpent should utlze the same coeffcents to accomplsh the matrx encodng. For example, n [7, 8, 3], the recpent needs to accurately locate the non-zero AC DCT that have been used n the embeddng process to conduct the matrx encodng, otherwse the secret message bts cannot be extracted accurately. A specal note of nterest s that whle applyng those advanced dstorton functons generated from our framework to JPEG steganography, the sender should frst dvde all the DCT coeffcents nto FPG and SPG. However, the sender does not need to share the dvdng scenaro wth the recpent, snce they (.e., the sender and recpent) both use all the DCT coeffcents to conduct matrx encodng. The recpent does not need to locate the DCT coeffcents n FPG or SFG n the recevng end, and he/she can exchange the secret message wth the sender easly va selectng the same matrx encodng strategy. 2.3 Three Dfferent Scenaros for Dvdng FPG and SPG The statstcs of DCT coeffcents are complcated and they may nteract wth each other whle beng modfed. Moreover the statstcs of DCT coeffcents may also have a close relatonshp wth the secret message bts to be embedded, and the type of embeddng operaton that modfes the coeffcents, etc. It s not easy to derve an optmal strategy for dvdng the coeffcents nto FPG and SPG. However, a seres of suboptmal scenaros can be found easly. 7

4 In the followng, three scenaros for dvdng the coeffcents nto FPG and SPG are exemplfed. Scenaro s a smple and drect way. Its separaton performance may not be as good as the followng two scenaros. However, our experments n next secton wll demonstrate that wth approprate selecton of the ordnary dstorton functon, hgh secure performance can stll be obtaned. The fundamental dea of the next two scenaros s that n the texture area of a carrer mage more coeffcents wll be dvded nto FPG, and n the flat area fewer coeffcents wll be dvded nto FPG. In Scenaro 2, the frst-prorty and secondprorty coeffcents are classfed accordng to the statstcs of coeffcents n DCT doman. In Scenaro 3, the coeffcents are dvded nto FPG and SPG wth resortng to the statstcs of JPEG mage n spatal doman. Scenaro : The AC DCT coeffcents are consdered as frstprorty coeffcents, and the DC DCT coeffcents are classfed as the second-prorty coeffcents. Scenaro 2: Compute the standard devaton ( N) of the quantzed AC DCT coeffcents n each 8 D 8 block of JPEG mage, where N represents the total number of 8 8 blocks n JPEG mage. The average value of all the standard devatons s D = N N D =, and the mum value among all the standard devatons s D = ( D, D2,, DN ). In each block, the number of AC DCT coeffcents that belongs to FPG s computed as follows., 64 ( D / D), A = 2 64 ( + D / D 2 63, ), f D f 32 < 32 D D f D D f D = D < D D < D where A ( N) represents the number of AC DCT coeffcents that should be dvded n FPG n each 8 8 block, and x s a functon that rounds the element x to ts nearest nteger less than or equal to x. In Equaton (6), the number 64 represents that there are 64 DCT coeffcents n each 8 8 block. As we ponted above, any DCT coeffcent can be modfed, and we can change any sngle coeffcent n a gven JPEG mage n the embeddng process. Other methods for dvdng the coeffcents nto FPG and SPG may stll work, e.g., we can change the number 32 to 3 or 3 n Equaton (6), and the obtaned dstorton functon may stll result n JPEG steganography wth hgh securty performance. Here, we only try to llustrate the applcablty of our framework and do not try to make a clear boundary between FPG and SPG. Scenaro 3: Compute the standard devaton ( N) of pxel values n each 8 8 block of the decompressed JPEG mage, P (6) where N represents the total number of 8 8 blocks n JPEG mage. The average value of all the standard devatons N s P = P, and the mum value among all the standard N = devatons s P = ( P, P2,, PN ). In each block, the number of AC DCT coeffcents that belongs to FPG s computed as follows., f P < P ( P / P), f P P < P (7) B = ( + P / P ), f P P < P 2 63, f P = P where B ( N) represents the number of AC DCT coeffcents that should be dvded n FPG n each 8 8 block. As seen, the phlosophy for choosng the frst-prorty coeffcents n Equaton (7) s smlar to that n Equaton (6). Dfferently, n Scenaro 3 the DCT coeffcents are dvded nto FPG and SPG accordng to the statstcal characterstcs of JPEG mage n spatal doman. Snce decompressng the JPEG mage s a nonlnear process (ncludng de-quantzaton and roundng process [8]), the selected frst-prorty coeffcents n Scenaro 3 wll be dfferent from that n Scenaro 2. In Scenaro 3, the B ( N) frst-prorty coeffcents n each block are also selected accordng to the zg-zag scannng order, and the rest AC and DC coeffcents are consdered as second-prorty coeffcents. In ths secton, we have ntroduced two ordnary dstorton functons and exemplfed three dfferent dvdng scenaros. Accordng to Equaton (4), sx dfferent advanced dstorton functons can be generated va combnng those dfferent ordnary dstorton functons and dvdng scenaros. Note that the framework proposed n ths paper s an open system. Frstly, PQ, NPQ and any other ordnary dstorton functon can be used on our framework. For nstance, n Equaton (4) the superscrpt ORD stands for the ordnary dstorton functon. Secondly, more advanced scenaros for splttng the DCT coeffcents nto FPG and SPG can also be used n our framework. For example, f the more advanced scenaro s found, the FPG and SPG n Equaton (4) may be updated accordngly. 3. EXPERIMENTAL RESULTS In ths secton, expermental results and analyss are presented to demonstrate the effcency of our proposed framework. The test mage set conssts of uncompressed mages whch are downloaded from the BOSSBase mage dataset [9]. All the mages are wth the sze of In the followng, the uncompressed mage s called nput mage and the JPEG compressed mage wthout any message embeddng s called cover mage. The cover and stego mages are created usng the same JPEG encoder [2], and the qualty factor s selected as 75 n all of our testng. The secret message bts are randomly 72

5 generated, and the embeddng rates are represented n terms of (bts per non-zero quantzed AC DCT coeffcents) values. The effcency of our proposed dstorton functons s tested wth three state-of-the-art feature-based steganalyzers, whch are called CC-PEV (Cartesan-calbrated Pevný) [2], SPAM (subtractve pxel adjacency matrx) [22] and CDF (cross doman feature) [23], respectvely. The 548-dmensonal CC-PEV feature vector s manly extracted from JPEG doman, whch s extended to twce ts sze by Cartesan calbraton from the 274 feature vector desgned for JPEG mages [24]. The 686-dmensonal SPAM feature vector s extracted from spatal doman, whch s the second-order Markov model of pxel dfferences. Through combng the CC-PEV and SPAM feature vector, we can get the,234-dmensonal CDF feature vector. Those feature vectors or ther mproved versons are popularly utlzed [25-28] n detectng the classcal algorthms such as F5 [5] and MB [29], and some modern steganographc schemes [3-33]. Snce the CDF feature vector s extracted n cross doman, t may have better detecton performance than CC-PEV and SPAM n general. The ensemble classfer presented n [34] s employed n our testng wth default parameters. It s a fully automatc framework wth an effcent utlzaton of out-of-bag (OOB) error estmates for stoppng crteron. As ponted out n [25], the proposed ensemble classfer conssts of a lot of base learners ndependently traned on a set of cover and stego mages. The decson threshold of each base learner s adjusted to mnmze the total detecton error under equal prors on the tranng set: P E = mn ( PFA + PMD( PFA)) (8) PFA 2 where P FA, P MD are the probabltes of false alarms and mssed detecton, respectvely. Matrx Embeddng: MME2; Steganalyzer: SPAM-686 Matrx Embeddng: MME2; Steganalyzer: CC-PEV PQ [] SN+PQ SN+NPQ. SN2+PQ.5 SN3+PQ.5..2 (a) Matrx Embeddng: MME3; Steganalyzer: CC-PEV PQ [] SN+PQ SN+NPQ. SN2+PQ.5 SN3+PQ.5..2 (b) Fg. The detecton error rates wth the steganalyzer CC-PEV-548. (a) MME2 embeddng strategy. (b) MME3 embeddng strategy..2 PQ [] SN+PQ SN+NPQ. SN2+PQ.5 SN3+PQ.5..2 (a) Matrx Embeddng: MME3; Steganalyzer: SPAM-686 PQ [].2 SN+PQ SN+NPQ SN2+PQ. SN3+PQ (b) Fg. 2 The detecton error rates wth the steganalyzer SPAM-686. (a) MME2 embeddng strategy. (b) MME3 embeddng strategy. Frstly, we have appled the advanced dstorton functons to JPEG steganography wth MME2 and MME3 embeddng strateges for a detal comparson. The PQ and NPQ are selected as the ordnary dstorton functons for a demonstraton. In Secton 2.3, we have exemplfed three scenaros for dvdng the DCT coeffcents nto FPG and SPG. The algorthms resulted 73

6 from dfferent dvdng scenaros (abbrevated as SN ) and ordnary dstorton functons are represented as SN+PQ, SN+NPQ, SN2+PQ, SN3+PQ,, respectvely. The orgnal PQ and NPQ dstorton functons are appled wth MME2 and MME3 embeddng strateges as n [8, 3]. Totally there are sxteen dfferent steganographc schemes. Half of them are conducted wth MME2 embeddng strategy, and the other half are conducted wth MME3 embeddng strategy. Note that n all our testng, the two control parameters of NPQ are selected as λ =, λ.2). ( 2 = The detecton error rates (ERs) correspondng to the three steganalyzers CC-PEV, SPAM, and CDF are llustrated n Fgs., 2 and 3, respectvely. In these three fgures, the horzontal axes represent the values, and the vertcal axes represent the detecton error rates. For the aforementoned sxteen steganographc schemes, the embeddng rates are ncreased from.5 to wth the step sze of.5. The embeddng strategy and the steganalyzer wth the dmenson sze of feature vector are llustrated n the ttle of each fgure Matrx Embeddng: MME2; Steganalyzer: CDF-234 PQ [] SN+PQ SN+NPQ SN2+PQ SN3+PQ (a) Matrx Embeddng: MME3; Steganalyzer: CDF-234 PQ [] SN+PQ SN+NPQ SN2+PQ SN3+PQ.5..2 (b) Fg. 3 The detecton error rates wth the steganalyzer CDF-234. (a) MME2 embeddng strategy. (b) MME3 embeddng strategy. It s observed from Fgs., 2 and 3 that whchever dvdng scenaro or ordnary dstorton functon s selected, the securty performance of the obtaned JPEG steganography may be greatly mproved under the gudance of those dstorton functons generated from our framework. Our expermental results also demonstrate that the selecton of dvdng scenaros and ordnary dstorton functons may have great mportance n our framework. Dfferent dvdng scenaros and ordnary dstorton functons may result n JPEG steganography wth dfferent securty performance. As seen, wth usng the same ordnary dstorton functon, JPEG steganography resulted from Scenaro 2 and Scenaro 3 may have hgher securty performance than that from Scenaro. Wth adoptng the same dvdng scenaro, PQ and NPQ may result n JPEG steganography wth dfferent securty performance too. Fortunately, va usng our proposed framework, the dfferent dvdng scenaros and ordnary dstorton functons can easly be combned to form effcent advanced dstorton functons, even though the dvdng scenaros and ordnary dstorton functons are not optmal. Secondly, n order to demonstrate the unversalty of our proposed framework, we have appled those generated dstorton functons to JPEG steganography wth STC. The Wang and N s method [7] has also been conducted for a comparson, whch s one of the most secure JPEG steganographc schemes wth usng STC. The steganalyzer CDF s selected for testng, and the expermental results are shown n Fg. 4. The horzontal axes represent the values, the vertcal axes represent the detecton error rates, and the dstorton functons are shown on the legend. As seen, when the embeddng rate s no more than, all the steganographc schemes resulted from our proposed and Wang and N s method have the smlar securty performance, and the obtaned detecton accuracy rates are near random guessng. However, wth the ncreasng of embeddng rate, the JPEG steganographc schemes resulted from our proposed dstorton functon may have much better securty performance than that resulted from Wang and N s method. Va comparng Fg. 4 and Fg. 3, we can also fnd out that va usng more effcent embeddng strategy, the securty performance of JPEG steganography resulted from our advanced dstorton functon can be mproved further..2 Embeddng Codes: STC; Steganalyzer: CDF-234 SN+NPQ Wang&N[7] Fg. 4 The effcency of our proposed framework wth usng STC. 74

7 4. CONCLUSIONS In ths paper, we have presented a new framework for desgnng dstorton functons of JPEG steganography wth uncompressed sde-mage, and a seres of advanced dstorton functons that may result n hgh secure JPEG steganography are exemplfed. Note that our proposed framework s an open system. It wll not be constraned to the aforementoned dvdng scenaros and ordnary dstorton functons. Other dvdng scenaros and ordnary dstorton functons can be adopted easly n our framework to form a seres of new dstorton functons. 5. ACKNOWLEDGEMENTS Ths work was supported by the Natonal Natural Scence Foundaton of Chna (67347, U35), the 973 Program of Chna (2CB3224), the Key Projects n the Natonal Scence & Technology Pllar Program (22BAK6B6), the Fundamental Research Funds for Central Unverstes (2lgpy3), and the Project Sponsored by the Scentfc Research Foundaton for the Returned Overseas Chnese Scholars, State Educaton Mnstry ([22]77). 6. REFERENCES [] J. Frdrch, P. Lsoněk and D. Soukal, On Steganographc embeddng effcency, n Proc. Informaton Hdng Workshop 26, LNCS 4437, pp , 27 [2] J. Frdrch, M. Goljan and D. Soukal, Perturbed quantzaton steganography wth wet paper codes, n Proc. the ACM Workshop on Multmeda & Securty, Magdeburg, Germany, September 2-2, pp. 4-5, 24. [3] J. Frdrch, T. Pevný and J. Kodovský, Statstcally undetectable JPEG steganography: dead ends, challenges, and opportuntes, n Proc. the ACM Workshop on Multmeda and Securty, Dallas, Texas, September 2-2, pp. 3-4, 27. [4] V. Sachnev, H. J. Km, and R. Zhang, Less detectable JPEG steganography method based on heurstc optmzaton and BCH syndrome codng, n Proc. the ACM Workshop on Multmeda & Securty, Prnceton, New Jersey, Sep. 7-9, pp. 3 4, 29. [5] T. Fller, J. Judas, and J. Frdrch, Mnmzng addtve dstorton n steganography usng Syndrome-Trells Codes, IEEE Transactons on Informaton Forenscs and Securty, vol. 6, no. 3, pp , 2. [6] V. Sachnev, H. J. Km, Modfed BCH data hdng scheme for JPEG steganography, Eurasp Journal on advances n sgnal processng, vol. 22, no., pp , 22 [7] C. Wang, J. N, An effcent JPEG steganographc scheme based on block-entropy of DCT coeffcents, n Proc. of IEEE ICASSP, Kyoto, Japan, Mar. 25-3, pp , 22 [8] F. Huang, J. Huang, and Y. Q. Sh, New channel selecton rule for JPEG steganography, IEEE Trans. Informaton Forenscs and Securty, vol. 7, no. 4, pp. 8-9, 22. [9] R. Crandall, Some notes on steganography, Posted on Steganography Malng Lst, westfeld/crandall.pdf [] A. Westfeld, Hgh capacty despte better steganalyss (F5-a steganographc algorthm), n Proc. Informaton Hdng, 4 th Internatonal Workshop, volume 237 of Lecture Notes n Computer Scence, pp , 2. [] J. Frdrch, M. Goljan, P. Lsoněk, and D. Soukal, Wrtng on wet paper, IEEE Trans. Sgnal Processng, vol. 53, no., pp , 25. [2] J. Frdrch, M. Goljan and D. Soukal, Wet paper codes wth mproved embeddng effcency, IEEE Trans. Informaton Forenscs and Securty, vol., no., pp. 2-, 26. [3] Y. Km, Z. Durc and D. Rchards, Modfed matrx encodng technque for mnmal dstorton steganography, n Proc. Informaton Hdng Workshop 26, LNCS 4437, pp , 27. [4] T. K. Moon, Error Correcton Codng, Mathematcal Methods and Algorthms. Hoboken, NJ: Wley, 25. [5] D. Schönfeld, A. Wnkler, Embeddng wth syndrome codng based on BCH codes, n Proc. the ACM Workshop on Multmeda & Securty, Geneva, Swtzerland, Sep , pp , 26 [6] R. Zhang, V. Sachnev, and H. J. Km, Fast BCH syndrome codng for steganography, n Proc. Informaton Hdng Workshop 29, LNCS 586, pp , 29. [7] J. Frdrch, and D. Soukal, Matrx embeddng for large payloads, IEEE Trans. Informaton Forenscs and Securty, vol., no. 3, pp , 26. [8] F. Huang, J. Huang, and Y. Q. Sh, Detectng double JPEG compresson wth the same quantzaton matrx, IEEE Trans. Informaton Forenscs and Securty, vol. 5, no. 4, pp , 2. [9] T. Fller, T. Pevny, and P. Bas. BOSS (Break Our Steganography System). July 2. [2] P. Shllee, Matlab JPEG Toolbox [Onlne]. Avalable: [2] J. Kodovský and J. Frdrch, Calbraton revsted, n Proc. the ACM Multmeda & Securty Workshop, Prnceton, New Jersey, Sep. 7-9, pp , 29. [22] T. Pevný, P. Bas, ad J. Frdrch, Steganalyss by subtractve pxel adjacency matrx, IEEE Trans. Informaton Forenscs and Securty, vol. 52, no. 2, pp , 2 [23] J. Kodovský, T. Pevný, and J. Frdrch, Modern steganalyss can detect YASS, n Proc. SPIE, Electronc Imagng, Securty Forenscs of Multmeda XII, San Jose, Calforna, Jan. 7 2, 2, vol. 754, pp [24] T. Pevný and J. Frdrch, Mergng Markov and DCT features for mult-class JPEG steganalyss, n Proc. SPIE Electronc Imagng, Securty, Steganography, and Watermarkng of Multmeda Contents Ⅸ, San Jose, Calforna, Jan Feb., 27, vol. 655, pp [25] F. Huang, J. Huang, and Y. Q. Sh, An expermental study on the securty performance of YASS, IEEE Trans. Informaton Forenscs and Securty, vol. 5, no. 3, pp , 2. [26] J. Kodovský and J. Frdrch, Steganalyss of JPEG mages usng rch models, n Proc. SPIE, Electronc Imagng, 75

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