Abstract
This paper investigates collusion-secure fingerprinting codes for digital data. Most previous works assume the threshold number of collusive users. Whereas, in order to treat a more general non-threshold collusion, we first introduce a notion of a potentially collusive family. Furthermore, we develop a novel way to measure collusion-secure codes according to combinatorial properties in a natural way. Our measurement immediately implies the definition of optimal codes. We then actually illustrate an optimal code. Finally, we give a necessary and sufficient condition for a code to be optimal by using a new notion of family-intersecting codes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Guruswami, V., Kaufman, T., Sudan, M.: Guessing secrets efficiently via list decoding. In: Proc. the thirteenth annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 254–262 (2002)
Banno, K., Orihara, S., Mizuki, T., Nishizeki, T.: Best security index for digital fingerprinting. In: Barni, M., Herrera-JoancomartÃ, J., Katzenbeisser, S., Pérez-González, F. (eds.) IH 2005. LNCS, vol. 3727, pp. 398–412. Springer, Heidelberg (2005)
Blakley, G.R., Meadows, C., Purdy, G.B.: Fingerprinting long forgiving messages. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 180–189. Springer, Heidelberg (1986)
Boneh, D., Shaw, J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inf. Theory 44(5), 1897–1905 (1998)
Cohen, G., Encheva, S., Litsyn, S., Schaathun, H.G.: Intersecting codes and separating codes. Discrete Applied Mathematics 128, 75–83 (2003)
Cohen, G., Lempel, A.: Linear intersecting codes. Discrete Mathematics 56, 35–43 (1985)
Cohen, G., Zemor, G.: Intersecting codes and independent families. IEEE Trans. Inf. Theory 40(6), 1872–1881 (1994)
Cotrina-Navau, J., Fernandez, M., Soriano, M.: A family of collusion 2-secure codes. In: Barni, M., Herrera-JoancomartÃ, J., Katzenbeisser, S., Pérez-González, F. (eds.) IH 2005. LNCS, vol. 3727, pp. 387–397. Springer, Heidelberg (2005)
Fernandez, M., Soriano, M.: Fingerprinting concatenated codes with efficient identification. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 459–470. Springer, Heidelberg (2002)
Furon, T.: A survey of watermarking security. In: Barni, M., Cox, I., Kalker, T., Kim, H.J. (eds.) IWDW 2005. LNCS, vol. 3710, pp. 201–215. Springer, Heidelberg (2005)
Guillaume, J.-L., Latapy, M.: Bipartite structure of all complex networks. Information Processing Letters 90(5), 215–221 (2004)
Guo, H., Georganas, N.D.: A novel approach to digital image watermarking based on a generalized secret sharing scheme. Multimedia Systems 9(3), 249–260 (2003)
Guth, H., Pfitzmann, B.: Error- and collusion-secure fingerprinting for digital data. In: Pfitzmann, A. (ed.) IH 1999. LNCS, vol. 1768, pp. 134–145. Springer, Heidelberg (2000)
Le, T.V., Burmester, M., Hu, J.: Short c-secure fingerprinting codes. In: Boyd, C., Mao, W. (eds.) ISC 2003. LNCS, vol. 2851, pp. 422–427. Springer, Heidelberg (2003)
Muratani, H.: A collusion-secure fingerprinting code reduced by Chinese remaindering and its random-error resilience. In: Moskowitz, I.S. (ed.) IH 2001. LNCS, vol. 2137, pp. 303–315. Springer, Heidelberg (2001)
Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)
Orihara, S., Mizuki, T., Nishizeki, T.: New security index for digital fingerprinting and its bounds. IEICE Trans. Fundamentals E86-A(5), 1156–1163 (2003)
Peikert, C., Shelat, A., Smith, A.: Lower bounds for collusion-secure fingerprinting. In: Proc. the fourteenth annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), pp. 472–479 (2003)
Staddon, J.N., Stinson, D.R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inf. Theory 47(3), 1042–1049 (2001)
Stinson, D.R., van Trung, T., Wei, R.: Secure frameproof codes, key distribution patterns, group testing algorithms and related structures. J. Stat. Plan. Inference 86(2), 595–617 (2000)
Tardos, G.: Optimal probabilistic fingerprint codes. Journal of the ACM (to appear)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)
Wu, M., Trappe, W., Wang, Z.J., Liu, K.J.R.: Collusion-resistant fingerprinting for multimedia. IEEE Signal Processing Magazine 21(2), 15–27 (2004)
Yoshioka, K., Shikata, J., Matsumoto, T.: Collusion secure codes: systematic security definitions and their relations. IEICE Trans. Fundamentals E87-A(5), 1162–1171 (2004)
Yoshioka, K., Shikata, J., Matsumoto, T.: On collusion security of random codes. IEICE Trans. Fundamentals E88-A(1), 296–304 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mizuki, T., Nounin, S., Sone, H., Toyota, Y. (2006). Worst-Case Optimal Fingerprinting Codes for Non-threshold Collusion. In: Safavi-Naini, R., Yung, M. (eds) Digital Rights Management. Technologies, Issues, Challenges and Systems. DRMTICS 2005. Lecture Notes in Computer Science, vol 3919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787952_16
Download citation
DOI: https://doi.org/10.1007/11787952_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35998-2
Online ISBN: 978-3-540-35999-9
eBook Packages: Computer ScienceComputer Science (R0)