Fingerprinting With Equiangular Tight Frames

Abstract

Digital fingerprinting is a framework for marking media files, such as images, music, or movies, with user-specific signatures to deter illegal distribution. Multiple users can collude to produce a forgery that can potentially overcome a fingerprinting system. This paper proposes an equiangular tight frame fingerprint design which is robust to such collusion attacks. We motivate this design by considering digital fingerprinting in terms of compressed sensing. The attack is modeled as linear averaging of multiple marked copies before adding a Gaussian noise vector. The content owner can then determine guilt by exploiting correlation between each user's fingerprint and the forged copy. The worst case error probability of this detection scheme is analyzed and bounded. Simulation results demonstrate that the average-case performance is similar to the performance of orthogonal and simplex fingerprint designs, while accommodating several times as many users.

Design of new fingerprinting codes using optical orthogonal codes

“…In what follows, our new fingerprints of Constructions 1 and 1.1 are examined by the error probabilities in detection process, where we use the analysis technique made in [7]. The error analysis then yields almost the same results as those of [7], replacing the coherence parameter by that of our new fingerprints.…”

“…This section reviews a mathematical model of [7] to describe fingerprint scheme, attack model, and detection process.…”

“…Our fingerprint design is motivated to remedy the potential drawbacks of the Steiner ETF fingerprints [7]. First of all, the indices of all nonzero entries of the base matrix need to be remembered in the Steiner ETF fingerprints, which requires large storage space when the signal dimension N and the number of users M are large in practice.…”

“…Kiyavash, Moulin and Kalker [6] proposed an optimal structure of n simplex fingerprints in terms of maximizing the error exponent of the detection test. Recently, Mixon, Quinn, Kiyavash and Fickus [7] designed a fingerprint system using equiangular tight frames (ETF) [8], where the Steiner system [9] has been exploited to construct the ETF. The performance of the ETF fingerprints is comparable to that of orthogonal and simplex fingerprints, but they can accommodate more users.…”

“…Then, the Hadamard matrix is employed to extend the base matrix, and each column of the resulting matrix is used as each user's fingerprint. The new fingerprint is motivated by the Steiner ETF fingerprint [7], but it offers a more flexible structure. Our fingerprint scheme just needs to remember a few binary sequences instead of the full base matrix, which requires less storage space in practical implementation.…”