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Xue, S. Z. Sun, and S. W. Cheng, “Modifications of competitive group testing,” SIAM Journal of Computing, vol. 23, pp. 82–96, Feb. 1994. [32] D. Z. Du and H. Park, “On competitive group testing,” SIAM Journal of Computing, vol. 23, pp. 1019–1025, Oct. 1994. [33] J. Dittmann, P. Schmitt, E. Saar, J. Schwenk, and J. Ueberberg, “Combining digital watermarks and collusion secure fingerprints for digital images,” SPIE Journal of Electronic Imaging, vol. 9, pp. 456–467, 2000. [34] T. W. Hungerford, Algebra, Springer-Verlag, 1974.

Right) User 1, 4, and 8 perform averaging, resulting in the output of the detector as (0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1). 35 Blind Detection Non-blind Detection Histogram of Detection Statistics of Embedded Fingerprints Histogram of Detection Statistics of Embedded Fingerprints 25 60 50 20 # of Occurrences # of Occurrences 40 15 10 30 20 5 10 0 −15 1 colluder −10 −5 0 5 10 0 −50 15 −40 −30 −20 Detection Statistics −10 0 10 20 30 40 50 Detection Statistics (a) (b) Histogram of Detection Statistics of Embedded Fingerprints Histogram of Detection Statistics of Embedded Fingerprints 25 60 50 20 # of Occurrences # of Occurrences 40 15 10 30 20 5 10 0 −15 2 colluders −10 −5 0 5 10 0 −60 15 −40 −20 Detection Statistics 0 20 40 60 80 60 80 Detection Statistics (c) (d) Histogram of Detection Statistics of Embedded Fingerprints Histogram of Detection Statistics of Embedded Fingerprints 25 70 60 20 15 # of Occurrences # of Occurrences 50 10 40 30 20 5 10 3 colluders 0 −15 −10 −5 0 5 10 Detection Statistics 15 0 −60 −40 −20 0 20 40 Detection Statistics (e) (f) Figure 9: Histograms of detection statistics of embedded fingerprints: (top row) single fingerprint case, (middle row) 2-user collusion case, (bottom row) 3-user collusion case; (left column) blind detection, (right column) non-blind detection.

J. Guth and B. Pfitzmann, “Error- and collusion-secure fingerprinting for digital data,” in Proc. 3rd Intl. Workshop on Information Hiding, 1999. [19] D. Kirovski, H. Malvar, and Y. Yacobi, “A dual watermarking and fingerprinting system,” Tech. Rep. MSR-TR-2001-57, Microsoft Research Laboratories, 2001. [20] M. Wu and B. Liu, “Modulation and multiplexing techniques for multimedia data hiding,” in Proc. of SPIE ITcom’01, SPIE vol 4518, Aug. 2001. [21] M. D. thesis, Princeton University, 2001. [22] H.

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