Performance Study on Multimedia Fingerprinting Employing Traceability Codes

Transcription

1 Performane Study on Multimedia Fingerprinting Employing Traeability Codes Shan He and Min Wu University of Maryland, College Park, U.S.A. Abstrat. Digital fingerprinting is a tool to protet multimedia ontent from illegal redistribution by uniquely marking opies of the ontent distributed to eah user. Collusion attak is a powerful attak whereby several differently-fingerprinted opies of the same ontent are ombined together to attenuate or even remove the fingerprint. Coded fingerprinting is one major ategory of fingerprinting tehniques against ollusion. Many fingerprinting odes are proposed with traing apability and ollusion resistane, suh as Traeability (TA) odes and Identifiable Parent Property (IPP) odes. Most of these works treat the important embedding issue in terms of a set of simplified and abstrat assumptions, and they do not examine the end-to-end performane of the oded multimedia fingerprinting. In this paper we jointly onsider the oding and embedding issues and examine the ollusion resistane of oded fingerprinting systems with various ode parameters. Our results show that TA odes generally offer better ollusion resistane than IPP odes, and a TA ode with a larger alphabet size and a longer ode length is preferred. Introdution Tehnology advanement has made multimedia ontent widely available and easy to proess. These benefits also bring ease to unauthorized users who an dupliate and manipulate multimedia ontent, and re-distribute it to a large audiene. The protetion of multimedia ontent beomes inreasingly important. Digital fingerprinting is an emerging tehnology to protet multimedia ontent from unauthorized dissemination, whereby eah user s opy is identified by a unique ID embedded in his/her opy and the ID, whih we all fingerprint, an be extrated to help identify ulprits when a suspiious opy is found. A powerful, ost-effetive attak from a group of users is ollusion attak, where the users ombine their opies of the same ontent to generate a new version. If designed improperly, the fingerprints an be weakened or removed by the ollusion attaks. A growing number of tehniques have been proposed in the literature to provide ollusion resistane in multimedia fingerprinting systems. Many of them fall in one of the two ategories, namely, the non-oded fingerprinting and the oded fingerprinting. The orthogonal fingerprinting is a typial example of non-oded This work was supported in part by the U.S. Offie of Naval Researh under Young Investigator Award N4634 and the U.S. National Siene Foundation under CAREER Award CCR The authors an be ontated via at {shanhe, minwu}@eng.umd.edu.

2 fingerprinting. It assigns eah user a spread spetrum sequene as the fingerprint and the sequenes among users are mutually orthogonal. The ollusion resistane of orthogonal fingerprinting has been well studied by Wang et al. [] and Ergun et al. [2]. Coded fingerprinting employs an expliit oding step to build the fingerprint sequenes. One of the earliest works is by Boneh and Shaw [3], where a two-level ode onstrution known as a -seure ode was proposed to resist up to olluders with a high probability. This binary ode was later used to modulate a diret spread spetrum sequene to embed the fingerprints in multimedia signals [4]. Following Boneh and Shaw s framework, many reent works onsider the onstrution of fingerprinting odes for generi data that have traing apability and are able to resist ollusion. We olletively all these odes traeability odes, whih inlude Identifiable Parent Property (IPP) odes and Traeability (TA) odes []- [9]. In [] and [], TA odes are applied to multimedia fingerprinting and extended to deal with symbol erasures ontributed by noise or ropping in multimedia signal domain. Fernandez and Soriano [2] employ TA odes onstruted through algebrai-geometry odes for fingerprinting multimedia ontent. They define identifiable olluders and propose to employ the Guruswami-Sudan soft-deision list deoding algorithm for algebrai-geometry odes to find suh users. Existing oded fingerprinting mainly fouses on the ode layer and treat the embedding issues through an abstrat model known as the marking assumption [3] []. It typially assumes that olluders an only hange fingerprint symbols where they have different values, and the olluders assemble piees of their odes to generate a olluded version. Although the marking assumption may work well with generi data, it alone is not always appropriate to model multimedia fingerprinting. Both oding and embedding issues need to be onsidered in multimedia fingerprinting. A reent work by Trappe et al. [3] has shown very promising results by this joint onsideration. In their work, a ode based on ombinatorial design was proposed, and eah ode bit is embedded in an overlapped fashion by modulating a spreading sequene that overs the entire multimedia signal. The overlap spreading onfines the types of manipulation from olluders, and olluders an be identified through the ode bits shared by them. In our reent work on oded fingerprinting [4] [] [6], we jointly onsider oding and embedding and have found that oded fingerprinting allows for a muh more effiient detetion than non-oded orthogonal fingerprinting [], but it has rather limited ollusion resistane. Based on this joint onsideration, we propose a Permuted Subsegment Embedding (PSE) tehnique [6] whih substantially improves the ollusion resistane of oded fingerprinting. With this improvement, oded fingerprinting has a better trade-off between ollusion resistane and detetion effiieny than the non-oded fingerprinting. One question The term traeability odes, in a broad sense, refers to the olletion of fingerprinting odes with traing apability, and in a narrow sense, refers to a speifi type of traeability odes that will be disussed later. To avoid onfusion, in this paper, we will use TA odes to represent the narrow-sense traeability odes.

3 that remains to be answered is the effet of the ode parameters on the performane of the fingerprinting systems. In this paper, building upon a ross-layer framework and employing our previously proposed PSE tehnique, we examine the effet of different odes on the ollusion resistane of oded multimedia fingerprinting. The paper is organized as follows. Setion 2 provides a general bakground on oded fingerprinting and reviews fingerprinting odes with emphasis on IPP ode and TA ode. We examine the ollusion resistane of multimedia fingerprinting based on IPP odes and TA odes through analysis and simulations in Setion 3. Finally the onlusions are drawn in Setion 4. 2 Bakground on Coded Fingerprinting for Multimedia 2. System Framework A typial framework for oded multimedia fingerprinting inludes a ode layer and a spread spetrum based embedding layer [4]. For anti-ollusion purposes, the fingerprint ode is onstruted suh that a olluded odeword by a oalition of olluders an be traed bak to one of the olluders. Eah odeword is then assigned to one user as the fingerprint. To embed a odeword, we first partition the host signal into L non-overlapped segments with one segment orresponding to one symbol. Then we build q mutually orthogonal spread spetrum sequenes {w j, j =, 2,..., q} with idential energy w 2 to represent the q possible symbol values in the alphabet. Eah user s fingerprint sequene is onstruted by onatenating the spreading sequenes orresponding to the symbols in his/her odeword. Before the embedding of the spreading sequene, we employ the Permuted Subsegment Embedding (PSE) tehnique proposed in our reent work [6] to get better ollusion resistane. In PSE, eah segment of the fingerprint sequene is partitioned into β subsegments and these subsegments are then randomly permuted aording to a seret key. The permuted fingerprint sequene is added to the host signal with pereptual saling to form the final fingerprinted signal. Fingerprinting Enoding (with alphabet size q) Modulation & PSE Embedding Deoding (with alphabet size q) Extrating & PSE Demodulation Detetion Fingerprinted Multimedia Channel Attaks Suspiious Multimedia Fig.. Framework of traeability ode based fingerprinting sheme

4 After the distribution of the fingerprinted opies, users may ollaborate and mount ost-effetive ollusion attaks. The existing works on oded fingerprinting have primarily targeted ode-level ollusion resistane. The widely onsidered ollusion model is the interleaving ollusion, whereby eah olluder ontributes a non-overlapped set of segments (orresponding to symbols) and these segments are assembled to form a olluded opy. Additional distortion may be added to the multimedia signal during the ollusion, whih we model as additive noise. Sine few olluders would be willing to take higher risk than others, they generally would make ontributions of an approximately equal amount in the ollusion. Another major type of ollusion is done in the signal domain. A typial example is the averaging ollusion [], whereby olluders average the orresponding omponents in their opies to generate a olluded version. The averaging ollusion an be modelled as follows: z = s j + x + d, () j S where z is the olluded signal, x is the host signal, d is the noise term, s j represents the fingerprint sequene for user j, S is the olluder set, and is the number of olluders. For simpliity in analysis, we assume that the additional noise under both ollusions follows i.i.d. Gaussian distribution. At the detetor side, our goal is to ath one olluder with a high probability. We first extrat the fingerprint sequene and inversely permute it aording to the seret key used in the PSE. We then determine the symbol that is most likely to be present in eah multimedia segment using a orrelation detetor ommonly used for spread spetrum embedding [7]. We searh the odebook and identify the olluder to be the one whose odeword has the smallest Hamming distane to the extrated odeword. Alternatively, after the inverse permutation of the fingerprint sequene, we an employ a orrelation detetor to orrelate the entire test signal diretly with every user s fingerprint signal s j. In this ase, the deision is based on the overall orrelation and no intermediate hard deision needs to be made at the symbol level. The user whose fingerprint has the highest orrelation with the test signal is identified as the olluder, i.e. ĵ = arg max j=,2,...,nu T N (j). Here, the detetion statisti T N (j) is defined as: T N (j) = (z x)t s j s 2 j =, 2,..., N u, (2) where z is the olluded signal, x is the original signal whih is often available in fingerprinting appliations, and s = s j for all j based on the equal energy onstrution. Compared with the former 2-step hard-deision sheme, the latter sheme takes advantage of the soft information on the symbol level and provides a better performane. 2.2 Fingerprinting Codes At the ode layer, a ode with traing apability is employed for the purpose of ollusion resistane. In the literatures of fingerprint ode design, odes suh as

5 Identifiable Parent Property(IPP) odes and Traeability(TA) odes are widely studied []- [9]. We briefly review these two kinds of odes in the following. -TA Code A -TA ode satisfies the ondition that any olluded odeword by any (or fewer) olluders has a smaller distane to at least one of these olluders odewords than to the innoent users []. We an onstrut a -TA ode using an established Error Correting Code (ECC), provided that the minimum distane D is large enough and satisfies [] D > ( ) 2 L. (3) Here L is the ode length and is the number of olluders that the ode is intended to resist. With the minimum distane ahieving the Singleton bound, a Reed-Solomon ode is a natural hoie for onstruting a -TA ode. Then, the number of -TA odewords over an alphabet of size q onstruted through a Reed-Solomon ode is N u = q k, where k = L/ 2. -IPP Code A -IPP ode satisfies the ondition that any olluded odeword by a oalition of size at most an be traed bak to at least one member of the oalition []. A -TA ode is a -IPP ode, but a -IPP ode is not neessarily a -TA ode. Therefore, the set of -TA odes is a subset of -IPP odes. In terms of the traeability, the -TA odes are stronger than those -IPP odes that are not -TA odes, whih we all proper -IPP odes. Van Trung et al. propose a method that an be used to onstrut a proper -IPP ode as follows [9]: Let A be an (L 2, N 2, q 2 ) -IPP ode with ode length L 2, odeword number N 2 and alphabet size q 2. Let B be an (L, q 2, q ) -IPP ode with ode length L, odeword number q 2 and alphabet size q. Then the onatenated ode C of A and B is an (L L 2, N 2, q ) -IPP ode with ode length L L 2, odeword number N 2 and alphabet size q. The onatenation of ode A and ode B is done by replaing eah symbol in the alphabet of ode A by a odeword in ode B. Sine a -TA ode is also a -IPP ode, the onstrution of a proper -IPP ode an be done by onatenating two -TA odes. In this paper, we are interested in the omparison of -TA odes with proper -IPP odes. From this point on, for the sake of brevity we use the term -IPP odes to refer to proper -IPP odes. 3 Performane Evaluation In this setion, we ompare the ollusion resistane of fingerprinting systems employing different odes. We try to answer the questions: what kind of ode is better for ollusion resistane and what parameter settings of the odes are favorable for building the fingerprint sequenes? We provide analysis on the relationship between ollusion resistane and ode parameters. Simulations are then used to validate the analysis and onjetures.

6 3. Analysis of Collusion Resistane We measure the ollusion resistane of a fingerprinting system in terms of the probability of athing one olluder, denoted as. To get the analyti approximation, first onsider an ideal fingerprinting system whose fingerprint sequenes have a onstant pairwise orrelation denoted as ρ. Without loss of generality, we assume that the first users perform averaging ollusion. (Notie that with the PSE tehnique, the interleaving ollusion has similar effet to the averaging ollusion. [6]) The vetor of detetion statistis T N s defined in (2) follows a N u -dimensional Gaussian distribution: with T = [T N (),..., T N (N u )] T N([m, m 2 ] T, σdσ) 2 (4) ( ( m = s + ) ) ρ, m 2 = s ρ n, where k is an all one vetor with dimension k-by-, and Σ is an n-by-n matrix whose diagonal elements are s and off-diagonal elements are ρ s, σd 2 is the variane of the noise, m is the mean vetor for olluders, and m 2 is the mean vetor for innoent users. Given the same olluder number and fingerprint strength s, the mean orrelation values with olluders and with innoents are separated more widely for a smaller ρ. This suggests that in the absene of any prior knowledge on ollusion patterns, a smaller ρ leads to a higher olluder detetion probability. Therefore, we prefer fingerprint sequenes with a small pairwise orrelation ρ in the system design. For the oded fingerprinting, the pairwise orrelation an be alulated by examining the ode onstrution. Codes with a larger minimum distane have a smaller upper bound on the orrelation and thus are preferable. This is onsistent with the priniple indiated in (3) to employ odes with large minimum distane. Under the ode onstrution with large minimum distane, the largest pairwise orrelation between the fingerprinting sequenes ρ will be lose to and we an use the above equal pairwise orrelation model with ρ = ρ to approximate the performane of the oded fingerprinting under averaging ollusion. Taking a Reed-Solomon ode based fingerprinting as an example, we alulate its pairwise orrelation. We denote the alphabet size as q, dimension k, and ode length L. The total number of odewords is N u = q k and the minimum distane is D = L k +. We use s i and s j to represent the fingerprint sequenes for user i and user j, respetively, and w im as the orthogonal sequene representing the symbol in user i s odeword at position m with w im = w. The normalized orrelation between s i and s j is < s i, s j > s 2 = < [w iw i2 w il ], [w j w j2 w jl ] > L w 2 L m= = w imwjm T L w 2 L D = k L L ρ. () We an hoose k and L to make ρ lose to to ahieve better ollusion resistane.

7 3.2 Comparisons on Collusion Resistane -IPP odes versus -TA odes Inequality (3) shows the suffiient ondition for a ode to be a -TA ode, and it does not hold for a -IPP ode. Rewriting inequality (3) as L D < L 2, and ombining it with Eqn.(), we an see that a -TA ode has pairwise orrelation ρ < / 2, while -IPP ode has pairwise orrelation ρ > / 2. Aording to the analysis in Setion 3., the fingerprinting system onstruted on -TA ode should have better performane than the fingerprinting system employing -IPP ode. To validate the analysis, we examine the performane of a -IPP ode based fingerprinting system and a -TA ode based fingerprinting system through simulation. For a host signal with length N = 4,, we design two systems that are apable of holding N u = 26 users as follows: System is built upon a 2-IPP ode (4,26,4) with ode length L=4, odeword number N u = 26 and alphabet size q=4. This 2-IPP ode is onstruted through the onatenation of two 2-TA Reed-Solomon odes (8,26,6) and (,6,4) following the method proposed in [9]. The pairwise orrelation of the fingerprint sequenes ρ is.3 aording to Eqn. (). System 2 is built upon a 2-TA Reed-Solomon ode (8,26,6) with ode length L=8, odeword number N u = 26 and alphabet size q=6. The pairwise orrelation ρ is. In both systems, we employ our previously proposed PSE tehnique and hoose the same subsegment size 2 for permutation. We examine the probability of athing one olluder of both systems against interleaving ollusion and averaging ollusion with olluder number ranging from 2 to 3 and Watermarkto-Noise-Ratio() ranging from -2dB to db. The simulation results are shown in Fig. 2. For ease of omparison, we show the ase of = 2dB in Fig. 2(e) and (f). From the results, we an see that under averaging ollusion (Fig. 2(b), (d) and (f)) 2-TA ode based System has 8% gain in the probability of detetion. Under interleaving ollusion (Fig. 2(a), () and (e)), the performane gain an be up to 3%. The results are onsistent with our analysis that due to the low pairwise orrelation among the fingerprint sequenes, 2-TA ode based system outperforms 2-IPP ode based system in all the ases we examined. -TA odes with different parameters From the above omparison results, we an see that the fingerprint sequenes onstruted based on a -TA ode have lower orrelation than the sequenes onstruted based on a -IPP ode. This low orrelation helps defending against ollusion attaks. A TA ode is thus preferred in designing the fingerprint sequenes. A natural question is, that given a host signal and the number of users the system needs to hold, how should we hoose the parameters of TA odes to ahieve good ollusion resistane.

8 2 IPP (4,26,4) beta(,) runn= Interleaving Collusion 2 IPP (4,26,4) beta(,) runn= Averaging Collusion (a) (b) 2 TA (8,26,6) beta(2,2) runn= Interleaving Collusion 2 TA (8,26,6) beta(2,2) runn= Averaging Collusion () 2 IPP and 2 TA ode based FP under Interleaving Collusion at = 2dB (d) 2 IPP and 2 TA ode based FP under Averaging Collusion at = 2dB TA 2 IPP (e) 2 TA 2 IPP (f) Fig. 2. Simulation results for IPP odes and TA odes based fingerprinting systems: the performane of 2-IPP ode based system under (a) interleaving ollusion and (b) averaging ollusion; the performane of 2-TA ode based system under () interleaving ollusion and (d) averaging ollusion. The performane of both systems under (e) interleaving ollusion and (f) averaging ollusion with = 2dB.

9 In the following, we onsider TA odes onstruted on Reed-Solomon odes over alphabet size of q with dimension k. Examining Eqn. () we find that in order to get a small ρ, we an derease k and inrease L. In order to meet the desired number of users N u and redue the dimension k, larger q is preferred. Moreover, for Reed-Solomon ode (inluding extended Reed-Solomon ode), L q+. In order to get larger L, a larger q is also preferred. Therefore, our onjeture is that the fingerprinting system onstruted on a TA ode with a larger alphabet size q and a longer ode length L should have better ollusion resistane. To validate our analysis, we examine the ollusion resistane of the systems with various parameters through simulations. We onstrut three fingerprinting systems as follows: System 3 is built upon a TA ode (, 496, 6) with ode length L =, odeword number N u = 496 and alphabet size q = 6. Aording to Eqn. (), the pairwise orrelation ρ is.3. System 4 is built upon a TA ode (4, 496, 64) with ode length L =4, odeword number N u =496 and alphabet size q =64. The pairwise orrelation ρ is.7. System is built upon a TA ode (62, 496, 64) with ode length L =62, odeword number N u =496 and alphabet size q =64. The pairwise orrelation ρ is.6. System 3 and System 4 have approximately the same ode length but different alphabet size. System 4 and System have the same alphabet size but different ode lengths. All the systems are designed to protet a host signal with length N =, and to aommodate N u = 496 users. We employ the PSE tehnique for the fingerprint embedding, and a subsegment size of is hosen for the permutation. We examine the probability of athing one olluder of all three systems against interleaving ollusion and averaging ollusion, with olluder number ranging from 2 to 2 and ranging from -2dB to db. We show the simulation results in Fig. 3, where the results for = db and -8dB ases are shown separately in Fig. 4 for better illustration. Comparing System 3 and System 4, we observe that under averaging ollusion (Fig. 4(b) and (d)) System 4 with a larger alphabet size has 8% gain in the probability of detetion. The performane gain under interleaving ollusion (Fig. 4(a) and ()) an be as high as 4%. The omparison of System 3 and System 4 shows that with the same ode length and the same subsegment permutation, the system with a larger alphabet size has better performane. Comparing System 4 and System, we an see that under both averaging and interleaving ollusions, System has about a % performane gain due to a longer ode length. This small performane gain is beause in this partiular experimental settings, the pairwise orrelations of both System 4 and are very small and lose to. There is little room for the improvement brought about by the smaller pairwise orrelation of System. The simulation results of all three systems are onsistent with our analysis in Setion 3. in that TA odes with larger alphabet size q and longer ode length L result in fingerprint sequenes with smaller pairwise orrelation, and thus better ollusion resistane.

10 ECCFP Code A (, 496, 6) beta(2,2) runn= Interleaving Collusion ECCFP Code A (, 496, 6) beta(2,2) runn= Averaging Collusion 2 2 (a) ECCFP Code B (4, 496, 64) beta(2,2) runn= Interleaving Collusion 2 2 (b) ECCFP Code B (4, 496, 64) beta(2,2) runn= Averaging Collusion 2 2 () 2 2 (d) ECCFP Code C (62, 496, 64) beta(,) runn= Interleaving Collusion ECCFP Code C (62, 496, 64) beta(,) runn= Averaging Collusion 2 2 (e) 2 2 (f) Fig. 3. Simulation results for systems with different ode parameters under ollusion attaks: System 3 under (a) Interleaving Collusion and (b) Averaging Collusion; System 4 under () Interleaving Collusion and (d) Averaging Collusion; System under (e) Interleaving Collusion and (f) Averaging Collusion.

11 System omparisons under Interleaving Collusion at = db System omparisons under Averaging Collusion at = db System 3 System 4 System System 3 System 4 System (a) System omparisons under Interleaving Collusion at = 8 db (b) System omparisons under Averaging Collusion at = 8 db.3. System 3 System 4 System.3. System 3 System 4 System () (d) Fig. 4. Simulation results for systems with different ode parameters under interleaving and averaging ollusion at = db and -8dB. (a) Interleaving Collusion with = db; (b) Averaging Collusion with = db; () Interleaving Collusion with = -8dB and (d) Averaging Collusion with = -8dB

12 3.3 Disussions The above results show that larger q and L values are preferred in ode onstrution. However, q and L annot be hosen arbitrarily. There are several onstraints on them depending on the ode onstrutions. Speifially, for the Reed-Solomon ode onstrution, we have following onstraints: System requirement on the total user number: q = k N u ; (6) Reed-Solomon ode onstrution onstraint: L q + ; (7) Orthogonality of the FP sequenes for eah segment: q N L. (8) where N is the host signal length, N u is the total number of users, q is the alphabet size and L is the ode length. Taking L as the maximum value q +, we get from (8) that q(q + ) N; (9) whih means the upper bound of q value is roughly on the order of N. Usually, in multimedia fingerprinting the host signal length N >> N u and k 2 for Reed-Solomon odes. Therefore, Eqn. (6) is a more stringent requirement on q. In Eqn. (6), the dimension k an be used to ahieve the desired trade-off between the ollusion resistane and the omputational omplexity in detetion whih is O(qN) aording to our previous study [6]. Notie that the extreme ase of k = redues to orthogonal fingerprinting whih has better ollusion resistane but high omputational omplexity in detetion [6]. Other -TA ode onstrutions an be analyzed in a similar way. It is worth mentioning that the TA ode proposed in [8] an be regarded as a TA ode with dimension k lying between and 2, whih offers a fine adjustment on the trade-off between the ollusion resistane and detetion effiieny. 4 Conlusions In this paper, we examine the ollusion resistane of the oded fingerprinting through jointly onsidering fingerprint enoding, embedding, and detetion. The results show that for a given host signal the pairwise orrelation among fingerprint sequenes is a key indiator of the ollusion resistane, the lower the orrelation the higher the ollusion resistane. Aording to this priniple, -TA odes an be used to introdue a lower orrelation among fingerprint sequenes and thus is preferred over -IPP odes in fingerprint design. Furthermore, a TA ode with a larger alphabet size and a longer ode length an provide better ollusion resistane. The fingerprinting ode onstrution provides a systemati way to introdue the orrelation and to ahieve a desired trade-off between the ollusion resistane and detetion effiieny.

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