TECHNICAL POINTS ABOUT ADAPTIVE STEGANOGRAPHY BY ORACLE (ASO) 161, rue Ada, 34095, Montpellier Cedex 05, France

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1 20th European Sgnal Processng Conference (EUSIPCO 2012) Bucharest, Romana, August 27-31, 2012 TECHNICAL POINTS ABOUT ADAPTIVE STEGANOGRAPHY BY ORACLE (ASO) Sarra Kouder 2, Marc Chaumont 1,2, Wllam Puech 2 1 Unversty of Nîmes, F Nîmes Cedex 1, France 2 LIRMM Laboratory, UMR 5506 CNRS, Unversty of Montpeller II, 161, rue Ada, 34095, Montpeller Cedex 05, France {sarra.kouder, marc.chaumont, wllam.puech}@lrmm.fr ABSTRACT ASO [1] s an adaptve embeddng scheme that has proved ts effcency compared to HUGO [2] algorthm. It s based on the use of a detectablty map that s correlated to the securty of the embeddng process. The detectablty map s calculated usng the Kodovský s ensemble classfers [3] as an oracle, whch preserves the dstrbuton of the cover mage and of the sender s database. In ths artcle, we gve the techncal ponts about ASO. We gve the detals of the detectablty map computaton, then we study the securty of the communcaton phase of ASO through the paradgm of the steganography by database. Snce the ntroduced paradgm allows the sender to choose the most secure stego mage(s) durng the transmsson of hs message, we propose some securty metrcs that can help hm to dstngush between secure and nsecure mages. We thus sgnfcantly ncrease the securty of ASO. Index Terms Steganography, Detectablty map, Ensemble classfers, Oracle, Steganography by database. 1. INTRODUCTION Steganography s the art of secret communcaton. The goal s to hde a secret message n an unsuspcous object n such a way that no one can detect t. Wth the Internet spread, several phlosophes of desgnng steganographc methods were proposed. One of the most used embeddng methods for real dgtal mages s the steganography by mnmzng of the embeddng mpact 1. Let x = (x 1,..., x n ) be a cover support composed of n elements. The goal of steganography by mnmzng the embeddng mpact s to communcate a secret message m = (m 1,..., m m ) by makng small perturbatons of cover object x to produce a stego object y = (y 1,..., y n ). For ths, we defne a dstorton functon D(x, y) that we mnmze under the constrant of a fxed payload. Ths dstorton functon s generally based on the use of a detectablty map ρ R n + 1 The prncple of mnmzng the embeddng mpact was proposed n 2007 [4]. It s based on the adaptvty of the embeddng operaton by the use of a detectablty map. whch assgns to each cover element x wth {1,..., n}, a detectablty cost ρ R + that models the mpact on the securty caused by the modfcaton of the th element. The HUGO algorthm [2] used durng the BOSS 2 competton [5] uses a detectablty map, whch attrbutes to each pxel of a cover mage a detectablty cost ρ [0, ], as suggested n [6]. The calculaton of the detectablty cost s based on the use of hgh-dmensonal features, whch are calculated from the cover mage. These features correspond to the condtonal probabltes n each pxel of the fltered mage. The MOD 3 algorthm proposed n 2011 [7], extends the HUGO proposal by defnng a parametrc detectablty cost ρ [0, ], whch s parametrzed by a hgh number of parameters. The ASO 4 embeddng algorthm that we proposed n [1], mproves the concept of the detectablty map ntroduced by HUGO. It uses a non parametrc detectablty map whereas MOD use a parametrc approach. The detectablty map ρ = {ρ [0, [} n =1 s defned by usng the functonaltes of the Kodovský s ensemble classfers [3] as an oracle. Ths preserves not only the cover mage dstrbuton, but also the dstrbuton of the sender s database. Thus, ASO ntroduces a new paradgm n steganography whch s the steganography by database that, furthermore, offers to the sender the possblty to choose the most secure mage(s) durng the transmsson phase. In ths paper, we pursue the study about the adaptve steganography by oracle [1]. We gve the techncal ponts about the embeddng algorthm (ASO), and we dscuss about the securty of the ASO s embeddng process thanks to the steganography by database paradgm. For ths, we propose some new securty measures that reflect the securty level of the stego mages. The rest of ths paper s organzed as follows. In Secton 2.1, we recall some notons about the ASO algorthm. In Sec- 2 BOSS (Break Our Steganography System) s the frst challenge on Steganalyss. The challenge started the September 9th 2010 and ended the 10th of January The goal of the player was to fgure out, whch mages contan a hdden message and whch mages do not. The steganographc algorthm was HUGO [2]. 3 MOD: Model Optmzed Dstorton. 4 ASO: Adaptve Steganography by Oracle [1]. EURASIP, ISSN

2 ton 2.2, we gve the techncal ponts about the detectablty map constructon. In Secton 2.3, we dscuss the paradgm of the steganography by database and we propose the securty metrcs. We gve expermental results n Secton 3, and we conclude n Secton 4. For the sake of smplcty, we denote by x = (x 1,..., x n ) X = {0,..., 255} n and y = (y 1,..., y n ) Y = {0,..., 255} n grayscale cover and stego mages wth n pxels. The use of any other dgtal meda s also possble. 2. ADAPTIVE STEGANOGRAPHY BY ORACLE (ASO) 2.1. General scheme ASO 5 [1] s an adaptve embeddng scheme that s based on the prncple of mnmzng embeddng mpact [4, 6]. It strves to hde a gven message m n a cover support x, whle mnmzng an ad hoc dstorton measure that s correlated to the securty of the embeddng process. The embeddng s ether smulated [4], or done by usng the STC 6 approach [6]. These embeddng algorthms requre to defne a detectablty map ρ that model the statstcal detectablty. In ASO an oracle s used to calculate a detectablty map ρ = {ρ R} n =1 that assgns a detectablty costs ρ to each pxel x : ( ρ = mn ρ (+), ρ ( ) ), (1) wth ρ (+) (resp. ρ ( ) ) the detectablty cost of changng the th pxel by +1 (resp. 1). Snce the Kodovský s FLD ensemble classfers [3] allows to splt the features space nto cover and stego regons, ASO [1] uses ths separaton as an oracle to defne the detectablty costs ρ (+) ρ (+) = where ρ (l)(+) and ρ ( ) : ρ (l)(+), and ρ ( ) =, (2) (resp. ) s the detectablty cost provded by the l th classfer, and L s the number of the FLD classfers. For each FLD classfer F l, wth l {1,..L}, that performed ts learnng on a subspace of d red dmenson, the detectablty cost ρ (l)(+) s defned as: w (l). (f ) (l)(+) (l) x x ρ (l)(+) f x =, (3) s (l) and the detectablty cost by: w (l). (f ) (l)( ) (l) x x f x =, (4) s (l) 5 For more detals about the ASO embeddng algorthm, please refer to [1], avalable on: kouder/publcatons.html. 6 STC: Syndrome Trells Codes. wth w (l) the vector orthogonal to the hyperplane separatng the two classes calculated by the classfer F l, f x (l) the feature vector that we wsh to classfy by the classfer F l, f x x (l)(+) (resp. f x x (l)( ) ) the feature vector obtaned after the modfcaton of the th pxel by +1 (resp. 1), and s (l) R + the normalzaton factor of the l th classfer F l (see [1]). By usng the functonaltes of the Kodovský s ensemble classfers [3] and the acqured knowledge of the learnng phase, ASO [1] manages to preserve not only the dstrbuton model of the current cover mage, but also the dstrbuton model of the sender s database. It thus mproves the securty of the embeddng process. ASO I II cover mage cover database Kodovský s FLD classfers «HUGO» Calculaton of the detectablty map Kodovský s FLD classfers «ASO» Calculaton of the detectablty map Process of message embeddng Process of message embeddng stego mage stego database Fg. 1. General scheme of the Adaptve Steganography by Oracle (ASO) [1]. As shown n Fgure 1, the embeddng process of ASO [1] conssts of two steps. The frst step (labeled I n Fgure 1) ams to produce a frst draft of ASO s stego mages. In ths step, the computaton of the detectablty map ρ (Eq. 1) s performed by usng the Kodovský s ensemble classfers [3] that s traned to dstngush between cover and the stego mages embedded wth HUGO [2]. The second step (labeled II n Fgure 1) s an teratve step that ams to mprove the securty of ASO. The detectablty map s calculated usng a Kodovský s ensemble classfers [3] that s traned to dstngush between the cover and the ASO s stego mages from the prevous teraton. At the end of the embeddng process, ASO allows to obtan a set of a stego mages, rather than only one stego mage Techncal ponts about detectablty map computaton The computaton of a feature vector f x R d, wth vector dmenson d d red, s CPU consumng. In our case f x s obtaned by frst applyng many hgh-pass flter and then count the m-uplets co-occurrences n the dfferent hgh-pass mages. In the ASO algorthm, the computaton of the detectablty map ρ requres to compute the values ρ (l)(+) and for each pxel x, whch nvolves the calculaton of the 1704

3 Fg. 2. Computaton of the feature varatons on a square wndow area of r = 9 wdth. The resdual 1-Dmenson flter used to compute the features has a sze (s = 3). two new feature vectors f x x (l)(+) and f x x (l)( ) resultng from the modfcaton +1 or 1 of the th pxel (see Eq. 3 and Eq. 4). Snce the vector w (l) and the normalsaton factor s (l) are calculated durng the learnng phase of the classfer, we do not need to calculate them agan durng the computaton of ρ (l)(+) and. The computatonal complexty for the constructon of the detectablty map ρ comes manly from the computaton of f x x (l)(+) and f x x (l)( ). To address ths problem, nstead of calculatng separately the feature vectors f x x (l)(+) and f x x (l)( ), we propose to only calculate, on a reduced area, the varaton (f x x (l)(+) f x (l) ) and (f x x (l)( ) f x (l) ) ntroduced by the modfcaton +1 or 1 of each pxel x. We thus defne for each pxel x a square wndow area of r wdth centred on x. Ths wndow area gves the set of pxels responsble of the changes between the vectors f x (l) and f x x (l)(+) (resp. f x x (l)( ) and f x (l) ). The pxels that are outsde of ths area do not ntroduce change between f x (l) and f x x (l)(+) (resp. f x x (l)( ) and f x (l) ). We thus do not consder those pxels durng the computaton of the feature varatons. The wdth r of the square wndow area depends on the sze s of the hgh-pass 1-Dmenson flter, and the order m of the co-occurrence matrce used to calculate the feature vectors [8]. The sze of the wndow area, on whch we calculate the varatons (f x x (l)(+) f (l) x ) and (f x x (l)( ) f (l) x ), must be large enough to cover all possble modfcatons nvolved by changng the pxel x. Knowng that changng a gven pxel x by +1 or 1 may affect (non pathologcal case) the m-uplets (x +a, x +(a+1),..., x +(a+m) ), wth a { r 2,..., r 2 m}, n all drectons, choosng r = s + 2(m 1) guarantees a vald result for the computaton of the feature varatons (f (l)(+) x x f (l) x ) and (f (l)( ) x x f (l) x ). To take an example, for a resdual 1-Dmenson flter wth s = 3 sze and m = 4 (Fgure 2), the nvolved varatons (f x x (l)(+) f x (l) ) and (f x x (l)( ) f x (l) ) are calculated on a square wndow area of wdth r = 9. Our mplementaton of ASO, for d = 5330, L = 30, d red = 250, and N = mages of , usng the parallel OpenMP lbrary on an archtecture of 8 processors Quad-Core AMD Opeteron(tm) Processor 8384, at 2.69 GHz, took less than one day and half. Knowng that on a monoprocessor, wthout the trck of the square wndow (Eq. 3 and Eq. 4), the calculaton of one feature vector f x took about 0.013s, the computaton tme of the detectablty map ρ of the mages would take 0.013s = s (more than two years) Paradgm of the steganography by database As mentoned n Secton 2.1, ASO ntroduces the new steganography by database paradgm. The embeddng process of ASO takes nto account not only the model dstrbuton of the current cover mage, but also the dstrbuton of the sender s database, thus mprovng the securty of the embeddng process. Moreover, t allows to obtan a set of stego mages nstead of just one stego mage, whch offers to the sender the opportunty to choose the most secure mage(s) durng the transmsson of hs secret message. Choosng the most relable mage(s) durng the transmsson phase can mprove the securty of ASO. In order to select the less detectable stego mage(s), we compute for each stego mage a score value that reflects ts securty level. One possble powerful method that offers ASO conssts to compute for each stego mage the number of FLD classfers that have classfed t as cover nstead of stego, from the Kodovský s ensemble classfers [3]. We thus defne the securty score as: where: S F LD f : R d {0,..., L} x Sf F LD (x), Sf F LD (x) = L F l (f x ), (5) wth F l (f x ) the decson of the classfer F l (1 for stego and 0 for cover), and f x the feature vector of the stego mage x. The hgher the score Sf F LD (x) s, the greater s the securty of the stego mage. Note that wth that measure, we obtan several stego mages wth the same score. For more fner granularty of the score value, we may use the sparsty measures that are generally used wth the One Class Neghbor Machne (OC-NM) steganalyzer [9, 10]. Let us assume that we have K cover mages from whch we compute K d-dmensonal features. By takng the set of cover mages as a tranng base, the OC-NM computes for each samples x a sparsty measure Sf oc (x) that characterzes the closeness of x to the cover mages. The OC-NM steganalyzer strves to dentfy the best threshold γ so that all samples x wth Sf oc (x) > γ are classfed as stego. Several types of sparsty measures are proposed n the orgnal publcaton on OC-NM [9]. One of the most used measure that can be adopted as a securty score, s the socalled Hlbert kernel densty estmator: Sf oc : R d R x Sf oc (x), 1705

4 where: ( ) Sf oc 1 (x) = log K k=1 1/ ( ), (6) f x f k hd 2 wth f x the feature vector of the stego mage x, f k the feature vector of the k th cover mage of the tranng set,. 2 the L 2 norm, d the feature vectors dmenson, and h a parameter of smoothness. Intutvely, snce the sparsty measures reflect the closeness of a gven mage to the covers, usng these measures as a securty score allows us to evaluate the detectablty of the used stego mage(s). The smaller s the sparsty Sf oc (x) of a gven stego mage, the greater s ts securty. 3. EXPERIMENTAL RESULTS Our experments were conducted usng the BossBase v1.00 cover database 7 contanng grayscale cover mages n the pgm format, and the same mages embedded wth ASO 8 for each payload from 0.1 bpp to 0.5 bpp. Each mage s represented by a feature vector of d = 5330 MINMAX features. The set of features comes from the 1458 dmensonal MINMAX vector wth the truncaton threshold T = 4, and the 3872 dmensonal SUM3 vector from the HOLMES features [8]. To evaluate the necessty and the mportance of the ntroduced paradgm of the steganography by database, we have bult for each payload α from 0.1 bpp to 0.5 bpp two testng databases of 500 ASO s stego mages. The base B (α) 1 conssts of 500 ASO s stego mages that have been randomly selected from the BossBase v1.00 ASO s stego mages. The base B (α) 2 s composed of the most secure 500 ASO s stego mages selected from the BossBase v1.00 ASO s stego mages usng the securty measure Sf F LD (see Eq. 5). Once calculated, for each payload, the two testng databases are then steganalyzed usng the One-Class Support Vector Machne (OC-SVM) of LIBSVM 9. The OC-SVM was traned on the BossBase v1.00 cover database usng the Gaussan kernel k(x, y) = exp( γ x y 2 ) wth γ = and ν = 0.01 whch s the desred false postve rate. The tranng data were scaled before, so that all features were n the range [ 1, +1] (the scalng parameters were derved from cover mages only). By usng the OC-SVM for the steganalyss of the two testng databases (B (α) 1 and B (α) 2 ) for each relatve payload α from 0.1 bpp to 0.5 bpp, we seek to test f the stego mages that have been selected usng the securty measure crteron 7 BossBase v1.00: A database of mages avalable on 8 The embeddng process of ASO was done usng L = 30 classfers, d = 5330, and d red = 250 [1]. 9 LIBSVM: A Lbrary for Support Vector Machnes, avalable on cjln/lbsvm/. (Eq. 5 and Eq. 6) are more secure than those selected randomly by the sender. In other words, we want to prove the mportance of choosng the most relable mage(s) durng the secret communcaton phase (.e. prove the addtonal securty feature of the steganography by database paradgm). Detecton Recall (%) Relatve payload (bpp) ASO random(b ( α ) 1 ) ASO secure(b ( α ) ) 2 Fg. 3. Detecton Recall (R) of B (α) 1 and B (α) 2 for fve relatve payloads. From the results shown n Fgure 3, for the fve relatve payloads from 0.1 bpp to 0.5 bpp the securty of the stego database B (α) 2 bult usng the securty measure crteron, s better than the securty of the randomly selected stego database B (α) 1. For all relatve payloads the detecton recall 10 R of the OC-SVM steganalyzer on B (α) 2 s lower than that on B (α) 1. For nstance, for α = 0.5 bpp, the detecton S F LD f recall R on B (α) 1 s 78%, whereas t s only 56% on B (α) 2. Smlarly, the detecton recall R on B (α) 2 at 0.4 bpp s less than that on B (α) 1 ; 55% compared to 66%. In bref, the detecton recall R on B (α) 2 for all relatve payloads s close to 50-55%. The OC-SVM steganalyzer classfes ncorrectly one out of two tmes a gven stego mage as cover mage. In other words, on B (α) 2, the OC-SVM has a random behavour, snce t can not dstngush between the cover and stego mages. secure than the stego base B (α) 1 Ths confrms that the stego database B (α) 2 s more Note that the detecton recall R of B (α) 2 at 0.1 bpp s hgher than that at 0.2 bpp. It s 53.6% at 0.1 bpp, whereas t s 50.2% at 0.2 bpp. Indeed, for payloads under 0.2 bpp, the ASO embeddng algorthm does not perform as well as at hgher payloads, snce the oracle used for computng the detectablty map (Secton 2.1) can not manage to dstngush between secure and nsecure areas [1]. The obtaned results show that the set B (α) 2 of the stego mages selected usng the securty measure Sf F LD are more secure than those of B (α) 1 that have been randomly selected. 10 number of stego mages correctly classfed The detecton recall R =. total number of stego mages 1706

5 SfFLD(x) = 30 SfFLD(x) = 28 SfFLD(x) = 29 SfFLD(x) = 27 Fg. 4. Some exemples of the selected stego mages usng the securty measure SfF LD crteron (α = 0.5 bpp, and L = 30). By usng a smple securty metrcs, such as SfF LD, we obtan a strong securty. The used steganalyzer can not dstngush between cover and stego mages. Ths confrms the relevance of choosng the most relable mage(s) durng the transmsson phase of the secret message. Moreover, we beleve that usng a more fner securty measure such as Sfoc (Eq. 6) may mprove even more the securty of the message communcaton11. Some examples of the stego mages that have been selected usng the securty measure SfF LD crteron are gven n Fgure 4. As we can see, the selected stego mages that have been judged as the most secure mages correspond to the nosy and textured mages. [3] [4] [5] 4. CONCLUSION In ths paper, we present the techncal ponts about the adaptve steganography by oracle (ASO). Frst, we dscuss about the detectablty map computaton of ASO that reduce sgnfcantly ts computatonal complexty. Then, we study the securty of ASO thanks to the paradgm of the steganography by database. Snce our embeddng ASO algorthm allows to obtan a set of stego mages nstead of just one stego mage, we offer to the sender the opportunty to choose the most undetectable stego mage(s) durng the transmsson of hs secret message. To do ths, we propose some securty metrcs that help hm to select the most relable stego mage(s). Expermental results show that usng a smple securty metrc, such as SfF LD (Eq. 5), for choosng the most secure stego mage(s), mproves sgnfcantly the securty of the communcaton phase of ASO. [6] [7] [8] ACKNOWLEDGMENTS. Ths work was supported by the Mnstry of Hgher Educaton and Scentfc Research of Peoples Democratc Republc of Algera. 5. REFERENCES [9] [1] Sarra Kouder, Marc Chaumont, and Wllam Puech, Adaptve Steganography by Oracle (ASO), n submsson. [2] Tom asˇ Pevn y, Tom asˇ Fller, and Patrck Bas, Usng HghDmensonal Image Models to Perform. Hghly Undetectable Steganography, n Informaton Hdng - 12th Internatonal 11 Because of lack of tme, we dd not test the S oc securty measure crtef ron [10] Conference, Berln, Hedelberg, October , vol of Lecture Notes n Computer Scence, IH 10, pp , Sprnger-Verlag. Jan Kodovsk y and Jessca J. Frdrch, Steganalyss n Hgh Dmensons: Fusng Classfers Bult on Random Subspaces, n Meda Watermarkng, Securty, and Forenscs XIII, part of IS&T SPIE Electronc Imagng Symposum, San Francsco, CA, January , vol. 7880, paper. 21, pp. L Jessca J. Frdrch and Tom asˇ Fller, Practcal Methods for Mnmzng Embeddng Impact n Steganography, n Securty, Steganography, and Watermarkng of Multmeda Contents IX, part of IS&T SPIE Electronc Imagng Symposum, San Jose, CA, January 29-February , vol. 6505, pp Patrck Bas, Tom asˇ Fller, and Tom as Pevn y, Break Our Steganographc System the ns and outs of organzng BOSS, n Informaton Hdng - 13th Internatonal Workshop, Prague, Czech Republc, May , vol of Lecture Notes n Computer Scence, IH 11, pp , SprngerVerlag. Tom asˇ Fller, Jan Judas, and Jessca J. Frdrch, Mnmzng Embeddng Impact n Steganography usng Trells-Coded Quantzaton, n Meda Forenscs and Securty II, part of IS&T SPIE Electronc Imagng Symposum, San Jose, CA, USA, January , vol. 7541, paper. 05. Tom asˇ Fller and Jessca J. Frdrch, Desgn of Adaptve Steganographc Schemes for Dgtal Images, n Meda Watermarkng, Securty, and Forenscs XIII, part of IS&T SPIE Electronc Imagng Symposum, San Francsco, CA, January , vol. 7880, paper. 13, pp. F Jessca J. Frdrch, Jan Kodovsk y, Vojtech Holub, and Mroslav Goljan, Steganalyss of Content Adaptve Steganography n Spatal Doman, n Informaton Hdng - 13th Internatonal Conference, Tom as Fller, Tom as Pevn y, Scott Craver, and Andrew D. Ker, Eds., Prague, Czech Republc, May , vol of Lecture Notes n Computer Scence, IH 11, Sprnger. Alberto Munoz and Javer M. Moguerza, Estmaton of hghdensty regons usng one-class neghbor machnes, IEEE Transactons on Pattern Analyss and Machne Intellgence, vol. 28(3), pp , March Tom as Pevn y and Jessca J. Frdrch, Novelty detecton n blnd steganalyss, n workshop on Multmeda and securty, part of MM&Sec 08 Proceedngs of the 10th ACM multmeda, New York, NY, USA, September , pp , ACM.