Abstract
We give an overview of the most important mathematical results related to different types of tracing traitors schemes, or schemes with identifiable parent property, especially for the case when the scheme’s “length” goes to infinity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wagner, N.R.: Fingerprinting. In: Proceedings of the Symposium on Security and Privacy, Oakland, CA, pp. 18–22, April 1983
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). https://doi.org/10.1007/3-540-39799-X_15
Chor, B., Fiat, A., Naor, M.: Tracing traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_25
Hollmann, H.D., van Lint, J.H., Linnartz, J.P., Tolhuizen, L.M.: On codes with the identifiable parent property. J. Comb. Theory Ser. A 82(2), 121–133 (1998)
Boneh, D., Shaw, J.: Collusion-secure fingerprinting for digital data. IEEE Trans. Inf. Theory 44, 1897–1905 (1998)
Barg, A., Blakley, G.R., Kabatiansky, G.: Digital fingerprinting codes: problems statements, constructions, identification of traitors. IEEE Trans. Inf. Theory 49(4), 852–865 (2003)
Stinson, D.R., Wei, R.: Combinatorial properties and constructions of traceability schemes and frameproof codes. SIAM J. Discrete Math. 11(1), 41–53 (1998)
Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, vol. 48, pp. 313–317 (1979)
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Collins, M.J.: Upper bounds for parent-identifying set systems. Des. Codes Crypt. 51(2), 167–173 (2009)
MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes, vol. 16, North-Holland Mathematical Library (1977)
Kabatiansky, G.A.: Good ternary 2-traceability codes exist. In: Proceedings of the IEEE Symposium on Information Theory, Chicago, IL, p. 203 (2004)
Kabatiansky, G.A.: Codes for copyright protection: the case of two pirates. Probl. Inf. Transm. 41, 182–186 (2005)
Blackburn, S.R., Etzion, T., Ng, S.-L.: Traceability codes. J. Comb. Theory Ser. A 117(8), 1049–1057 (2010)
Alon, N., Spencer, J.H.: The Probabilistic Method, 4th edn., Wiley Series in Discrete Mathematics and Optimization (2016)
Barg, A., Kabatiansky, G.: Class of I.P.P codes with effective tracing algorithm. J. Complex. 20(2–3), 137–147 (2004)
Safavi-Naini, R., Wang, Y.: New results on frame-proof codes and traceability schemes. IEEE Trans. Inf. Theory 47(7), 3029–3033 (2001)
Lofvenberg, J., Larsson, J.-A.: Comments on “new results on frame-proof codes and traceability schemes”. IEEE Trans. Inf. Theory 56(11), 5888–5889 (2010)
Egorova, E., Kabatiansky, G.: Analysis of two tracing traitor schemes via coding theory. In: Barbero, Á.I., Skachek, V., Ytrehus, Ø. (eds.) ICMCTA 2017. LNCS, vol. 10495, pp. 84–92. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66278-7_8
Barg, A., Cohen, G., Encheva, S., Kabatiansky, G., Zémor, G.: A hypergraph approach to the identifying parent property: the case of multiple parents. SIAM J. Discrete Math. 14(3), 423–431 (2001)
Alon, N., Cohen, G., Krivelevich, M., Litsyn, S.: Generalized hashing and parent-identifying codes. J. Comb. Theory Ser. A 104(1), 207–215 (2003)
Friedman, A.D., Graham, R.L., Ullman, J.D.: Universal single transition time asynchronous state assignments. IEEE Trans. Comput. 18(6), 541–547 (1969)
Sagalovich, Y.L.: Separating systems. Prob. Inf. Transm. 30(2), 105–123 (1994)
Cohen G.D., Schaathun H.G.: Asymptotic overview on separating codes. Technical report 248, Department of Informatics, University of Bergen, Bergen, Norway (2003)
Staddon, J.N., Stinson, D.R., Wei, R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inf. Theory 47, 1042–1049 (2001)
Vorob’ev, I.V.: Bounds on the rate of separating codes. Prob. Inf. Transm. 53(1), 30–41 (2017)
Kautz, W., Singleton, R.: Nonrandom binary superimposed codes. IEEE Trans. Inf. Theory 10(4), 363–377 (1964)
Dyachkov, A.G., Rykov, V.V.: Bounds on the length of disjunctive codes. Prob. Inf. Transm. 18(2), 166–171 (1982)
Furedi, Z., Erdos, P., Frankl, P.: Families of finite sets in which no set is covered by the union of r others. Israel J. Math. 51(1), 79–89 (1985)
Gu, Y., Miao, Y.: Bounds on traceability schemes. IEEE Trans. Inf. Theory 64(5), 3450–3460 (2018)
Acknowledgements
I am very grateful to Alexander Barg, Marcel Fernandez and Elena Egorova for very fruitful collaboration in the area of tracing traitors and around!
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Kabatiansky, G. (2019). On the Tracing Traitors Math. In: Carlet, C., Guilley, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2019. Lecture Notes in Computer Science(), vol 11445. Springer, Cham. https://doi.org/10.1007/978-3-030-16458-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-16458-4_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-16457-7
Online ISBN: 978-3-030-16458-4
eBook Packages: Computer ScienceComputer Science (R0)