Abstract
We use powerful new techniques for list decoding error-correcting codes to efficiently trace traitors. Although much work has focused on constructing traceability schemes, the complexity of the tracing algorithm has received little attention. Because the TA tracing algorithm has a runtime of O(N) in general, where N is the number of users, it is inefficient for large populations. We produce schemes for which the TA algorithm is very fast. The IPP tracing algorithm, though less efficient, can list all coalitions capable of constructing a given pirate. We give evidence that when using an algebraic structure, the ability to trace with the IPP algorithm implies the ability to trace with the TA algorithm. We also construct schemes with an algorithm that finds all possible traitor coalitions faster than the IPP algorithm. Finally, we suggest uses for other decoding techniques in the presence of additional information about traitor behavior.
Silverberg would like to thank MSRI, Bell Labs Research Silicon Valley, NSA, and NSF.
Much of this work was completed while Staddon was employed by Bell Labs Research Silicon Valley.
Walker is partially supportedb y NSF grants DMS-0071008 andDMS-0071011.
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References
N. Alon, J. Bruck, J. Naor, M. Naor and R. Roth. Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs. IEEE Transactions on Information Theory 38 (1992), 509–516.
A. Barg, G. Cohen, S. Encheva, G. Kabatiansky and G. Zémor. A hypergraph approach to the identifying parent property: the case of multiple parents, DIMACS Technical Report 2000-20.
O. Berkman, M. Parnas and J. Sgall. Efficient dynamic traitor tracing, in 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2000), 586–595.
E. R. Berlekamp, R. J. McEliece and H. C. A. van Tilborg. On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory 24 (1978), 384–386.
D. Boneh and M. Franklin. An efficient public key traitor tracing scheme, in “Advances in Cryptology — Crypto’ 99”, Lecture Notes in Computer Science 1666 (1999), 338–353.
D. Boneh and J. Shaw. Collusion secure fingerprinting for digital data, in “Advances in Cryptology — Crypto’ 95”, Lecture Notes in Computer Science 963 (1995), 452–465.
D. Boneh and J. Shaw. Collusion secure fingerprinting for digital data, IEEE Transactions on Information Theory 44 (1998), 1897–1905.
I. Cox, J. Kilian, T. Leighton and T. Shamoon. Secure spreadsp ectrum watermarking for multimedia. IEEE Transactions on Information Theory 6 (1997), 1673–1687.
B. Chor, A. Fiat and M. Naor. Tracing traitors, in “Advances in Cryptology —Crypto’ 94”, Lecture Notes in Computer Science 839 (1994), 480–491.
B. Chor, A. Fiat, M. Naor and B. Pinkas. Tracing traitors, IEEE Transactions on Information Theory 46 (2000), 893–910.
C. Dwork, J. Lotspiech and M. Naor. Digital Signets: Self-Enforcing Protection of Digital Information, in Proc. 28th ACM Symposium on Theory of Computing (STOC 1997), 489–498.
G.-L. Feng. Very Fast Algorithms in Sudan Decoding Procedure for Reed-Solomon Codes. Preprint.
G.-L. Feng. Fast Algorithms in Sudan Decoding Procedure for Hermitian Codes. Preprint.
A. Fiat and M. Naor. Broadcast Encryption, in “Advances in Cryptology — Crypto’ 93”, Lecture Notes in Computer Science 773 (1994), 480–491.
A. Fiat and T. Tassa. Dynamic traitor tracing, in “Advances in Cryptology — Crypto’ 99”, Lecture Notes in Computer Science 1666 (1999), 354–371.
E. Gafni, J. Staddon and Y. L. Yin. Efficient methods for integrating traceability and broadcast encryption, in “Advances in Cryptology — Crypto’ 99”, Lecture Notes in Computer Science 1666 (1999), 372–387.
J. Garay, J. Staddon and A. Wool, Long-Lived Broadcast Encryption, in “Advances in Cryptology — Crypto 2000”, Lecture Notes in Computer Science 1880 (2000), 333–352.
V. D. Goppa. Geometry and codes. Kluwer Academic Publishers, Dordrecht, 1988.
V. Guruswami and M. Sudan. Improved decoding of Reed-Solomon and algebraicgeometry codes, IEEE Transactions on Information Theory 45(6) (1999), 1757–1767.
V. Guruswami and M. Sudan. List decoding algorithms for certain concatenated codes, in Proc. 32nd ACM Symposium on Theory of Computing (STOC 2000), 181–190.
T. Høholdt and R. R. Nielsen. Decoding Reed-Solomon codes beyond half the minimum distance, in Coding theory, cryptography and related areas (Guanajuato, 1998), Springer, Berlin (2000), 221–236.
T. Høholdt and R. R. Nielsen. Decoding Hermitian codes with Sudan’s algorithm. To appear in the 13th AAECC Symposium.
H. D. L. Hollmann, J. H. van Lint, J-P. Linnartz and L. M. G. M. Tolhuizen. On codes with the identifiable parent property, Journal of Combinatorial Theory A 82 (1998), 121–133.
R. Koetter and A. Vardy. Algebraic soft-decision decoding of Reed-Solomon codes. Preprint. http://www.dia.unisa.it/isit2000/lavori/455.ps.
R. Kumar, S. Rajagopalan and A. Sahai. Coding constructions for blacklisting problems without computational assumptions, in “Advances in Cryptology — Crypto’ 99”, Lecture Notes in Computer Science 1666 (1999), 609–623.
K. Kurosawa, M. Burmester and Y. Desmedt. A proven secure tracing algorithm for the optimal KD traitor tracing scheme. DIMACS Workshop on Management of Digital Intellectual Properties, April, 2000, and Euro crypt 2000 rump session.
K. Kurosawa and Y. Desmedt. Optimal traitor tracing andasymmetric schemes, in “Advances in Cryptology — Eurocrypt’ 98”, Lecture Notes in Computer Science 1438 (1998), 145–157.
J. H. van Lint. Introduction to coding theory. Third edition. Graduate Texts in Mathematics 86, Springer-Verlag, Berlin (1999).
M. Naor and B. Pinkas. Efficient Trace and Revoke Schemes, to appear in Proceedings of Financial Cryptography 2000.
V. Olshevsky and A. Shokrollahi. A displacement structure approach to efficient decoding of algebraic geometric codes, in Proc. 31st ACM Symposium on Theory of Computing (STOC 1999), 235–244.
B. Pfitzmann. Trials of tracedtraitors, in Information Hiding, First International Workshop, Lecture Notes in Computer Science 1174 (1996), 49–64.
R. M. Roth and G. Ruckenstein. Efficient decoding of Reed-Solomon codes beyond half the minimum distance. IEEE Transactions on Information Theory 46 (2000), 246–257.
R. Safavi-Naini and Y. Wang. Sequential Traitor Tracing, in “Advances in Cryptology — CRYPTO 2000”, Lecture Notes in Computer Science 1880 (2000), 316–332.
B.-Z. Shen. A Justesen construction of binary concatenatedco des that asymptotically meet the Zyablov boundfor low rate, IEEE Transactions on Information Theory 39 (1993), 239–242.
M. A. Shokrollahi and H. Wassermann. Decoding Algebraic-Geometric Codes Beyondthe Error-Correction Bound, in Proc. 30th ACM Symposium on Theory of Computing (STOC 1998), 241–248.
M. A. Shokrollahi and H. Wassermann. List Decoding of Algebraic-Geometric Codes. IEEE Transactions on Information Theory 45 (1999), 893–910.
J. N. Staddon, D. R. Stinson and R. Wei. Combinatorial properties of frameproof and traceability codes. To appear in IEEE Transactions on Information Theory.
H. Stichtenoth. Algebraic Function Fields and Codes. Springer-Verlag, Berlin, 1993.
D. R. Stinson, Tran van Trung and R. Wei. Secure frameproof codes, key distribution patterns, group testing algorithms andrelatedstructures, Journal of Statistical Planning and Inference 86 (2000), 595–617.
D. R. Stinson and R. Wei. Combinatorial properties andconstructions of traceability schemes andframepro of codes, SIAM Journal on Discrete Mathematics 11 (1998), 41–53.
D. R. Stinson and R. Wei. Key preassigned traceability schemes for broadcast encryption, in “SelectedAreas in Cryptology — SAC’ 98”, Lecture Notes in Computer Science 1556 (1999), 144–156.
M. Sudan. Decoding of Reed Solomon codes beyond the error-correction bound. Journal of Complexity 13(1) (1997), 180–193.
M. Sudan. Decoding of Reed Solomon codes beyond the error-correction diameter, in Proc. 35th Annual Allerton Conference on Communication, Control and Computing (1997), 215–224.
M. A. Tsfasman and S. G. Vlăduţ. Algebraic-geometric codes. Kluwer Academic Publishers, Dordrecht, 1991.
M. A. Tsfasman, S. G. Vlăduţ. and Th. Zink. Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound. Math. Nachr. 109 (1982), 21–28.
W.-G. Tzeng and Z.-J. Tzeng. A Traitor Tracing Scheme Using Dynamic Shares, to appear in PKC2001.
X.-W. Wu and P. H. Siegel. Efficient List Decoding of Algebraic Geometric Codes Beyondthe Error Correction Bound, submittedto IEEE Transactions on Information Theory.
F. Zane. Efficient Watermark Detection andCollusion Security, to appear in Proceedings of Financial Cryptography 2000.
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Silverberg, A., Staddon, J., Walker, J.L. (2001). Efficient Traitor Tracing Algorithms Using List Decoding. In: Boyd, C. (eds) Advances in Cryptology — ASIACRYPT 2001. ASIACRYPT 2001. Lecture Notes in Computer Science, vol 2248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45682-1_11
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