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Saddle-point Solution of the Fingerprinting Capacity Game Under the Marking Assumption
"... Abstract — We study a fingerprinting game in which the collusion channel is unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value o ..."
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Abstract — We study a fingerprinting game in which the collusion channel is unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maxmin games with mutual information as the payoff function. However, these games generally do not admit saddle-points and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point. If the coalition size is k and the fingerprint alphabet is binary, we derive equations that can solve the capacity game for arbitrary k. We also show that the capacity Ck,2 satisfies (k 2 2 ln 2) −1 ≤ Ck,2 ≤ (k 2 ln 2) −1. By examining the saddle-point solutions for small k, we conjecture that the lower bound is asymptotically tight. I.
WORST CASE ATTACKS AGAINST BINARY PROBABILISTIC TRAITOR TRACING CODES
"... This article deals with traitor tracing which is also known as active fingerprinting, content serialization, or user forensics. We study the impact of worst case attacks on the well-known Tardos binary probabilistic traitor tracing code, and especially its optimum setups recently advised by Amiri an ..."
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This article deals with traitor tracing which is also known as active fingerprinting, content serialization, or user forensics. We study the impact of worst case attacks on the well-known Tardos binary probabilistic traitor tracing code, and especially its optimum setups recently advised by Amiri and Tardos, and by Huang and Moulin. This paper assesses that these optimum setups are robust in the sense that a discrepancy between the foreseen numbers of colluders and its actual value doesn’t spoil the achievable rate of a joint decoder. On the other hand, this discrepancy might have a dramatic impact on a simple decoder. Since the complexity of the today’s joint decoder is prohibitive, this paper mitigates the impact of the optimum setups in current realizable schemes. Index Terms — Traitor tracing, Tardos codes, worst case attack, achievable rate. 1.
Optimal symmetric Tardos traitor tracing schemes
- DES. CODES CRYPTOGR.
, 2012
"... For the Tardos traitor tracing scheme, we show that by combining the symbol-symmetric accusation function of Skoric et al. with the improved analysis of Blayer and Tassa we get further improvements. Our construction gives codes that are up to 4 times shorter than Blayer and Tassa’s, and up to 2 time ..."
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Cited by 15 (8 self)
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For the Tardos traitor tracing scheme, we show that by combining the symbol-symmetric accusation function of Skoric et al. with the improved analysis of Blayer and Tassa we get further improvements. Our construction gives codes that are up to 4 times shorter than Blayer and Tassa’s, and up to 2 times shorter than the codes from Skoric et al. Asymptotically, we achieve the theoretical optimal code-length for Tardos’ distribution function and the symmetric score function. For large coalitions, our codelengths are asymptotically about 4.93 % of Tardos’ original code-lengths, which also improves upon results from Nuida et al.
On the Saddle-point Solution and the Large-coalition Asymptotics Of Fingerprinting Games
, 2011
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EM decoding of Tardos traitor tracing codes
"... This paper proposes a major shift in the decoding of probabilistic Tardos traitor tracing code. The goal of the decoder is to accuse colluders but it ignores how they have been mixing their copies in order to forge the pirated content. As originally proposed by Tardos, so far proposed decoders are a ..."
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Cited by 9 (3 self)
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This paper proposes a major shift in the decoding of probabilistic Tardos traitor tracing code. The goal of the decoder is to accuse colluders but it ignores how they have been mixing their copies in order to forge the pirated content. As originally proposed by Tardos, so far proposed decoders are agnostic and their performances are stable with respect to this unknown collusion attack. However, this stability automatically leads to non-optimality from a detection theory perspective. This is the reason why this paper proposes to estimate the collusion attack in order to approximate the optimal matched decoder. This is done iteratively thanks to the application of the well-known Expectation-Maximization algorithm. We have dropped the stability: the power of our decoding algorithm deeply depends on the collusion attack. Some attacks are worse than others. However, even for the worst collusion channel, our decoder performs better than the original Tardos decoding.
A Capacity-Achieving Simple Decoder for Bias-Based Traitor Tracing Schemes
"... Abstract—We investigate alternative suspicion functions for bias-based traitor tracing schemes, and present a practical construction of a simple decoder that attains capacity in the limit of large coalition size c. We derive optimal suspicion functions in both the Restricted-Digit Model and the Comb ..."
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Cited by 7 (2 self)
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Abstract—We investigate alternative suspicion functions for bias-based traitor tracing schemes, and present a practical construction of a simple decoder that attains capacity in the limit of large coalition size c. We derive optimal suspicion functions in both the Restricted-Digit Model and the Combined-Digit Model. These functions depend on information that is usually not available to the tracer – the attack strategy or the tallies of the symbols received by the colluders. We discuss how such results can be used in realistic contexts. We study several combinations of coalition attack strategy versus suspicion function optimized against some attack (another attack or the same). In many of these combinations the usual codelength scaling ℓ ∝ c 2 changes to a lower power of c, e.g. c 3/2. We find that the interleaving strategy is an especially powerful attack. The suspicion function tailored against interleaving is the key ingredient of the capacity-achieving construction. Index Terms—Collusion resistance, traitor tracing. I.
Optimal Suspicion Functions for Tardos Traitor Tracing Schemes
"... We investigate alternative suspicion functions for Tardos traitor tracing schemes. In the simple decoder approach (computation of a score for every user independently) we derive suspicion functions that optimize a performance indicator related to the sufficient code length ℓ in the limit of large co ..."
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Cited by 6 (2 self)
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We investigate alternative suspicion functions for Tardos traitor tracing schemes. In the simple decoder approach (computation of a score for every user independently) we derive suspicion functions that optimize a performance indicator related to the sufficient code length ℓ in the limit of large coalition size c. Our results hold for the Restricted-Digit Model as well as the Combined-Digit Model. The scores depend on information that is usually not available to the tracer – the attack strategy or the tallies of the symbols received by the colluders. We discuss how such results can be used in realistic contexts. We study several combinations of coalition attack strategy vs. suspicion function optimized against some attack (another attack or the same). In many of these combinations the usual scaling ℓ ∝ c 2 is replaced by a lower power of c, e.g. c 3/2. We find that the interleaving strategy is an especially powerful attack, and the suspicion function tailored against interleaving is effective against all considered attacks.
BLIND DECODER FOR BINARY PROBABILISTIC TRAITOR TRACING CODES
"... This paper presents a new decoder for probabilistic binary traitor tracing codes which is based on classical hypothesis testing and estimation theory. This new decoder is blind, in the sense of ignoring a priori the collusion attack it is facing. It basically performs a joint estimation of the collu ..."
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Cited by 6 (4 self)
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This paper presents a new decoder for probabilistic binary traitor tracing codes which is based on classical hypothesis testing and estimation theory. This new decoder is blind, in the sense of ignoring a priori the collusion attack it is facing. It basically performs a joint estimation of the collusion channel and the probability that each user takes part in the collusion. The experimental results shown in the paper have been obtained with the classical Tardos code, although the proposed decoder works with arbitrary probabilistic binary codes. Another remarkable advantage of this blind decoder is its ability to successfully cope with collusion channels far more general than the classical Marking Assumption, including channels that produce erasures and random decoding errors. Index Terms — Traitor tracing, Tardos code, collusion channel estimation, likelihood ratio, optimal decoding.
Asymptotically false-positive-maximizing attack on non-binary Tardos codes
- In Information Hiding, volume 6958 of LNCS
, 2011
"... Abstract. We use a method recently introduced by Simone and Škorić to study accusation probabilities for non-binary Tardos fingerprinting codes. We generalize the pre-computation steps in this approach to in-clude a broad class of collusion attack strategies. We analytically derive properties of a ..."
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Cited by 3 (1 self)
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Abstract. We use a method recently introduced by Simone and Škorić to study accusation probabilities for non-binary Tardos fingerprinting codes. We generalize the pre-computation steps in this approach to in-clude a broad class of collusion attack strategies. We analytically derive properties of a special attack that asymptotically maximizes false ac-cusation probabilities. We present numerical results on sufficient code lengths for this attack, and explain the abrupt transitions that occur in these results. 1
