FROM IMAGE TO AUDIO WATERMARKING USING SELF-INVERTING PERMUTATIONS

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1 FROM IMAGE TO AUDIO WATERMARKING USING SELF-INVERTING PERMUTATIONS Maria Chroi, Agelos Fylakis, ad Stavros D. Nikolopoulos Departmet of Computer Sciece ad Egieerig, Uiversity of Ioaia, GR Ioaia, Greece {mchroi, afylakis, Keywords: Abstract: Watermarkig Techiques; Audio Watermarkig Algorithms; Self-ivertig Permutatios; Represetatios of Permutatios; Frequecy Domai; Embeddig/Extractig Algorithms; Performace Evaluatio. The itellectual property ifrigemet i music due to the proliferatio of the iteret ad the ease of creatig ad distributig idetical digital objects has brought watermarkig techiques to the forefrot of digital rights protectio. Towards this directio, a sigificat umber of watermarkig techiques have bee proposed i recet years i order to create robust ad imperceptible audio watermarks. I this work we propose a audio watermarkig techique which efficietly ad secretly embeds iformatio, or equivaletly watermarks, ito a audio digital sigal. Our techique is based o the mai idea of a recetly proposed image watermarkig techique expadig thus the digital objects that ca be efficietly watermarked through the use of self-ivertig permutatios. More precisely, our audio watermarkig techique uses the 1D represetatio of self-ivertig permutatios ad utilizes markig at specific areas thaks to partial modificatios of the audio s Discrete Fourier Trasform (DFT); these modificatios are made o the magitude of specific frequecy bads. We have evaluated the embeddig ad extractig algorithms by testig them o various ad differet i characteristics audio sigals that were i WAV format ad we have obtaied positive results. The algorithms have bee developed ad tested usig the mathematical software package Matlab. 1 INTRODUCTION Digital watermarkig is a techique for protectig the itellectual property of a digital object; the idea is simple: a uique marker or idetifier, which is called watermark, is embedded ito a digital object which may be used to verify its autheticity or the idetity of its owers (Grover, 1997; Collberg ad Nagra, 010). Audio Watermarkig. I a copyright protectio framework, a audio watermarkig techique aims to embed a uique idetifier, i.e., the watermark w, ito audio s data through maily the itroductio of errors ot detectable by huma perceptio. Withi the same framework, audio watermarkig ca be described as the problem of embeddig a watermark w i the host sigal S producig thus the watermarked audio sigal S w such that w ca be reliably located ad extracted from S w eve after S w has bee subjected to trasformatios such as compressio, filterig, oise additio, croppig, etc. It is worth otig that, if a watermarked audio sigal S w is copied or trasferred through the iteret the the watermark w is also carried with the copy ito the audio s ew locatio esurig thus the maiteace of copyright protectio. Recetly, a sigificat umber of watermarkig techiques have bee proposed i the literature i order to create robust ad imperceptible audio watermarks. Iitial research o audio watermarkig dates back to the mid-ieties where Beder et al. (Beder et al., 1996) preseted data hidig techiques for audio sigals; the first techiques were directly ispired from previous research o image watermarkig. A broad rage of audio watermarkig techiques goes from simple least sigificat bit (LSB) scheme to the various spread spectrum methods ad ca be classified accordig to the domai where the watermarkig takes place i frequecy, time, ad compressed domai (Sharma et al., 01; Cox et al., 008; Alsalami ad Al-Akaidi, 003; Hartug ad Kutter, 1999). Motivatio. Nowadays, digital audio is a represetative sample of iteret data that has bee subjected to extesive itellectual property violatio. Thus, we cosider importat the developmet of methods that deter malicious users from claimig others owership, motivatig thus iteret users to feel more safe to publish their work olie. Audio watermarkig, i cotrast with other techiques, allows audio sigals to be available to third

2 iteret users but simultaeously carry a id that is actually the owership s proof. This way audio watermarkig achieves its target of deterrig copy ad usage without ower s permissio. Watermarkig digital objects such as image, audio, video, text ad software eables the proof of owership o copyrighted objects prevetig thus the itellectual property ifrigemet. Cotributio. I this work we preset a efficiet ad easily implemeted techique for watermarkig audio sigals. What is importat of the proposed techique is the fact that it suggests a way i which a iteger umber w ca be represeted first as a self-ivertig permutatio π ad the as a oedimesioal array (or, equivaletly, 1D represetatio). The idea comes from our previous work o image watermarkig where the iteger watermark umber w is represeted as a two dimesioal array. More precisely, our proposed algorithm embeds a self-ivertig permutatio π over elemets ito a audio sigal S by first mappig the elemets of π ito a matrix A ad the, based o the iformatio stored i A, markig specific areas of audio S i the frequecy domai resultig thus the watermarked audio S w. A efficiet algorithm extracts the embedded self-ivertig permutatio π from the watermarked audio S w by locatig the positios of the marks i S w ; it eables us to recostruct the 1D represetatio of π ad, the, obtai the watermark w. At this poit we would like to poit out that the primary purpose of the paper is ot to fill a gap of the existig audio watermarkig methods by proposig a ew embeddig techique, but to expad the idea used o our previous work ad show that it ca be efficietly applied for audio watermarkig depictig thus the high versatility of the whole cocept. Evaluatio. We have evaluated the embeddig ad extractig algorithms by testig them o various ad differet i characteristics audio sigals that were i WAV format ad we had positive results as the watermark was successfully extracted. What is more, the method is ope to extesios as the same method might be used with a differet markig procedure. Note that, all the algorithms have bee developed ad tested i MATLAB (Igle ad Proakis, 010). OUR WATERMARKING TOOLS I this sectio we preset the structural ad algorithmic tools we use towards the watermarkig of a audio sigal. We first briefly discuss a codec system which ecodes a iteger umber w ito a selfivertig permutatio π, ad the we preset a trasformatio of a self-ivertig permutatio ito D ad 1D represetatios..1 Self-ivertig Permutatios I a formal (i.e., mathematical) way, a permutatio of a set of objects S is defied as a bijectio from S to itself, that is, a map S S for which every elemet of S occurs exactly oce as image value. Permutatios may be represeted i may ways, where the most straightforward is simply a rearragemet of the elemets of the set N = {1,,...,}; for example, the permutatio π = (4,7,6,1,5,3,) is a rearragemet of the elemets of the set N 7 (Sedgewick ad Flajolet, 1996; Golumbic, 1980). Defiitio.1.1. Let π = (π 1,π,...,π ) be a permutatio over the set N, where > 1. The iverse of the permutatio π is the permutatio q = (q 1,q,...,q ) with q πi = π qi = i. A self-ivertig permutatio (or, for short, SiP) is a permutatio that is its ow iverse, that is π πi = i. There are several systems that correspod iteger umbers ito permutatios (Sedgewick ad Flajolet, 1996). Recetly, we have proposed algorithms for such a system which efficietly ecode a iteger w ito a self-ivertig permutatio π ad efficietly decode it; our algorithms ru i O() time, where is the legth of the biary represetatio of w.. D ad 1D Represetatios I the D represetatio, the elemets of the permutatio π = (π 1,π,...,π ) are mapped i specific cells of a matrix A as follows: umber π i etry A(π 1 π i,π i ) or, equivaletly, the cell at row i ad colum π i is labeled by the umber π i, for each i = 1,,...,. Figure 1(a) shows the D represetatio of the selfivertig permutatio π = (4,7,6,1,5,3,). Based o the previously defied D represetatio of a permutatio π, we ext propose a twodimesioal marked represetatio (DM represetatio) of π which is a efficiet tool for watermarkig images. I our DM represetatio, a permutatio π over the set N is represeted by a matrix A as follows: the cell at row i ad colum π i is marked by a specific symbol, for each i = 1,,...,; where, i our implemetatio, the used symbol is the asterisk, i.e., the character. Figure 1(b)

3 (a) (b) Figure 1: The D, DM ad 1DM represetatios of the self-ivertig permutatio π = (4, 7, 6, 1, 5, 3, ). shows the DM represetatio of the permutatio π = (4,7,6,1,5,3,). (c) I our 1D represetatio, the elemets of the permutatio π are mapped i specific cells of a array B of size as follows: umber π i... etry B((π 1 π i 1) + π i ) or, equivaletly, the cell at the positio (i 1)+π i is labeled by the umber π i, for each i = 1,,...,. We ext describe the 1DM represetatio acquired i a similar maer as the DM represetatio. I our 1DM represetatio, a permutatio π over the set N is represeted by a array B as follows: the cell at the positio (i 1) + π i is marked by a specific symbol, for each i = 1,,...,; where, i our implemetatio, the used symbol is agai the asterisk character. Figure 1(c) shows the 1DM represetatio of the same permutatio π = (4,7,6,1,5,3,). Hereafter, we shall deote by π a self-ivertig permutatio ad by the umber of elemets of π. 3 PREVIOUS RESULTS ON IMAGE WATERMARKING I a recet work of ours, we have proposed a image watermarkig techique that embeds watermarks ito... digital images by iterferig i the frequecy domai of images. Sice our audio watermarkig techique, that is goig to be later described, is maily based o the idea of image watermarkig, we ext briefly describe the mai steps of our image watermarkig techique ad state poits regardig some of its mai characteristics. The embeddig image watermarkig algorithm first computes the DM represetatio of the permutatio π, that is, the array A (see, Subsectio.). Next, it takes the iput image I, covers it with a imagiary grid C, resultig i grid-cells C i j, ad takes the Discrete Fourier Trasform (DFT) F i j of each C i j. The algorithm goes to each grid-cell C i j, takes the magitude M i j, ad places o it two imagiary ellipsoidal auli deoted as Red ad Blue. It the computes the average of the magitude values grouped by the Red ad the Blue auli, say, AvgR i j ad AvgB i j, respectively, ad after that, for each M i j computes the value D i j = AvgB i j AvgR i j if AvgB i j < AvgR i j, otherwise D i j = 0. Subsequetly, the algorithm computes for each row i the maximum value MaxD i. Oce agai the embeddig algorithm goes to each grid cell C i j ad if A i j = it icreases the values of M i j grouped by the Red aulus by AvgB i j AvgR i j + MaxD i + c opt. Fially, it recostructs each DFT cell F i j usig the modified M i j with the trigoometric formula ad with the iverse DFT it recostructs the grid cells C i j. The extractig algorithm works i a similar maer. Regardig the mai characteristics of this techique, we should first metio that it is efficiet. As the experimetal results showed, watermarks are imperceptible leadig also to high fidelity. Moreover, watermarks are robust to distortios as we got positive results testig the watermarked images agaist JPEG compressio ad other attacks. 4 THE AUDIO WATERMARKING TECHNIQUE I this sectio we preset a algorithm for ecodig a self-ivertig permutatio π ito a audio sigal S by markig specific time segmets of S i the frequecy domai resultig thus the watermarked audio sigal S w. We also preset a decodig algorithm which extracts the embedded permutatio π from S w by locatig the positios of the marks i S w. 4.1 Embed Watermark ito Audio The embeddig algorithm of our proposed techique ecodes a self-ivertig permutatio (SiP) π ito a

4 Figure : Segmetatio of the S s sigal ito specific frames accordig to 1DM represetatio of the permutatio π. Figure 3: The DFT represetatio of a marked frame. digital audio sigal S. Recall that, the permutatio π is obtaied over the set N, where = + 1 ad is the legth of the biary represetatio of a iteger w which actually is the audio s watermark (author s techique). The mai idea of embeddig. The watermark w, or equivaletly the correspodig self-ivertig permutatio π, is imperceptibly iserted i the frequecy domai of specific frames o the audio track sigals S; see, Figure. More precisely, we mark certai frames gettig the DFT ad do alteratios at the magitude values of high frequecies for each audio frame to be marked; see, Figure 3. This is achieved by choosig two groups of magitude values specified with two segmets of the magitude vector amely Red ad Blue ad the alteratios are actually o their differece; see, Figure 4. I our implemetatio we use fixed segmets widths ad distaces from the ceter of symmetry of the DFT s magitude vector. The added value is specified by the maximum value i the defied area. The embeddig algorithm. Our embeddig algorithm takes as iput a SiP π ad a audio sigal S ad returs the watermarked audio sigal S w ; it performs the followig mai processes: i. costruct the 1DM represetatio of the watermark umber w; ii. trasform the iput audio sigal S ad acquire the frequecy represetatio of it; iii. modify sigals frequecy represetatio accordig to the 1DM represetatio of the sigal S; iv. returs the watermarked audio sigal S w ; We describe below i detail the embeddig algorithm i steps. Algorithm Embed SiP-to-Audio Iput: the watermark π w ad the origial audio sigal S; Output: the watermarked audio sigal S w ; Step 1: Compute first the 1DM represetatio of the permutatio π, i.e., costruct the array B of size = ; recall that the etry B ((i 1) + π i ) cotais the symbol, 1 i. Step : Segmet the audio sigal S ito ooverlappig frames f i of size f i [a,b] = N 1, 1 i, where N is the legth of the audio sigal. Step 3: For each frame f i, compute the Discrete Fourier Trasform (DFT) usig the Fast Fourier Trasform (FFT) algorithm, resultig i DFT frames F i of size F i [a,b] = N 1, 1 i, that is, F i = FFT( f i ). Step 4: For each DFT frame F i, compute its magitude M i ad phase P i vectors (or, arrays) which are both of size M i [a,b] = P i [a,b] = N 1, 1 i. Step 5: The, the algorithm takes each of the magitude vectors M i ad determies two segmets i M i, 1 i, deoted as Red ad Blue (see, Figure 4). I our implemetatio, Figure 4: The Red ad Blue segmets o DFT.

5 each Red segmet [x r,y r ] has legth l r (eve), where x r = N 1 l r ad y r = N 1 + l r ; each Blue segmet [x b,y b ] has legth l b (eve), where x b = x r l b ad y b = y r + l b The Red ad the Blue segmets determie two groups of magitude values o M i ; the Red Values ad the Blue Values (see, Figure 4). Step 6: For each magitude vector M i, 1 i, compute the average value AvgR i of the Red Values ad the average value AvgB i of the Blue Values of M i. Step 7: For each magitude vector M i, 1 i, compute first the variable D i as follows: D i = AvgB i AvgR i, if AvgB i AvgR i D i = 0, otherwise. Step 8: Partitio the values D 1, D,..., D ito sets E 1,E,...,E, each of size (recall that = ); let {D i1,d i,...,d i } be the elemets of the i-th set E i, 1 i. The, compute the values MaxD 1, MaxD,..., MaxD where MaxD i is the maximum value of the i-th set E i = {D i1,d i,...,d i }, 1 i. Step 9: For each marked cell B (i) of the 1DM represetatio matrix B of the permutatio π (i.e., the call which cotais the symbol ), mark the correspodig frame F i, 1 i ; the markig is performed by icreasig all the Red Values i M i by the value AvgB i AvgR i + MaxD k + c, (1) where k = i ad c = c opt. The additive value of c opt is a predefied value which eables successful extractig. Step 10: Recostruct the DFT of the correspodig modified magitude vector M i, usig the trigoometric form formula (Gozalez ad Woods, 007), ad the perform the Iverse Fast Fourier Trasform (IFFT) for each frame F i, 1 i, i order to obtai the audio sigal S w. Step 11: Retur the watermarked audio sigal S w. Note that cocerig the placemet of the Red ad Blue segmets, their positio ca vary accordig to the frequecy bad i which we wat to mark a frame. At the above illustratio we mark it i the high frequecies but there ca be a differet approach. Specifically, we ca mark istead lower frequecies ad that is performed by movig the segmets from the ceter to the right ad left edges of the magitude array of the Discrete Fourier Trasform (DFT) represetatio. 4. Extract Watermark from Audio I this sectio we describe the decodig algorithm of our proposed techique. The algorithm extracts the SiP π from a watermarked digital audio sigal S w, which ca be later represeted as a iteger w. The mai idea of extractig. The mai idea behid the extractig algorithm is that the self-ivertig permutatio π is obtaied from the frequecy domai of specific frames of the watermarked audio sigal S w. More precisely, usig the same two Red ad Blue segmets, we detect certai areas of the watermarked audio sigal S w so that the differece betwee the average values of the Red segmet have the maximum positive differece over the average values of the Blue segmets. I this way we ca detect marked frames that eable us to obtai the 1DM represetatio of the permutatio π. The extractig algorithm. We ext describe the extractig algorithm which cosists of the followig steps. Algorithm Extract SiP-from-Audio Iput: the watermarked audio S w marked with π ; Output: the watermark π = w; Step 1: Take the iput watermarked audio S w ad compute its size N. The, segmet S w ito ooverlappig frames f i of size f i [a,b] = N 1, 1 i. Step : The, usig the Fast Fourier Trasform (FFT), get the Discrete Fourier Trasform (DFT) for each frame f i, resultig i DFT frames F i, 1 i. Step 3: For each DFT frame F i, compute its magitude M i ad phase P i vectors, which are both of size M i [a,b]=p i [a,b]= N 1, 1 i. Step 4: For each magitude vector M i, compute the average values AvgR i ad AvgB i of the Red Values ad Blue Values of M i, respectively, as described i the embeddig algorithm. Step 5: Partitio the vectors M i, 1 i, ito sets L 1,L,...,L, each of size ; let {M i1,m i,...,m i } be the elemets of the i-th set L i ad let AvgR i j ad AvgB i j be the average values of the Red Values ad Blue Values, respectively, of the vector M i j, 1 i, j. Step 6: For each set L i = {M i1,m i,...,m i } fid the k th vector M i j such that AvgB ik AvgR ik is miimum ad set π i = k, 1 k. Step 7: Retur the self-ivertig permutatio π.

6 DFT for each frame F i Iitial sigal S B Watermarked sigal Sw Figure 5: The ecodig process of audio sigal watermarkig. Havig preseted the embeddig ad extractig algorithms, we ext briefly commet o the purpose of the additive value c = c opt (see, Step 9 of the embeddig algorithm). Similar to image watermarkig, we add at the correspodig embeddig markig step the additive value c opt which by gettig greater icreases the robustess of the marks; i our audio watermarkig case, we just used a very small value for it. 5 EXPERIMENTAL RESULTS This sectio summarizes the experimetal results of the proposed audio watermarkig codec algorithms; we implemeted our algorithms ad carried out tests usig the geeral-purpose mathematical software package Matlab (Versio 7.7.0) (Igle ad Proakis, 010). Testig of our embeddig ad extractig algorithms has bee made by the use of various 16-bit digital audio tracks i wav format with 44.1 KHz samplig frequecy. Cocerig the audio samples used, they where relatively short abstracts with differet characteristics. For istace there were tracks cotaiig speech which have may silet segmets as well as music track samples ad tracks with extreme features such as low ad high frequecy souds. May of the audio tracks that we used for testig were acquired from a web audio repository called wavsource ad eriched by some other audio tracks from various sources. It is well kow i the field of watermarkig that there are three mai characteristics to take ito accout describig ad evaluatig a digital watermarkig system: Fidelity, Robustess, ad Capacity (Cox et al., 008). Cocerig our watermarkig system, it seems to be of high fidelity as watermarked tracks were ot distiguished over the origial oes ad the results usig the PSNR metric were iterestigly positive. Cocertig the markig procedure of our implemetatio, we set both legths l r ad l b of the Red ad Blue segmets respectively, equal to 0% of half the legth of magitude vector as it is mirrored (see, Sectio 4.1). Recall that, the value 0% is a relatively small percetage which allows us to modify the audio track segmets i a satisfactory level i order to detect the watermark ad successfully extract it without affectig audio tracks iitial quality. Moreover, we choose to alter higher frequecies ad thus the two segmets are at the ceter of the magitude vector. This is because high frequecies are less perceptible accordig to the huma auditory system. What is more, at high frequecies audio tracks cotai less iformatio which meas that iformatio is less likely to be lost due to post alteratios. Fidelity. I order to evaluate the watermarked audio track quality obtaied from our proposed watermarkig method we used the Peak Sigal to Noise Ratio (PSNR) metric. Our aim was to prove that the watermarked audio track is closely related to the origial track provig the high fidelity attribute of our system. This is somethig vital as watermarkig should ot itroduce audible distortios i the origial audio track, as that would certaily reduce its commercial value. Givig a short itroductio to the PSNR metric, we should metio that it is defied as the ratio betwee the referece (or, origial) sigal ad the distorted (or, watermarked) sigal of a audio track ad it is give i decibels (db). It is well kow that PSNR is most commoly used as a measure of quality of recostructio of lossy compressio codecs (e.g., for image or audio compressio methods). The higher the PSNR value the closer the distorted sigal is to

7 Fileame Gaussia Noise Croppig Resamplig Requatizatio MP3 Compressio bach.wav clariet.wav castaets.wav elvis riverside.wav family ma.wav high10sec.wav low10sec.wav Table 1: The hammig distace of the watermark w ad the extracted watermark w after commo sigal attacks. the origial or the better the watermark coceals. We metios that PSNR is a popular metric due to its simplicity. For a iitial audio sigal S of size N ad its watermarked equivalet sigal S w, PSNR is defied by the formula: PSNR(S,S w ) = 10log 10 N max MSE, () where N max is the maximum sigal value that exists i the origial audio track ad MSE is the Mea Square Error which is give by the followig formula: MSE(S,S w ) = 1 N N 1 i=0 (S(i) S w (i)). (3) Comparig the origial audio tracks with the watermarked oes, we immediately get to otice that they depict excellet fidelity accordig to the PSNR values that we have obtaied. I every case PSNR is over 50 db which proves that fact that there is a strikig similarity betwee the origial ad the watermarked sigal of a audio track. Fileame PSNR bach.wav 67. clariet.wav 67.9 castaets.wav 68. elvis riverside.wav 75.3 family ma.wav 73.8 high10sec.wav 58.8 low10sec.wav 64.5 Table : The PSNR values of the watermarked audio sigals. I Table you ca see the performace of our method as we demostrate the PSNR values of some audio tracks that we used i this work. Each of them was sampled at 41.1 KHz ad the duratio was of about 10 sec. Additioally, each oe has much differet characteristics. More specifically, the audio tracks bach.wav, clariet.wav ad castaets.wav where a cocert, a clariet ad castaets solo respectively. The audio track elvis riverside.wav combies huma voice with music, while the family ma.wav cotais oly speech which meas that it also has periods of silece. Lastly the audio tracks high10sec.wav ad low10sec.wav are some extreme cases of high ad low frequecy souds. Robustess. The watermarked sigals were subjected to distortios or commo sigal attacks i order to evaluate the robustess of our audio watermarkig algorithms. We tested the performace of each audio track uder white oise additio, croppig, resamplig, requatizatio ad MP3 compressio. Below we describe i more details each oe of the five differet attacks that we applied i our experimets. (a) Gaussia Noise. A white gaussia oise of SNR 0 db was added to the origial audio sigal. (b) Croppig. A 10% of the begiig of the watermarked audio sigal was cropped ad subsequetly replaced by zeros. (c) Resamplig. The watermarked sigal, origially sampled at 44.1 KHz, is resampled at.05 KHz, ad the restored back by samplig agai at 44.1 KHz (d) Requatizatio. The 4-bit watermarked audio sigal is re-quatized dow to 16 bits/sample ad the back to 4 bits/sample. (e) MP3 compressio. The watermarked audio sigal is compressed usig a bit rate of 18 Kb/s ad the decompressed back to the WAV format. Sice the watermark that we embed i our audio sigal is a permutatio, i.e. a vector over the set N ( > 1), we test after each attack the similarity of the

8 extracted watermark with the origial oe usig the Hammig distace (Hammig, 1950). The Hammig distace d(x, y) betwee two vectors x ad y is the umber of coefficiets i which they differ (Hammig, 1950). The Hammig distace equals to zero, i.e., d(x,y) = 0, if x ad y agree i all coordiates; it happes if ad oly if x = y. I our case the Hammig distace is computed betwee the watermark w = π that we embedded ito the audio track ad the watermark π ext that we extract from the audio. If d(π,π ext) = 0 the watermark w = π successfully extracts from the attacked audio sigal. Additioally, it is worth otig that if d(π,π ext) is relatively small, the the watermark π ca be recostructed with high probability by exploitig the self-ivertig properties of the permutatio π. I Table 1 we demostrate similarity results betwee the watermark that we embedded ito the audio track ad the watermark that we extracted after various sigal processig attacks. As the experimetal results show, our audio watermarkig algorithm is robust agaist additive gaussia oise of SNR 0 db, croppig, resamplig ad requatizatio. Evaluatig our method s robustess over lossy compressio we tested it usig the MP3 ecodig format with a bit rate of 18 Kb/s. I order to optimize the results as high frequecy iformatio is mostly lost usig MP3 we made the appropriate adjustmets cocerig the width of the segmets to be marked as well as the additive value c = c opt (see, Algorithm Embed SiPto-Audio). For most cases the results were positive as despite ot beig able i every case to successfully extract all the elemets of the watermark, usig the properties of self-ivertig permutatios recovery of the iitial watermark ca be successfully operated. Closig the robustess evaluatio of our method, we should poit out that a drawback of our method is actually whe we wat to watermark a audio track with extreme high frequecies; it is somethig that could be ecoutered o future work. Capacity. The capacity of our audio watermark method has bee computed by measurig the percetage of the watermarked parts of a audio track over the legth of the etire audio track. Our method partitios the audio track ito frames, where is the legth of the permutatio π, ad marks oly oe frame of a set of frames; recall that our embeddig method groups the frames ito sets each cotaiig frames (see, Algorithm Embed SiP-to- Audio). That meas, a total over frames are marked, so the ratio of the watermarked part over the etire legth of the audio track is ( ). Thus, our audio watermarkig method has 1 capacity. 6 CONCLUDING REMARKS I this paper we preseted a audio watermarkig techique which efficietly ad ivisibly embeds iformatio, i.e., watermarks, ito a audio digital sigal. Our techique is based o the same mai idea of a recetly proposed image watermarkig techique expadig thus the digital objects that ca be efficietly watermarked through the use of self-ivertig permutatios. We experimetally tested our embeddig ad extractig algorithms o WAV audio sigals. Our testig procedure icludes the phases of embeddig a umerical watermark w = π ito several audio sigals S, storig the watermarked audio S w i WAV format, ad extractig the watermark w = π from the audio S w. We obtaied positive results as the watermarks were ivisible, they did t affect the audio s quality ad they were extractable. The performace evaluatio of our audio watermarkig techique o several other attacks remais a problem for further ivestigatio. REFERENCES Alsalami, M. A. ad Al-Akaidi, M. M. (003). Digital audio watermarkig: survey. De Motfort Uiversity, pages Beder, W., Gruhl, D., ad Morimoto, N. (1996). Techiques for data hidig. I Proc. IBM systems joural, volume 35(3.4), pages Collberg, C. ad Nagra, J. (010). Surreptitious Software. Addiso-Wesley. Cox, I. J., Miller, M. L., Bloom, J. A., Fridrich, J., ad Kalker, T. (008). Digital Watermarkig ad Stegaography. Morga Kaufma, d editio. Golumbic, M. (1980). Algorithmic Graph Theory ad Perfect Graphs. Academic Press, Ic., New York. Gozalez, R. C. ad Woods, R. E. (007). Digital Image Processig. Pretice-Hall, 3rd editio. Grover, D. (1997). The Protectio of Computer Software - Its Techology ad Applicatios. Cambridge Uiversity Press, New York. Hammig, R. W. (1950). Error detectig ad error correctig codes. Bell System Techical Joural, 9(): Hartug, F. ad Kutter, M. (1999). Multimedia watermarkig techiques. I Proceedigs of the IEEE, volume 87(70), pages Igle, V. K. ad Proakis, J. G. (010). Digital Sigal Processig usig Matlab. Cegage Learig, 3rd editio. Sedgewick, R. ad Flajolet, P. (1996). A Itroductio to the Aalysis of Algorithms. Addiso-Wesley. Sharma, S., Rajpurohit, J., ad Dhakar, S. (01). Survey o differet level of audio watermarkig techiques. It l Joural of Comput. Applicatios, 49(10):41 48.