Capacity and optimal collusion attack channels for Gaussian fingerprinting games (original) (raw)

On the Capacity Game of Private Fingerprinting Systems Under Collusion Attacks

IEEE Transactions on Information Theory, 2005

The problem of fingerprinting in the presence of collusive attacks is considered. It is modeled as a game between a fingerprinter and a decoder on the one hand, and a coalition of two or more attackers on the other. The fingerprinter distributes, to different users, different fingerprinted copies of a host data (covertext) embedded with different fingerprints. The coalition members create a forgery of the data while aiming at erasing the fingerprints in order not to be detected. Their action is modeled by a multiple-access channel (MAC). The decoder, who has access to the original covertext data, observes the forgery and decodes one of the messages in order to identify one of the members of the coalition. Motivated by a worst case approach, we assume that the coalition of attackers is informed of the hiding strategy taken by the fingerprinter and the decoder, while they are uninformed of the attacking scheme. A single-letter expression for the capacity is derived under the assumption that the host data is drawn from a memoryless stationary source and some mild assumptions on the operation of the encoder. It is shown that for a coalition consisting of members, the capacity scales with (1), and whenever grows with the length of the covertext, the capacity is essentially zero. Also, a lower bound on the error exponent is derived as a by-product of the achievability part, and asymptotically optimum strategies of the parties involved are characterized.

On the Saddle-Point Solution and the Large-Coalition Asymptotics of Fingerprinting Games

IEEE Transactions on Information Forensics and Security, 2012

We study a fingerprinting game in which the number of colluders and the collusion channel are 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 maximin games with mutual information as their payoff functions. However, these games generally do not admit saddlepoint solutions 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 solution. If the maximal coalition size is k and the fingerprinting alphabet is binary, we show that capacity decays quadratically with k. Furthermore, we prove rigorously that the asymptotic capacity is 1/(k 2 2 ln 2) and we confirm our earlier conjecture that Tardos' choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotics, numerical solutions to the game for small k are also presented.

Saddle-point solution of the fingerprinting capacity game under the marking assumption

2009 IEEE International Symposium on Information Theory, 2009

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-point solutions 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 zerosum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is k and the fingerprint alphabet is binary, we derive equations that can numerically solve the capacity game for arbitrary k. We also provide tight upper and lower bounds on the capacity. Finally, we discuss the asymptotic behavior of the fingerprinting game for large k and practical implementation issues.

Universal fingerprinting: Capacity and random-coding exponents

2008 IEEE International Symposium on Information Theory, 2008

This paper studies fingerprinting games in which the number of colluders and the collusion channel are unknown. The fingerprints are embedded into host sequences representing signals to be protected and provide the receiver with the capability to trace back pirated copies to the colluders. The colluders and the fingerprint embedder are subject to signal fidelity constraints. Our problem setup unifies the signal-distortion and Boneh-Shaw formulations of fingerprinting. The fundamental tradeoffs between fingerprint codelength, number of users, and fidelity constraints are then determined. Several bounds on fingerprinting capacity have been presented in recent literature. This paper derives exact capacity formulas and presents a new randomized fingerprinting scheme with the following properties: (1) the encoder and receiver do not need to know the coalition size and collusion channel; (2) a tunable parameter ∆ trades off false-positive and false-negative error exponents; (3) the receiver provides a reliability metric for its decision; and (4) the scheme is capacity-achieving when the false-positive exponent ∆ tends to zero and the coalition size is known to the encoder. A fundamental component of the new scheme is the use of a "time-sharing" randomized sequence. The decoder is a maximum penalized mutual information decoder, where the significance of each candidate coalition is assessed relative to a threshold, and the penalty is proportional to the coalition size. A much simpler threshold decoder that satisfies properties (1)-(3) above but not (4) is also given.

On fingerprinting capacity games for arbitrary alphabets and their asymptotics

2012 IEEE International Symposium on Information Theory Proceedings, 2012

The fingerprinting capacity has recently been derived as the value of a two-person zero-sum game. In this work, we study the fingerprinting capacity games with k pirates in a new collusion model called the mixed digit model, which is inspired by the combined digit model ofŠkorić et al. For small k, the capacities along with optimal strategies for both players of the game are obtained explicitly. For large k, we extend our earlier asymptotic analysis for the binary alphabet with the marking assumption to q-ary alphabets with this general model and show that the capacity is asymptotic to A/(2k 2 ln q) where the constant A is specified as the maximin value of a functional game. Saddle-point solutions to the game are obtained using methods of variational calculus. For the special case of qary fingerprinting in the restricted digit model, we show that the interleaving attack is asymptotically optimal, a property that has motivated the design of optimized practical codes.

Asymmetric fingerprinting for larger collusions

Proceedings of the 4th ACM conference on Computer and communications security - CCS '97, 1997

Fingerprinting schemes deter people from illegally redistributing digital data by enabling the original merchant of the data to identify the original buyer of a redistributed copy. So-called traitor-tracing schemes have the same goal for keys that can be used to decrypt information that is broadcast in encrypted form. Recently, asymmetric fingerprinting and traitor-tracing schemes were introduced. Here, only the buyer knows the fingerprinted copy after a sale, and if the merchant finds this copy somewhere, he obtains a proof that he found the copy of this particular buyer. First constructions showed the validity of the concept.

Capacity and Random-Coding Error Exponent for Public Fingerprinting Game

2006 IEEE International Symposium on Information Theory, 2006

Capacity and random-coding error exponent formulas are derived for a public fingerprinting (traitor tracing) game. The original media copy is available to the encoder, but not to the decoder. We derive the random-coding error exponent for a stacked binning scheme. The exponent is strictly positive at all rates below capacity. The converse part of the capacity proof is based on the Gel'fand-Pinsker technique.

New Traceability Codes Against a Generalized Collusion Attack for Digital Fingerprinting

Lecture Notes in Computer Science

In this paper, we discuss collusion-secure traceability codes for digital fingerprinting which is a technique for copyright protection of digital contents. We first state a generalization of conventional collusion attacks where illicit users of a digital content collude to create an illegal digital content. Then we propose a collusion-secure traceability code which can detect at least one colluder against it. We show the rate and properties of the proposed traceability code.

A collusion attack optimization framework toward spread-spectrum fingerprinting

Applied Soft Computing, 2013

Understanding the weaknesses and the limitations of existing digital fingerprinting schemes and designing effective collusion attacks play an important role in the development of digital fingerprinting. In this paper, we propose a collusion attack optimization framework for spread-spectrum (SS) fingerprinting. Our framework is based upon the closed-loop feedback control theory. In the framework, we at first define a measure function to test whether the fingerprint presents in the attacked signal after collusion. Then, an optimization mechanism is introduced to attenuate the fingerprints from the forgery. We evaluate the performance of the proposed framework for three different SS-based embedding methods. The experimental results show that the proposed framework is more effective than the other examined collusion attacks. About three pieces of fingerprinted content are able to interrupt the fingerprinting system which accommodates about 1000 users, if we require the detection probability to be less than 0.9. Meanwhile, a high fidelity of the attacked content is retained.

On the Fingerprinting Capacity Under the Marking Assumption

IEEE Transactions on Information Theory, 2000

We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition. Lower bounds are obtained by considering typical coalitions, which represents a new idea in the area of fingerprinting and enables us to improve the previously known lower bounds for coalitions of size two and three. For upper bounds, the fingerprinting problem is modelled as a communications problem. It is shown that the maximum code rate is bounded above by the capacity of a certain class of channels, which are similar to the multiple-access channel. Converse coding theorems proved in the paper provide new upper bounds on fingerprinting capacity.