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99
Sequential Monte Carlo for rare event estimation
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2012
"... This paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a FeynmanKac representation of that system to analyze their fluctuations. Our precise analysis of the varia ..."
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Cited by 30 (8 self)
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This paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a FeynmanKac representation of that system to analyze their fluctuations. Our precise analysis of the variance of a standard multilevel splitting algorithm reveals an opportunity for improvement. This leads to a novel method that relies on adaptive levels and produces estimates with optimal variance. The motivation for this theoretical work comes from problems occurring in watermarking and fingerprinting of digital contents, which represents a new field of applications of rare event simulation techniques. Some numerical results show the performance of our technique for these practical applications.
On the design and optimization of Tardos probabilistic fingerprinting codes
"... Abstract. G. Tardos [1] was the first to give a construction of a fingerprinting code whose length meets the lowest known bound in O(c 2 log n ɛ1). This was a real breakthrough because the construction is very simple. Its efficiency comes from its probabilistic nature. However, although G. Tardos al ..."
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Cited by 22 (3 self)
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Abstract. G. Tardos [1] was the first to give a construction of a fingerprinting code whose length meets the lowest known bound in O(c 2 log n ɛ1). This was a real breakthrough because the construction is very simple. Its efficiency comes from its probabilistic nature. However, although G. Tardos almost gave no argument of his rationale, many parameters of his code are precisely finetuned. This paper proposes this missing rationale supporting the code construction. The key idea is to render the statistics of the scores as independent as possible from the collusion process. Tardos optimal parameters are rediscovered. This interpretation allows small improvements when some assumptions hold on the collusion process. 1 In Gabor Tardos ’ shoes This article deals with active fingerprinting, also known as traitor tracing, or forensics, when applied on multimedia content. Fingerprinting is the application where a content server distributes personal copies of the same content to n
An improvement of discrete Tardos fingerprinting codes
 CODES CRYPTOGR
, 2009
"... It has been known that the code lengths of Tardos’s collusionsecure 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 on Tardos’s codes already revealed. In t ..."
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Cited by 18 (4 self)
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It has been known that the code lengths of Tardos’s collusionsecure 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 on Tardos’s codes already 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 assumption (Marking Assumption). Our analysis shows that our codes have significantly shorter lengths than Tardos’s codes. For example, in a practical setting, the code lengths of our codes are about 3.01%, 4.28%, and 4.81 % of Tardos’s codes if the numbers of pirates are 2, 4, and 6, respectively.
Answering n2+o(1) counting queries with differential privacy is hard.
 CoRR
, 2012
"... ABSTRACT A central problem in differentially private data analysis is how to design efficient algorithms capable of answering large numbers of counting queries on a sensitive database. Counting queries are of the form "What fraction of individual records in the database satisfy the property q? ..."
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Cited by 18 (5 self)
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ABSTRACT A central problem in differentially private data analysis is how to design efficient algorithms capable of answering large numbers of counting queries on a sensitive database. Counting queries are of the form "What fraction of individual records in the database satisfy the property q?" We prove that if oneway functions exist, then there is no algorithm that takes as input a database D ∈ ({0, 1} d ) n , and k = Θ(n 2 ) arbitrary efficiently computable counting queries, runs in time poly (d, n), and returns an approximate answer to each query, while satisfying differential privacy. We also consider the complexity of answering "simple" counting queries, and make some progress in this direction by showing that the above result holds even when we require that the queries are computable by constantdepth (AC 0 ) circuits. Our result is almost tight because it is known that Ω(n 2 ) counting queries can be answered efficiently while satisfying differential privacy. Moreover, many more than n 2 queries (even exponential in n) can be answered in exponential time. We prove our results by extending the connection between differentially private query release and cryptographic traitortracing schemes to the setting where the queries are given to the sanitizer as input, and by constructing a traitortracing scheme that is secure in this setting.
Saddlepoint 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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Cited by 16 (2 self)
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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 saddlepoints and are very hard to solve numerically. Here under the socalled BonehShaw marking assumption, we reformulate the capacity as the value of a single twoperson zerosum game, and show that it is achieved by a saddlepoint. 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 saddlepoint solutions for small k, we conjecture that the lower bound is asymptotically tight. I.
Estimating the minimal length of Tardos code
"... Abstract. This paper estimates the minimal length of a binary probabilistic traitor tracing code. We consider the code construction proposed by G. Tardos in 2003, with the symmetric accusation function as improved by B. Skoric et al. The length estimation is based on two pillars. First, we consider ..."
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Abstract. This paper estimates the minimal length of a binary probabilistic traitor tracing code. We consider the code construction proposed by G. Tardos in 2003, with the symmetric accusation function as improved by B. Skoric et al. The length estimation is based on two pillars. First, we consider the Worst Case Attack that a group of c colluders can lead. This attack minimizes the mutual information between the code sequence of a colluder and the pirated sequence. Second, an algorithm pertaining to the field of rare event analysis is presented in order to estimate the probabilities of error: the probability that an innocent user is framed, and the probabilities that all colluders are missed. Therefore, for a given collusion size, we are able to estimate the minimal length of the code satisfying some error probabilities constraints. This estimation is far lower than the known lower bounds.
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 wellknown Tardos binary probabilistic traitor tracing code, and especially its optimum setups recently advised by Amiri an ..."
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Cited by 15 (6 self)
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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 wellknown 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 symbolsymmetric 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 symbolsymmetric 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 codelength for Tardos’ distribution function and the symmetric score function. For large coalitions, our codelengths are asymptotically about 4.93 % of Tardos’ original codelengths, which also improves upon results from Nuida et al.