A FIBONACCI LSB DATA HIDING TECNIQUE

Transcription

1 A FIBONACCI LSB DATA HIDING TECNIQUE Dego De Luca Pcone (*)(**), Federca Battst (*)(**), Marco Carl (*), Jaakko Astola (**), and Karen Egazaran (**) (*) AE Department, Unverst of Roma TRE, Rome, Ital, (**) Insttute of Sgnal Processng, Tampere Unverst of Technolog, Tampere, Fnland emals: (jta, ABSTRACT In ths paper, a novel data-hdng technque based on the Fbonacc representaton of dgtal mages s presented. A generalzaton of the classcal Least Sgnfcant Bt (LSB) embeddng method s performed. The Fbonacc representaton of gre level mages requres 12 bt planes nstead of the usual 8 planes of bnar representaton. Expermental results show that, such a redundant scheme outperforms the classcal LSB method resultng n marked mages havng less perceptual dstorton even f dfferent planes from the lowest bt plane are selected for embeddng. The computatonal cost of the embeddng scheme s compatble wth the classcal LSB data hdng scheme. 1. INTRODUCTION The use of multmeda dgtal data has become ver popular n the last decade due to the spread of Internet-based servces, and the ntroducton of the thrd-generaton moble communcaton sstems (UMTS/CDMA2000). Thanks to the avalablt of low cost edtng tools, dgtal data can be easl captured or coped, modfed and retransmtted n the network b an user. To effectvel support the growth of multmeda communcatons, t s essental to develop tools that protect and authentcate dgtal nformaton. In ths contrbuton, we present a novel embeddng scheme based on the Fbonacc decomposton. The results of the new scheme are compared wth the classcal LSB method wth respect to PSNR. In Secton 2, the classcal LSB scheme s descrbed. Secton 3 deals wth the Fbonacc decomposton and ts related propertes. In Secton 4, the embeddng scheme s descrbed; Secton 5 reports the results of smulatons. We conclude n Secton 6 wth some bref remarks. 2. LSB DECOMPOSITION One of the smplest sstems for embeddng dgtal data nto a dgtal cover s the Least Sgnfcant Bt method [10] Consder an NxM mage n whch each pxel value s represented b a decmal number n the range determned b the number of bts used. In a gra-scale mage, wth 8 bt precson per pxel, each pxel assumes a value between [0, 255] and each postve number β 10 can be represented b: n 1 2 β10 = b0 + bg 1 + b2g + = bg = 0 where G s equal to 2. Ths propert allows the decomposton of an mage nto a collecton of bnar mages b separatng the b nto n bt planes. In the classcal LSB embeddng methods, the secret message s nserted nto the least-sgnfcant bt plane of the cover mage ether b drectl replacng those bts or b modfng those bts accordng to a partcular nverse functon. The embeddng strateg can also be based on sequental nserton or selectve embeddng of the message n "nos" areas or random scatterng throughout the mage. Recent methods appl LSB not onl n the least sgnfcant plane but also n other btplanes or a mxture of both [10]. The amount of data to be embedded ma also be fxed or varable n sze dependng on the number of pxels selected dependng on lumnance and contrast features. The man advantage of such a technque s that the modfcaton of the LSB plane does not affect the human percepton of the overall mage qualt as the ampltude varaton of the pxel values s bounded b ±1. The maskng propertes of the Human Vsual Sstem allows sgnfcant amounts of embedded nformaton to be unnotced b mperceptble b the average observer under normal vewng condtons. Maskng refers to the phenomenon where a sgnal can be mperceptble to an observer n the presence of another sgnal. A detaled revew of these technques s gven n [1] [3] [4] Other advantages of LSB data hdng ncluded hgh embeddng capact and low computatonal complext. The man dsadvantages are the weaknesses wth respect to robustness, tamperng, geometrc attacks, flterng, and compresson. 3. FIBONACCI DECOMPOSITION The classcal Fbonacc numbers were ntroduced n the 13th centur b Leonardo of Psa a.k.a. Fbonacc n hs book, Lber Abac [2] He ntroduced there the famous rabbt problem leadng to the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,.

2 The sequence of Fbonacc numbers s defned b the followng recurrent relaton: 0 1 F( n 1) + F( n 2) n < 0 n = 0 n > 0 The bass F n of the Fbonacc representaton are the numbers of the sequences F n = F n 1 + F n 2 n 2 ( ) ( ) ( ) Table 1: The sstem of bnar and Fbonacc numbers, for some values of n. N Bn Fb Table 2: Maxmum bt error for each plane after embeddng. Bt Plane Bn Fb From Table 1, t s eas to see the dfference between the two representatons: For the same number of bts (for N>2), a larger numerc range s avalable for bnar representaton. For 8 bts, the range s [0, 255] for bnar representaton compared to [0, 54] for Fbonacc representaton. The bnar representaton does not ntroduce redundanc. To represent values n the range [0, 255] n Fbonacc doman, we need 12 bts, 4 bts more than n the bnar representaton. As a result, a gre level mage wll be represented n 12 bt Fbonacc planes. As shown n Table 2, the dstorton amount ntroduced b changng the bt value n the planes s bgger n power of two representatons than n Fbonacc representaton. The Fbonacc representaton s redundant, snce a gven natural number can have man representatons as a sum of Fbonacc numbers. For example, the number 16 can be represented as 13+3, as well as 8+5+3, or Nevertheless, there s one Fbonacc representaton, called the normal representaton, whch allow a unque decomposton of a natural number. It s based on Zeckendorf s theorem [8] whch states that Each postve nteger m can be represented as the sum of dstnct numbers n the sequence of Fbonacc numbers usng no two consecutve Fbonacc numbers. As a consequence of the Zeckendorf s theorem, an postve nteger can be represented as n 1 2 βf = b0 + bf 1 + b2f + = bf = 0 where there are no 2 consecutve 1 s n the sequence. 4. EMBEDDING SCHEME The embeddng procedure conssts of the followng two steps. Frst, the selecton of areas n an mage to embed the mark s performed. In the classcal scheme, one bt s embedded n each pxel of the mage. To ncrease the amount of data to be embedded, more than one bt-plane ma be used. These methods acheve hgh capact but ntroduce notceable dstortons n the mage. Recent studes show that the annoance and vsblt of artefacts depend on the salenc of the affected areas whose map can be computed b drect explotaton of the characterstcs of the HVS [11] [12] [14] Pschophscal studes demonstrate that among the factors mpactng the human attenton, contrast, colour, moton, brghtness, object sze and shape are the most sgnfcant. The relatve mportance of these factors has et to be determned. We have appled dfferent strateges to select areas of embeddng, ncludng local varance [5], spatal segmentaton b LPA-ICI rule [9]. The selecton of areas provdes an embeddng map for selectng pxels to be decomposed n the Fbonacc doman. The watermark s a sequence of N bts B = (b 0, b 1,.., b N-1 ) that s spread b a pseudo-random sequence p(x; ) of ±1 representng the secret ke. The second step n the embeddng procedure s to decompose the selected pxels n the Fbonacc doman, and also to select the plane n whch to embed. The same embeddng scheme can be also appled to dfferent planes resultng n more robust data hdng and possbl hgher vsual dstorton. Wth respect to the classcal LSB methods, Fbonacc LSB usuall does not allow a fxed sze embeddng snce not ever pxel n the block s a good canddate for the embeddng. To deal wth Fbonacc redundanc, t s necessar to compl wth Zeckendorf s theorem. If the selected pxel s not a good canddate (meanng that the current bt to be changed b 1 has a neghbour n the prevous bt plane havng also a value 1), then the next canddate pxel s selected and a sde nformaton table, contanng embeddng nformaton, s updated. It s mportant to note that the scope of ths work was to determne f the Fbonacc doman s sutable for spatal embeddng. The robustness or securt of the data hdng sstem are not fundamental as n an LSB based scheme. The fnal am s to nvestgate the possblt of nsertng a mark wthout alterng the perceptual qualt of the fnal mage. The extracton of the watermark requres the knowledge of the secret mage S and the ke K used for spatal dsperson of the watermark mage. The extracton operaton s the nverse of the embeddng operaton. The watermarked mage under nspecton s parttoned nto areas n a manner smlar to the selecton of embeddng area. Usng the sde nformaton, onl the selected pxels are tested for mark presence. Followng, a de-spreadng operaton s performed, the receved watermark s obtaned.

3 5. EXPERIMENTAL TEST To evaluate the performance of the proposed scheme, we have compared the results of LSB embeddng performed n the bnar doman [5] [6] [7] wth the one adapted to the Fbonacc decomposton. In [6], the authors, n order to reduce the detectablt of watermark, have used m sequences to encode the LSB of the mage data. Due to ther balance, random appearance, and good autocorrelaton propertes (a sngle peak wth no sde-lobes), applcaton of these codes does not ntroduce apparent mage degradaton or detectablt b a casual vewer. The m sequences of maxmal length (2n 1) for a vector of length n, can be formed from startng vectors b a Fbonacc recurson relaton. The man propert s that the autocorrelaton functon (and hence, the spectral dstrbuton) of the m sequences resemble that of a random Gaussan nose dstrbuton. Ths smlart becomes closer as the sequence length ncreases. That s, mages encoded wth m sequences and one bt Gaussan nose are shown to be ndstngushable from the orgnal and from each other. In practce, longer m sequences were emploed that were commensurate wth the mage sze (2n) and exhbted a null n the autocorrelaton around the man peak. To nsert a watermark, t s necessar to frst generate a watermarkng sgnal usng a ke to seed a generator for m sequences (a maxmum-length random sequence). The elements (bnar valued) of the m sequences are then arranged nto a 2D watermarkng sgnal. Thus, the obtaned m sequences are now embedded nto the LSB of the mage. The decodng process makes use of the unque and optmal autocorrelaton functon of m-sequences. The second technque [15], s based on the prelmnar computaton of a checksum of the mage data, followed b the embeddng of the checksum nto the LSB plane of randoml chosen pxels. The goal s a selecton of a checksum scheme wthout ntroducng artefacts n the mage. A checksum s the modulo-2 addton of a sequence of fxed-length bnar words. A unforml dstrbuted pseudo random number generator s used to map the checksum bts onto a path of randoml selected pxel locatons wthn the lmts of the mage (random walk). At each locaton, the LSB of the pxel value s forced to match the value of the correspondng n-th checksum bt as n goes from 0 to N 1. When adoptng Fbonacc representaton, onl small modfcatons are needed n computng the checksum (sequences to be added are 8 11 bt segments) and to the fnal embeddng scheme (whch s not completel random due to Zeckendorf s representaton). The last scheme consdered s based on [5]. The embeddng algorthm can be summarzed as follows: The cover mage s parttoned nto nonoverlappng blocks of sze (8 8) pxels. For each block the varance s computed and the blocks are then sorted accordng to ther varance values. For each block, the LSB plane s selected and the mark nserted. The same scheme ma also be appled to dfferent planes resultng n more robust data hdng whch mght result n hgher vsual dstorton. The watermark, after a classcal spreadng operaton, s nserted pxel b pxel n each block, startng from blocks of lower varance. The same method s also performed n the Fbonacc doman wth onl few modfcatons. The extracton of the watermark requres knowledge of the secret mage S and the ke K used for spatal dsperson of the watermark mage. The watermarked mage under nspecton s parttoned nto nonoverlappng block of sze 8 8 pxels. Usng the sde nformaton, onl the selected blocks are tested for mark presence. Followng, a de-spreadng operaton, the watermark s recovered. A qualtatve estmaton of the extracted watermark W x,, W ( x, ), wth respect to the embedded verson ( ) ma be expressed as a Normalzed Cross Correlaton (NCC): W x, W x, NCC = x x ( ) ( ) (, ) 2 W x where the maxmum value of NCC = 1 corresponds to a perfect match. We have performed several tests on mages watermarked n both the bnar and Fbonacc domans usng PSNR and NCC as a performance measure. Our results ndcate that embeddng n the Fbonacc doman ma ntroduce less perceptual dstorton and hgher PSNR. The LSB based methods are well known to be not robust. We have tred some smple modfcatons on to evaluate the robustness of the Fbonacc-based method. The followng modfcatons were consdered: Medan flterng wth 3x3 wndow; Addtve Gaussan nose: varance 0.1 on the 50% of pxels of mages; Reszng: the watermarked mages were scaled to one half of ther orgnal sze and back to the orgnal dmensons; JPEG compresson (compresson rato 1:45) Image croppng. We have used three test mages: Cameraman, Clock, and Fshng Boat. The results of the frst three modfcatons are shown n Table 3. From our smulatons, we found that there are no sgnfcant dfferences n results obtaned usng bnar and Fbonacc representatons. The frst embeddng method modfes just the LSB plane resultng n lttle changes n the PSNR for both representatons. Fgure 1 (a) shows the Cameraman mage used as a cover mage (b) shows the watermark, M,

4 (c) and (d) are the watermarked mages. Note that PSNR=46.71 db means that the qualt degradatons could hardl be perceved b a human ee. In the Fbonacc doman, the PSNR for the watermarked mage s about db. Robustness aganst dfferent attacks for the thrd method s shown n Table 3. Table 3. Performance comparson between the classcal LSB and Fbonacc-based LSB embeddng for the Cameraman mage. Bnar doman Fbonacc doman PSNR db NCC PSNR db NCC JPEG Medan Nose Reszng We have performed a correlaton test between the two representatons. Usuall, the computaton of the correlaton wth orgnal mage s a useful wa to measure the level of degradaton ntroduced. Fgure 2 shows ths tendenc. On the x- axs of both plots we have the normalzed pxel value (from 0 to 1) of orgnal mage I, and on the -axs we have the normalzed pxel value of watermarked mage I2 and the Fbonacc watermarked mage (IF). When two mages are smlar, the correlaton between pxels at the same locaton (x,) s hgh. Hence, the closer are the ponts to the dagonal lne, the hgher s the correlaton between correspondng pxels, and, therefore, the smaller s a degradaton ntroduced. 6. CONCLUDING REMARKS In ths paper, we have presented our prelmnar stud on the use of Fbonacc representaton of dgtal mages for embeddng purposes. The comparson has been performed wth respect to the classcal LSB embeddng methods. When Fbonacc representaton s used under the constrant that the same embeddng condtons are used as n the bnar case, a smlar or hgher PSNR s obtaned. If the embeddng s done not to the LSB, but prevous btplanes, the artefacts ntroduced are less annong for Fbonacc than for a bnar representaton. Test performed to measure the robustness aganst an addtve nose confrms the weakness of the spatal doman LSBbased methods. Fnall, we have performed a test of the marked mage croppng modfcaton. To mprove the method, a prelmnar reshufflng of the mark data have been per-formed usng a Fbonacc scramblng technque proposed n [13]. It demonstrated ncreased robustness relatve to the LSB embeddng method. Fgure 1: Fgure (a) s the orgnal mage Cameraman 256x256. Fgure (b) s the watermark used, two level mage 16x16. Fgure c) s the watermarked mage bnar representaton, Fgure (d) the watermarked mage n Fbonacc doman. Fgure 2: Correlaton between mages. The plot at left s between the orgnal mage I and the bnar watermarked mage I2; and at rght s between mage I and the Fbonacc watermarked mage IF

5 Fgure 3: 8 bt planes decompostons. Fgure 4: Fbonacc s 12 bt planes decomposton. ACKNOWLEDGMENT The authors would lke to thanks Chn Koh for hs help n fnal stage of paper preparaton. [3] M.M. Yeung and F.C. Mntzer, "An Invsble Watermarkng Technque for Image Verfcaton," Proc. IEEE Int l Conf. Image Processng 1997, Vol. 2, Oct. 1997, pp. II [4] N. Memon and P.W. Wong, "Protectng Dgtal Meda Content," Comm. ACM, Vol. 41, No. 7, Jul 1998, pp [5] S.P.Mat and M.K.Kundu, "Robust and Blnd Spatal Watermarkng n Dgtal Image," Proc. 3rd Indan Conf. on Computer Vson, Graphcs and Image Processng (ICVGIP 2002), pp , Ahmedabad, Inda, 16-18th December, [6] R.G. van Schndel, A.Z. Trkel, and C.F. Osborne, "A dgtal watermark," n Proc.IEEE Int. Conf. Image Processng, vol. 2, Austn, TX, Nov. 1994, pp [7] M.M. Yeung and F.C. Mntzer, "An Invsble Watermarkng Technque for Image Verfcaton," Proc. IEEE Int l Conf. Image Processng 1997, Vol. 2, Oct. 1997, pp. II [8] Verner E. Jr. Hoggatt, Fbonacc and Lucas Numbers, The Fbonacc Assocaton, Santa Clara, Calforna, USA, [9] Katkovnk V., A. Fo, K. Egazaran, and J. Astola, Ansotropc local lkelhood: theor, algorthms, applcatons, Proc. of SPIE Electronc Imagng 2005: Image Processng: Algorthm and Sstems IV, , [10] L. Shao-Hu, C. Tan-Hang, Y. Hong-Xun,G. Wen, - "A varable depth LSB data hdng technque n mages" n Proc. Machne Learnng and Cbernetcs, Proceedngs of 2004 Internatonal Conference on Volume 7, Aug Page(s): vol.7 [11] M.S. Moore, Pschophscal Measurement and Predcton of Dgtal Vdeo Qualt, Ph.D. thess, Unverst of Calforna Santa Barbara, June [12] A. J. Maeder W. Osberger, Automatc dentfcaton of perceptuall mportant regons n a mage, n Internatonal Conference on Pattern Recognton, Brsbane, Australa, pp: , vol.1, [13] Jancheng Zou, Rabab K. Ward, Dongxu Q, A new dgtal mage scramblng method based on Fbonacc numbers, n Proc. IEEE ISCAS 2004, vo. III, pp [14] X. Zhang and S. Wang, Steganograph usng multplebase notatonal sstem and human vson senstvt, IEEE Sgnal Process. Lett., vol. 12, no. 1, pp , Jan [15] A. Ker, Improved detecton of LSB steganograph n grascale mages, n Proc. Informaton Hdng Workshop, vol. 3200, Sprnger LNCS, 2004, pp REFERENCES [1] E. T. Ln and E. J. Delp, "A Revew of Data Hdng n Dgtal Images," Proceedngs of the Image Processng, Image Qualt, Image Capture Sstems Conference (PICS '99), Savannah, GA, Aprl 25-28, 1999, pp [2] A. Hordam, "A generalzed Fbonacc sequence", Amercan Mathematcal Monthl, no. 68, pp , 1961.