Fingerprinting With Equiangular Tight Frames

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.

[1]  David P. Varodayan,et al.  Collusion-aware traitor tracing in multimedia fingerprinting using sparse signal approximation , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[2]  Dan Collusion-Secure Fingerprinting for Digital Data , 2002 .

[3]  Pierre Moulin,et al.  Regular Simplex Fingerprints and Their Optimality Properties , 2005, IEEE Transactions on Information Forensics and Security.

[4]  Pierre Moulin,et al.  High-Rate Random-Like Spherical Fingerprinting Codes With Linear Decoding Complexity , 2009, IEEE Transactions on Information Forensics and Security.

[5]  Dustin G. Mixon,et al.  The Road to Deterministic Matrices with the Restricted Isometry Property , 2012, Journal of Fourier Analysis and Applications.

[6]  Pierre Moulin,et al.  Sphere packing lower bound on fingerprinting error probability , 2007, Electronic Imaging.

[7]  Min Wu,et al.  Anti-collusion forensics of multimedia fingerprinting using orthogonal modulation , 2005, IEEE Transactions on Image Processing.

[8]  Dustin G. Mixon,et al.  Certifying the Restricted Isometry Property is Hard , 2012, IEEE Transactions on Information Theory.

[9]  Ronald A. DeVore,et al.  Deterministic constructions of compressed sensing matrices , 2007, J. Complex..

[10]  Amos Fiat,et al.  Tracing traitors , 2000, IEEE Trans. Inf. Theory.

[11]  Dustin G. Mixon,et al.  Steiner equiangular tight frames , 2010, 1009.5730.

[12]  Pierre Moulin,et al.  Universal fingerprinting: Capacity and random-coding exponents , 2008, 2008 IEEE International Symposium on Information Theory.

[13]  Naoki Hayashi,et al.  Collusion-Resistant Fingerprinting Scheme Based on the CDMA-Technique , 2007, IWSEC.

[14]  Neri Merhav,et al.  Achievable Error Exponents for the Private Fingerprinting Game , 2007, IEEE Transactions on Information Theory.

[15]  Ersen Ekrem,et al.  A Detection Theoretic Approach to Digital Fingerprinting With Focused Receivers Under Uniform Linear Averaging Gaussian Attacks , 2010, IEEE Transactions on Information Forensics and Security.

[16]  Alexander Barg,et al.  On the Fingerprinting Capacity Under the Marking Assumption , 2006, IEEE Transactions on Information Theory.

[17]  Josep Cotrina Navau,et al.  A Family of Asymptotically Good Binary Fingerprinting Codes , 2010, IEEE Transactions on Information Theory.

[18]  Dustin G. Mixon,et al.  Sparse Signal Processing with Frame Theory , 2012, ArXiv.

[19]  Alexander Barg,et al.  Robust parent-identifying codes , 2010, 2010 IEEE Information Theory Workshop.

[20]  Frank Hartung,et al.  Multimedia watermarking techniques , 1999, Proc. IEEE.

[21]  Aggelos Kiayias,et al.  Robust fingerprinting codes: a near optimal construction , 2010, DRM '10.

[22]  Dan Boneh,et al.  Collusion-Secure Fingerprinting for Digital Data , 1998, IEEE Trans. Inf. Theory.

[23]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[24]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[25]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[26]  Pierre Moulin,et al.  Performance of Orthogonal Fingerprinting Codes Under Worst-Case Noise , 2009, IEEE Transactions on Information Forensics and Security.

[27]  Robert E. Tarjan,et al.  Resistance of digital watermarks to collusive attacks , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[28]  Hans Georg Schaathun,et al.  The Boneh-Shaw fingerprinting scheme is better than we thought , 2006, IEEE Transactions on Information Forensics and Security.

[29]  Wade Trappe,et al.  Collusion-resistant fingerprints from WBE sequence sets , 2005, IEEE International Conference on Communications, 2005. ICC 2005. 2005.

[30]  R. Curtis A course in combinatorics (2nd edn), by J. H. van Lint and R. M. Wilson. Pp. 602. £24.95. 2001. ISBN 0 521 00601 5 (Cambridge University Press). , 2003, The Mathematical Gazette.

[31]  L. B. Milstein,et al.  Theory of Spread-Spectrum Communications - A Tutorial , 1982, IEEE Transactions on Communications.

[32]  Richard M. Wilson,et al.  A course in combinatorics , 1992 .

[33]  Neri Merhav,et al.  On the capacity game of private fingerprinting systems under collusion attacks , 2003, IEEE Transactions on Information Theory.

[34]  Marc E. Pfetsch,et al.  The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing , 2012, IEEE Transactions on Information Theory.

[35]  Alexander Barg,et al.  Digital fingerprinting codes: problem statements, constructions, identification of traitors , 2003, IEEE Trans. Inf. Theory.

[36]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[37]  R. Varga Geršgorin And His Circles , 2004 .

[38]  Olgica Milenkovic,et al.  Compressive list-support recovery for colluder identification , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[39]  H. Hanani,et al.  On steiner systems , 1964 .

[40]  Minquan Cheng,et al.  On Anti-Collusion Codes and Detection Algorithms for Multimedia Fingerprinting , 2011, IEEE Transactions on Information Theory.

[41]  Ingemar J. Cox,et al.  Digital Watermarking , 2003, Lecture Notes in Computer Science.

[42]  Min Wu,et al.  Anti-collusion fingerprinting for multimedia , 2003, IEEE Trans. Signal Process..

[43]  Joe Kilian,et al.  A Note on the Limits of Collusion-Resistant Watermarks , 1999, EUROCRYPT.

[44]  Hefei Ling,et al.  A Novel Collusion Attack Strategy for Digital Fingerprinting , 2010, IWDW.

[45]  Hiroki Koga,et al.  A Digital Fingerprinting Code Based on a Projective Plane and Its Identifiability of All Malicious Users , 2011, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[46]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[47]  N. Merhav,et al.  On the capacity game of private fingerprinting systems under collusion attacks , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[48]  Ying Wang,et al.  Capacity and optimal collusion attack channels for Gaussian fingerprinting games , 2007, Electronic Imaging.

[49]  Thomas Strohmer,et al.  GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION , 2003, math/0301135.

[50]  Michael B. Wakin,et al.  Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property , 2009, IEEE Transactions on Information Theory.

[51]  Ingemar J. Cox,et al.  Secure spread spectrum watermarking for multimedia , 1997, IEEE Trans. Image Process..

[52]  Shih-Chun Lin,et al.  Fingerprinting With Minimum Distance Decoding , 2007, IEEE Transactions on Information Forensics and Security.

[53]  C. Colbourn,et al.  Frameproof codes and compressive sensing , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).