Multimedia Fingerprinting Research Articles

Complete traceability multimedia fingerprinting codes resistant to averaging attack and adversarial noise with optimal rate

In this paper we consider complete traceability multimedia fingerprinting codes resistant to averaging attacks and adversarial noise. Recently it was shown that there are no such codes for the case of an arbitrary linear attack. However, for the case of averaging attacks complete traceability multimedia fingerprinting codes of exponential cardinality resistant to constant adversarial noise were constructed in Egorova et al. (Probl Inf Transm 56(4):388–398, 2020). We continue this work and provide an improved lower bound on the rate of these codes.

Combinatorial secure codes for copyright protection and related problems

The rapid development of modern science and technology not only provides convenience for data communication, but also poses a tremendous threat to the copyright of digital content. This paper focuses on the mathematical theory of traitor-tracing for copyright protection and its latest progress. First, for applications in different scenarios, such as broadcast encryption and multimedia fingerprinting, weintroduce unified models to characterize the (key/fingerprint) distribution schemes with traceability property and frameproof property, respectively. Next, we review several classes of combinatorial secure codes with the traceability property and frameproof property, and the combinatorial methods used to investigate the bounds on the maximum code size and the explicit constructions, as well as the latest results and the open problems. The relationships between the combinatorial problems in copyright protection and the related problems in group testing and multiple access communication are discussed as well.

Existence and Construction of Complete Traceability Multimedia Fingerprinting Codes Resistant to Averaging Attack and Adversarial Noise

It was shown very recently in [1] that there are no multimedia digital fingerprinting codes capable of fully recovering a coalition of malicious users under the general linear attack and adversarial noise. We show that such codes exist if the class of attacks is narrowed to the averaging attack. The arising mathematical problem is close to the problem of constructing signature codes for a noisy binary adder channel.

Signature Codes for Weighted Binary Adder Channel and Multimedia Fingerprinting

In this paper, we study the signature codes for weighted binary adder channel (WbAC) and collusion-resistant multimedia fingerprinting. Let $A(n,t)$ denote the maximum cardinality of a $t$-signature code of length $n$, and $A(n,w,t)$ denote the maximum cardinality of a $t$-signature code of length $n$ and constant weight $w$. First, we derive asymptotic and general upper bounds of $A(n,t)$ by relating signature codes to $B_t$ codes and bipartite graphs with large girth respectively, and also show the upper bounds are tight for certain cases. Second, we determine the exact values of $A(n,2,2)$ and $A(n,3,2)$ for infinitely many $n$ by connecting signature codes with $C_4$-free graphs and union-free families, respectively. Third, we provide two explicit constructions for $t$-signature codes which have efficient decoding algorithms and applications to two-level signature codes. Furthermore, we show from the geometric viewpoint that there does not exist any binary code with complete traceability for noisy WbAC and multimedia fingerprinting. A new type of signature codes with a weaker requirement than complete traceability is introduced for the noisy scenario.

Multimedia IPP codes with efficient tracing

Binary multimedia identifiable parent property codes (binary $t$-MIPPCs) are used in multimedia fingerprinting schemes where the identification of users taking part in the averaging collusion attack to illegally redistribute content is required. In this paper, we first introduce a binary strong multimedia identifiable parent property code (binary $t$-SMIPPC) whose tracing algorithm is more efficient than that of a binary $t$-MIPPC. Then a composition construction for binary $t$-SMIPPCs from $q$-ary $t$-SMIPPCs is provided. Several infinite series of optimal $q$-ary $t$-SMIPPCs of length $2$ with $t = 2, 3$ are derived from the relationships among $t$-SMIPPCs and other fingerprinting codes, such as $\overline{t}$-separable codes and $t$-MIPPCs. Finally, combinatorial properties of $q$-ary $2$-SMIPPCs of length $3$ are investigated, and optimal $q$-ary $2$-SMIPPCs of length $3$ with $q \equiv 0, 1, 2, 5 \pmod 6$ are constructed.

Improved Bounds for Separable Codes and $B_2$ Codes

Separable codes and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> codes are combinatorial structures which could be applied to identify traitors in multimedia fingerprinting and to uniquely decode messages in multiple access communication respectively. In this letter we provide new lower and upper bounds for the largest code rates of q-ary separable codes and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> codes, which improve the existing results when the alphabet size q is relatively small.

Probabilistic Existence Results for Parent-Identifying Schemes

Parent-identifying schemes provide a way to identify causes from effects for some information systems such as digital fingerprinting and group testing. In this paper, we consider combinatorial structures for parent-identifying schemes. First, we establish an equivalent relationship between parent-identifying schemes and forbidden configurations. Based on this relationship, we derive probabilistic existence lower bounds for two related combinatorial structures, that is, $t$-parent-identifying set systems ($t$-IPPS) and $t$-multimedia parent-identifying codes ($t$-MIPPC), which are used in broadcast encryption and multimedia fingerprinting respectively. The probabilistic lower bound for the maximum size of a $t$-IPPS has the asymptotically optimal order of magnitude in many cases, and that for $t$-MIPPC provides the asymptotically optimal code rate when $t=2$ and the best known asymptotic code rate when $t\geq 3$. Furthermore, we analyze the structure of $2$-IPPS and prove some bounds for certain cases.

Signature codes for weighted noisy adder channel, multimedia fingerprinting and compressed sensing

We propose a new approach to construct noise-resistant multimedia fingerprinting codes. Our approach is based on the theory of the signature codes for multiple access channels, mainly, for a weighted noisy adder channel. The corresponding multimedia fingerprinting codes allow to trace the entire coalition of pirates. The codes provide significantly better rate than previously known multimedia fingerprinting schemes. We establish the relationship between multimedia fingerprinting and compressed sensing problems.

Signature codes for weighted noisy adder channel, multimedia fingerprinting and compressed sensing

We propose a new approach to construct noise-resistant multimedia fingerprinting codes. Our approach is based on the theory of the signature codes for multiple access channels, mainly, for a weighted noisy adder channel. The corresponding multimedia fingerprinting codes allow to trace the entire coalition of pirates. The codes provide significantly better rate than previously known multimedia fingerprinting schemes. We establish the relationship between multimedia fingerprinting and compressed sensing problems.

Bounds and constructions for 3 ¯ $\overline {3}$ -strongly separable codes with length 3

Separable code (SC, Cheng and Miao IEEE Trans. Inf. Theory 57, 4843–4851, 2011), frameproof code (FPC, Boneh and Shaw IEEE Trans. Inf. Theory 44, 1897–1905, 1998) and strongly separable code (SSC, Jiang et al. Des. Codes Cryptogr. 79:303–318, 2016) are used to construct anti-collusion codes. SSC is better than FPC and SC in the applications for multimedia fingerprinting since SSC has lower identifying complexity than that of SC (the same complexity as FPC) and weaker structure than that of FPC. In this paper, we first derive several upper bounds on the number of codewords of a $\overline {t}$ -SSC. Then we focus on $\overline {3}$ -SSCs with codeword length 3 and obtain the following two main results: (1) An equivalence between an SSC and an SC is derived; (2) An improved lower bound Ω(q 5/3 + q 4/3 − q) on the size of a q-ary SSC when $q={q_{1}^{6}}$ for any prime power q 1 ≡ 1 (mod 6), which is better than the previously known bound $\lfloor \sqrt {q}\rfloor ^{3}$ , is obtained by means of a difference matrix and a known result on the subsets of $\mathbb {F}^{n}_{q}$ containing no three points on a line.

Codes with the identifiable parent property for multimedia fingerprinting

Let ${\cal C}$ be a $q$-ary code of length $n$ and size $M$, and ${\cal C}(i) = \{{\bf c}(i) \ | \ {\bf c}=({\bf c}(1), {\bf c}(2), \ldots, {\bf c}(n))^{T} \in {\cal C}\}$ be the set of $i$th coordinates of ${\cal C}$. The descendant code of a sub-code ${\cal C}^{'} \subseteq {\cal C}$ is defined to be ${\cal C}^{'}(1) \times {\cal C}^{'}(2) \times \cdots \times {\cal C}^{'}(n)$. In this paper, we introduce a multimedia analogue of codes with the identifiable parent property (IPP), called multimedia IPP codes or $t$-MIPPC$(n, M, q)$, so that given the descendant code of any sub-code ${\cal C}^{'}$ of a multimedia $t$-IPP code ${\cal C}$, one can always identify, as IPP codes do in the generic digital scenario, at least one codeword in ${\cal C}^{'}$. We first derive a general upper bound on the size $M$ of a multimedia $t$-IPP code, and then investigate multimedia $3$-IPP codes in more detail. We characterize a multimedia $3$-IPP code of length $2$ in terms of a bipartite graph and a generalized packing, respectively. By means of these combinatorial characterizations, we further derive a tight upper bound on the size of a multimedia $3$-IPP code of length $2$, and construct several infinite families of (asymptotically) optimal multimedia $3$-IPP codes of length $2$.

Asymptotically optimal 2 ¯ $\overline {2}$ -separable codes with length 4

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. Separable codes can be used to construct fingerprints resistant to the averaging collusion attack on multimedia contents. In this paper, we first show an equivalent condition of a $\overline {2}$ -SC (4,M,q), and then construct two infinite families of $\overline {2}$ -SCs of length 4, one of which is asymptotically optimal.

Secure social multimedia content distribution based on social network analysis

Multimedia fingerprinting is an effective technique to trace traitor who redistribute copyrighted social multimedia contents. However, several traitors can make an average collusion attack with their fingerprinted copies to avoid to be traced by digital fingerprints; furthermore, the commercial value of the colluded fingerprinted copy is often time-sensitive in social networks. The earlier the colluded content being redistributed in social network, the more profit the colluder will make from it. In this paper, a new desynchronisation fingerprinting is proposed. Random grid templates are used to produce desynchronised copies. This research has dealt with random distortions due to local geometric transformations of random grid template of image based on chaos, and then the processed fingerprinted content is distributed using social network analysis. The experimental results show that the average collusion will produce collude copy with low commercial value, and although colluders can try to use image registration to resynchronisation with expensive computational cost, and the visual quality does not improve with the increase of the number of copies.

Secure social multimedia content distribution based on social network analysis

Multimedia fingerprinting is an effective technique to trace traitor who redistribute copyrighted social multimedia contents. However, several traitors can make an average collusion attack with their fingerprinted copies to avoid to be traced by digital fingerprints; furthermore, the commercial value of the colluded fingerprinted copy is often time-sensitive in social networks. The earlier the colluded content being redistributed in social network, the more profit the colluder will make from it. In this paper, a new desynchronisation fingerprinting is proposed. Random grid templates are used to produce desynchronised copies. This research has dealt with random distortions due to local geometric transformations of random grid template of image based on chaos, and then the processed fingerprinted content is distributed using social network analysis. The experimental results show that the average collusion will produce collude copy with low commercial value, and although colluders can try to use image registration to resynchronisation with expensive computational cost, and the visual quality does not improve with the increase of the number of copies.

Strongly separable codes

Binary $t$-frameproof codes ($t$-FPCs) are used in multimedia fingerprinting schemes where the identification of authorized users taking part in the averaging collusion attack is required. In this paper, a binary strongly $\bar{t}$-separable code ($\bar{t}$-SSC) is introduced to improve such a scheme based on a binary $t$-FPC. A binary $\bar{t}$-SSC has the same traceability as a binary $t$-FPC but has more codewords than a binary $t$-FPC. A composition construction for binary $\bar{t}$-SSCs from $q$-ary $\bar{t}$-SSCs is described, which stimulates the research on $q$-ary $\bar{t}$-SSCs with short length. Several infinite series of optimal $q$-ary $\bar{2}$-SSCs of length $2$ are derived from the fact that a $q$-ary $\bar{2}$-SSC of length $2$ is equivalent to a $q$-ary $\bar{2}$-separable code of length $2$. Combinatorial properties of $q$-ary $\bar{2}$-SSCs of length $3$ are investigated, and a construction for $q$-ary $\bar{2}$-SSCs of length $3$ is provided. These $\bar{2}$-SSCs of length $3$ have more than $12.5\%$ codewords than $2$-FPCs of length $3$ could have.

New Bounds on Separable Codes for Multimedia Fingerprinting

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia contents. Separable codes were introduced to detect colluders taking part in the averaging attack, which is the most feasible approach to perform a collusion attack. In this paper, we provide some improved bounds for the size of separable codes. Using a combinatorial technique named grouping coordinates, we have greatly reduced the upper bound. On the other hand, we also provide some lower bounds for the size of separable codes by both probabilistic and deterministic construction methods. In particular, 2̅-separable codes with asymptotically optimal rate are obtained by the deletion method.

New bounds on $$\bar{2}$$ 2 ¯ -separable codes of length 2

Let $$\mathbb{C }$$ be a code of length $$n$$ over an alphabet of $$q$$ letters. The descendant code $$\mathsf{desc}(\mathbb C _0)$$ of $$\mathbb C _0 = \{\mathbf{c}^1, \mathbf{c}^2, \ldots , \mathbf{c}^t\} \subseteq \mathbb{C }$$ is defined to be the set of words $$\mathbf{x} = (x_1, x_2, \ldots ,x_n)$$ such that $$x_i \in \{c^1_i, c^2_i, \ldots , c^t_i\}$$ for all $$i=1, \ldots , n$$ . $$\mathbb{C }$$ is a $$\overline{t}$$ -separable code if for any two distinct $$\mathbb{C }_1, \mathbb{C }_2 \subseteq \mathbb{C }$$ such that $$|\mathbb{C }_1| \le t$$ , $$|\mathbb{C }_2| \le t$$ , we always have $$\mathsf{desc}(\mathbb{C }_1) \ne \mathsf{desc}(\mathbb{C }_2)$$ . The study of separable codes is motivated by questions about multimedia fingerprinting for protecting copyrighted multimedia data. Let $$M(\overline{t},n,q)$$ be the maximal possible size of such a separable code. In this paper, we provide an improved upper bound for $$M(\overline{2},2,q)$$ by a graph theoretical approach, and a new lower bound for $$M(\overline{2},2,q)$$ by deleting suitable points and lines from a projective plane, which coincides with the improved upper bound in some places. This corresponds to the bounds of maximum size of bipartite graphs with girth $$6$$ and a construction of such maximal bipartite graphs.

Cooperation and Coalition in Multimedia Fingerprinting Colluder Social Networks

Users in multimedia social networks actively interact with each other. It is crucial to study the complex user dynamics and analyze its impact on the performance of multimedia social networks. This paper uses multimedia fingerprinting as an example and studies user dynamics in colluder social networks. During collusion, a group of attackers collectively attack multimedia fingerprinting system and use multimedia content illegally. This paper analyzes the incentives of cooperation among attackers and investigates how colluders form their coalitions to maximize their payoffs. We present a game-theoretic framework to model the complex dynamics among colluders, analyze when attackers cooperate with each other, and investigate how a colluder selects his/her fellow attackers to maximize his/her own payoff. We analyze multiuser collusion in two scenarios: when all attackers receive fingerprinted copies of the same resolution, and when they have copies of different resolutions. The proposed framework considers both the colluders' risk of being detected by the digital rights enforcer and the reward received from illegal usage of multimedia content. Our analysis shows that in both scenarios, colluding with more attackers does not always increase an attacker's utility, and attackers may not always want to cooperate with each other. We first examine the necessary conditions for attackers to collude together, and study how they select the collusion parameters such that cooperation benefits all colluders. We then study how the number of colluders affects each attacker's utility, and investigate the optimum strategy that an attacker should use to select fellow attackers and to form a coalition in order to maximize his or her own payoff.

Separable Codes

Multimedia fingerprinting is an effective technique to trace the sources of pirate copies of copyrighted multimedia information. Separable codes can be used to construct fingerprints resistant to the averaging collusion attack on multimedia contents. In this paper, we investigate -separable codes from a combinatorial point of view. We first derive several upper bounds on the sizes of -separable codes, and then turn our attention to the constructions of optimal -separable codes with short length. Two infinite families of optimal -separable codes of length 2 are constructed from projective planes, and all optimal -separable codes of length 3 are explicitly constructed by means of difference matrices. These optimal -separable codes with short length can be used to construct good -separable codes with long length by a known composition construction.

A multimedia digital fingerprinting scheme for resisting average attack

A multimedia digital fingerprinting scheme for resisting average attack