Abstract
It has been proven that the code lengths of Tardos’s collusion-secure fingerprinting codes are of theoretically minimal order with respect to the number of adversarial users (pirates). However, the code lengths can be further reduced as some preceding studies have revealed. In this article we improve a recent discrete variant of Tardos’s codes, and give a security proof of our codes under an assumption weaker than the original Marking Assumption. Our analysis shows that our codes have significantly shorter lengths than Tardos’s codes. For example, when c = 8, our code length is about 4.94% of Tardos’s code in a practical setting and about 4.62% in a certain limit case. Our code lengths for large c are asymptotically about 5.35% of Tardos’s codes.
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References
Blayer O., Tassa T.: Improved versions of Tardos’ fingerprinting scheme. Des. Codes Cryptogr. 48, 79–103 (2008)
Boneh D., Shaw J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inform. Theory 44(5), 1897–1905 (1998)
Carter M., van Brunt B.: The Lebesgue-Stieltjes Integral: A Practical Introduction. Springer-Verlag, Berlin (2000)
Guth H.-J., Pfitzmann B.: Error- and collusion-secure fingerprinting for digital data. In: Proceedings of Information Hiding 1999 (IH’99), LNCS 1768, pp. 134–145 (2000).
Hagiwara M., Hanaoka G., Imai H.: A short random fingerprinting code against a small number of pirates. In: Proceedings of 16th Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-16), LNCS 3857, pp. 193–202 (2006).
Nuida K., Hagiwara M., Watanabe H., Imai H.: Optimization of memory usage in Tardos’s fingerprinting codes. Preprint at arXiv repository. http://www.arxiv.org/abs/cs/0610036 (2006).
Nuida K., Hagiwara M., Watanabe H., Imai H.: Optimization of Tardos’s fingerprinting codes in a viewpoint of memory amount. In: Proceedings of 9th Information Hiding (IH 2007), LNCS 4567, pp. 279–293 (2007).
S̆korić B., Katzenbeisser S., Celik M.U.: Symmetric Tardos fingerprinting codes for arbitrary alphabet sizes. Des. Codes Cryptogr. 46, 137–166 (2008)
Tardos G.: Optimal probabilistic fingerprint codes. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC), pp. 116–125 (2003).
Tardos G.: Optimal probabilistic fingerprint codes. To appear in: Journal of the ACM. Preprint available online at http://www.renyi.hu/~tardos/publications.html.
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Communicated by H. van Tilborg.
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Nuida, K., Fujitsu, S., Hagiwara, M. et al. An improvement of discrete Tardos fingerprinting codes. Des. Codes Cryptogr. 52, 339–362 (2009). https://doi.org/10.1007/s10623-009-9285-z
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DOI: https://doi.org/10.1007/s10623-009-9285-z