Tardos Code Research Articles

Privacy-Preserving Fingerprinting Against Collusion and Correlation Threats in Genomic Data

Sharing genomic databases is critical to the collaborative research in computational biology. A shared database is more informative than specific genome-wide association studies (GWAS) statistics as it enables do-it-yourself calculations. Genomic databases involve intellectual efforts from the curator and sensitive information of participants, thus in the course of data sharing, the curator (database owner) should be able to prevent unauthorized redistributions and protect genomic data privacy. As it becomes increasingly common for a single database be shared with multiple recipients, the shared genomic database should also be robust against collusion attack, where multiple malicious recipients combine their individual copies to forge a pirated one with the hope that none of them can be traced back. The strong correlation among genomic entries also make the shared database vulnerable to attacks that leverage the public correlation models. In this paper, we assess the robustness of shared genomic database under both collusion and correlation threats. To this end, we first develop a novel genomic database fingerprinting scheme, called Gen-Scope. It achieves both copyright protection (by enabling traceability) and privacy preservation (via local differential privacy) for the shared genomic databases. To defend against collusion attacks, we augment Gen-Scope with a powerful traitor tracing technique, i.e., the Tardos codes. Via experiments using a real-world genomic database, we show that Gen-Scope achieves strong fingerprint robustness, e.g., the fingerprint cannot be compromised even if the attacker changes 45% of the entries in its received fingerprinted copy and colluders will be detected with high probability. Additionally, Gen-Scope outperforms the considered baseline methods. Under the same privacy and copyright guarantees, the accuracy of the fingerprinted genomic database obtained by Gen-Scope is around 10% higher than that achieved by the baseline, and in terms of preservations of GWAS statistics, the consistency of variant-phenotype associations can be about 20% higher. Notably, we also empirically show that Gen-Scope can identify at least one of the colluders even if malicious receipts collude after independent correlation attacks.

Boneh-Shaw fingerprint code and Tardos code analysis and optimization in minority collusion attack

Fingerprint codes are required to protect digital rights. These codes were embedded in digital media before distribution. Each of these digital media codes is unique. These codes identify pirated digital media copies. This method is used to identify the creator of an illegal copy. But such principles tend to be collectively attacked. In the Collusion Attack, criminal users conspired to integrate the attacks into these codes.Criminal users devise and switch digital fingerprint media with different codes to print the same content. The code is modified to accuse the innocent user. Thus, this attack is a threat to the protection of digital rights.The minority collusion assault being conducted against the Boneh-Shaw and Tardos codes to assess how serious this threat is can be used to demonstrate the significance of the research. Understanding these ideas is essential for improving the protection of digital rights in the face of changing security issues in the digital sphere. This study launches a minority collusion attack against both the Tardos code and the Boneh-Shaw fingerprint code to analyze the impact. The development of more resilient, adaptable codes to prevent changing collusion strategy is part of the prospective focus for Boneh-Shaw Fingerprint Code and Tardos Code Analysis and Optimization in Minority Collusion Attacks.

Near-Optimal Detection for Binary Tardos Code by Estimating Collusion Strategy

A previously proposed optimal detector for bias-based fingerprinting codes such as Tardos and Nuida requires two kinds of important information: the number of colluders and the collusion strategy used to generate the pirated codeword. An estimator has now been derived for these two parameters. The bias in the pirated codeword is measured by observing the number of zeros and ones and compared with possible bias patterns calculated using information about the collusion strategy and number of colluders. Computer simulation demonstrated that the collusion strategy and number of colluders can be estimated with high probability and that the traceability of a detector using the proposed estimator is extremely close to being optimal.

A two-stage traitor tracing scheme for hierarchical fingerprints

The multimedia traitor tracing field involves the embedding of a collusion secure fingerprint in the host signal to retrieve and prevent any multimedia content fraud. Trendy work aims at providing a tracing system which offers a good protection of the digital content and an efficient tracing process. These challenges depend on reducing the length of the embedded fingerprint and the complexity of the accusation process. Furthermore, addressing these issues becomes more and more relevant in media distribution applications involving an important number of users. In this paper, we propose a secure fingerprinting system based on a two-stage tracing strategy which combines two probabilistic tracing codes: Boneh Shaw with replication scheme and Tardos codes. This strategy is applied to a multilevel hierarchical fingerprint which is then embedded using a DCT-based audio watermarking technique. By taking the advantage of grouping users and applying a weight-based tracing process, the proposed fingerprinting system offers to reduce efficiently the computational costs of the tracing time. It has also a good robustness to different types of attacks. We have carried out different tests to evaluate the performance of the system in terms of robustness and imperceptibility. The experimental results show that the proposed fingerprinting system provides a suitable solution to the the infringement copyright problem in multimedia distribution platforms by reducing significantly the users’ retrieval space and performing good detection results in a reduced time.

Anticollusion solutions for asymmetric fingerprinting protocols based on client side embedding

In this paper, we propose two different solutions for making a recently proposed asymmetric fingerprinting protocol based on client-side embedding robust to collusion attacks. The first solution is based on projecting a client-owned random fingerprint, securely obtained through existing cryptographic protocols, using for each client a different random matrix generated by the server. The second solution consists in assigning to each client a Tardos code, which can be done using existing asymmetric protocols, and modulating such codes using a specially designed random matrix. Suitable accusation strategies are proposed for both solutions, and their performance under the averaging attack followed by the addition of Gaussian noise is analytically derived. Experimental results show that the analytical model accurately predicts the performance of a realistic system. Moreover, the results also show that the solution based on independent random projections outperforms the solution based on Tardos codes, for different choices of parameters and under different attack models.

False positive probabilities in q-ary Tardos codes: comparison of attacks

We investigate false positive (FP) accusation probabilities for q-ary Tardos codes in the Restricted Digit Model. We employ a computation method recently introduced by us, to which we refer as Convolution and Series Expansion (CSE). We present a comparison of several collusion attacks on q-ary codes: majority voting, minority voting, Interleaving, μ~-minimizing and Random Symbol (the q-ary equivalent of the Coin Flip strategy). The comparison is made by looking at the FP rate at approximately fixed False Negative rate. In nearly all cases we find that the strongest attack is either minority voting or μ~-minimizing, depending on the exact setting of parameters such as alphabet size, code length, and coalition size. Furthermore, we present results on the convergence speed of the CSE method, and we show how FP rate computations for the Random Symbol strategy can be sped up by a pre-computation step.

False Negative probabilities in Tardos codes

Forensic watermarking is the application of digital watermarks for the purpose of tracing unauthorized redistribution of content. One of the most powerful types of attack on watermarks is the collusion attack, in which multiple users compare their differently watermarked versions of the same content. Collusion-resistant codes have been developed against these attacks. One of the most famous such codes is the Tardos code. It has the asymptotically optimal property that it can resist \(c\) attackers with a code of length proportional to \(c^2\). Determining error rates for the Tardos code and its various extensions and generalizations turns out to be a nontrivial problem. In recent work we developed an approach called the convolution and series expansion (CSE) method to accurately compute false positive accusation probabilities. In this paper we extend the CSE method in order to make it possible to compute a bound on the False Negative accusation probabilities.

Binary and $$q$$ q -ary Tardos codes, revisited

The Tardos code is a much studied collusion-resistant fingerprinting code, with the special property that it has asymptotically optimal length $$m\propto c_0^2$$ m ? c 0 2 , where $$c_0$$ c 0 is the number of colluders. In this paper we give alternative security proofs for the Tardos code, working with the assumption that the strongest coalition strategy is position-independent. We employ the Bernstein inequality and Bennett inequality instead of the typically used Markov inequality. This proof technique requires fewer steps and slightly improves the tightness of the bound on the false negative error probability. We present new results on code length optimization, for both small and asymptotically large coalition sizes.

H.264/AVC video watermarking for active fingerprinting based on Tardos code

In this paper, we present a novel approach for active fingerprinting of state-of-the-art video codec H.264/AVC. Tardos probabilistic fingerprinting code is embedded in H.264/AVC video signals using spread spectrum watermarking technique in both luma and chroma. Tardos code is embedded in intra as well as inter frames. The embedding has been performed in the nonzero quantized transformed coefficients, which are above a certain threshold while taking into account the reconstruction loop, to avoid the uncontrollable increase in bitrate of video bitstream. A comprehensive analysis of payload and PSNR trade-off is presented for the benchmark video sequences. Different linear and nonlinear collusion attacks have been performed in the pixel domain to show the robustness of the proposed approach.

Impacts of Watermarking Security on Tardos-Based Fingerprinting

<?Pub Dtl=""?> This paper presents a study of the embedding of Tardos binary fingerprinting codes with watermarking techniques. By taking into account the security of the embedding scheme, we present a new approach for colluding strategies which relies on the possible estimation error rate of the code symbols (denoted <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\epsilon$</tex> </formula> ). We derive a new attack strategy called “ <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\epsilon$</tex></formula> -Worst Case Attack” and show its efficiency using the computation of achievable rates for simple decoding. Then we consider the interplay between security and robustness regarding the accusation performances of the fingerprinting scheme and show that 1) for the same accusation rate secure schemes can afford to be less robust than insecure ones, and 2) that secure schemes enable to cast the Worst Case Attack into an interleaving attack. Additionally, we use the security analysis of the watermarking scheme to derive from <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\epsilon$</tex></formula> a security attack for a fingerprinting scheme based on Tardos codes and a new scheme called stochastic spread-spectrum watermarking. We compare a removal attack against an AWGN robustness attack and we show that for the same distortion, the combination of a fingerprinting attack and a security attack easily outperform classical attacks even with a small number of observations.

Short collusion-secure fingerprint codes against three pirates

In this article, we propose a new construction of probabilistic collusion-secure fingerprint codes against up to three pirates and give a theoretical security evaluation. Our pirate tracing algorithm combines a scoring method analogous to Tardos codes (J. ACM, 2008) with an extension of parent search techniques of some preceding 2-secure codes. Numerical examples show that our code lengths are significantly shorter than (about 30% to 40% of) the shortest known c-secure codes by Nuida et al. (Des. Codes Cryptogr., 2009) with c = 3. Some preliminary proposal for improving efficiency of our tracing algorithm is also given.

Accusation probabilities in Tardos codes: beyond the Gaussian approximation

We study the probability distribution of user accusations in the q-ary Tardos fingerprinting system under the Marking Assumption, in the restricted digit model. In particular, we look at the applicability of the so-called Gaussian approximation, which states that accusation probabilities tend to the normal distribution when the fingerprinting code is long. We introduce a novel parametrization of the attack strategy which enables a significant speedup of numerical evaluations. We set up a method, based on power series expansions, to systematically compute the probability of accusing innocent users. The `small parameter' in the power series is 1/m, where m is the code length. We use our method to semi-analytically study the performance of the Tardos code against majority voting and interleaving attacks. The bias function `shape' parameter $${{\kappa}}$$ strongly influences the distance between the actual probabilities and the asymptotic Gaussian curve. The impact on the collusion-resilience of the code is shown. For some realistic parameter values, the false accusation probability is even lower than the Gaussian approximation predicts.

Tardos Fingerprinting Codes in the Combined Digit Model

We formalize a new attack model for collusion secure codes, incorporating attacks on the underlying watermarking scheme as well as cut-and-paste attacks traditionally considered for collusion secure codes. We use this model to analyze the collusion resistance of two versions of the Tardos code, both for binary and nonbinary alphabets. The model allows us to consider different signal processing attacks on the content, namely the addition of noise and averaging attacks. The latter may result in content segments that have multiple watermarks embedded. We study two versions of the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$q$</tex></formula> -ary Tardos code in which the accusation method has been modified so as to allow for the detection of multiple symbols in the same content segment. We show that both variants yield efficient codes in the new model, parametrized for realistic attacker strengths.

Décodage EM du code de Tardos pour le fingerprinting

This paper presents our recent work on multimedia fingerprinting, also known as traitor tracing. We focus on deriving a better accusation process for the well known Tardos codes. It appears that Tardos orginal decoding is very conservative: its performances are guaranteed whatever the collusion strategy. Indeed, major improvements stem from the knowledge of the collusion strategy. Therefore, this paper investigates how it is possible to learn and adapt to the collusion strategy. Our solution is based on an iterative algorithm a la EM, where a better estimation of the collusion strategy yields a better tracing of the colluders, which in return yields a better estimation of the collusion strategy etc.

An improvement of discrete Tardos fingerprinting codes

It has been proven that the code lengths of Tardos's collusion-secure fingerprinting codes are of theoretically minimal order with respect to the number of adversarial users (pirates). However, the code lengths can be further reduced as some preceding studies have revealed. In this article we improve a recent discrete variant of Tardos's codes, and give a security proof of our codes under an assumption weaker than the original Marking Assumption. Our analysis shows that our codes have significantly shorter lengths than Tardos's codes. For example, when c = 8, our code length is about 4.94% of Tardos's code in a practical setting and about 4.62% in a certain limit case. Our code lengths for large c are asymptotically about 5.35% of Tardos's codes.

An Efficient 2-Secure and Short Random Fingerprint Code and Its Security Evaluation

The code length of Tardos's collusion-secure fingerprint code is of theoretically minimal order with respect to the number of adversarial users (pirates). However, the constant factor should be further reduced for practical implementation. In this article, we improve the tracing algorithm of Tardos's code and propose a 2-secure and short random fingerprint code, which is secure against collusion attacks by two pirates. Our code length is significantly shorter than that of Tardos's code and its tracing error probability is practically small.