Abstract
We construct a fully collusion resistant tracing traitors system with sublinear size ciphertexts and constant size private keys. More precisely, let N be the total number of users. Our system generates ciphertexts of size \(O(\sqrt{N})\) and private keys of size O(1). We first introduce a simpler primitive we call private linear broadcast encryption (PLBE) and show that any PLBE gives a tracing traitors system with the same parameters. We then show how to build a PLBE system with \(O(\sqrt{N})\) size ciphertexts. Our system uses bilinear maps in groups of composite order.
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References
Barth, A., Boneh, D., Waters, B.: Privacy in encrypted content distribution using private broadcast encryption. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 52–64. Springer, Heidelberg (2006)
Berkman, O., Parnas, M., Sgall, J.: Efficient dynamic traitor tracing. In: Proceedings of SODA 2000 (2000)
Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Boneh, D., Franklin, M.K.: An efficient public key traitor tracing scheme. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 338–353. Springer, Heidelberg (1999)
Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-dnf formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)
Boneh, D., Naor, M.: Tracing traitors with constant size ciphertext using binary fingerprinting codes (unpublished, 2002)
Boneh, D., Sahai, A., Waters, B.: Fully collusion resistant traitor tracing with short ciphertexts and private keys. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 573–592. Springer, Heidelberg (2006), Full version available at: http://eprint.iacr.org/2006/045
Boneh, D., Shaw, J.: Collusion secure fingerprinting for digital data. IEEE Transactions on Information Theory 44(5), 1897–1905 (1998) (extended abstract in Crypto 1995)
Chabanne, H., Phan, D.H., Pointcheval, D.: Public traceability in traitor tracing schemes. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 542–558. Springer, Heidelberg (2005)
Chor, B., Fiat, A., Naor, M.: Tracing traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994)
Chor, B., Fiat, A., Naor, M., Pinkas, B.: Tracing traitors. IEEE Transactions on Information Theory 46(3), 893–910 (2000)
Dodis, Y., Fazio, N.: Public key trace and revoke scheme secure against adaptive chosen ciphertext attack. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 100–115. Springer, Heidelberg (2002)
Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994)
Fiat, A., Tassa, T.: Dynamic traitor tracing. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 354–371. Springer, Heidelberg (1999)
Gafni, E., Staddon, J., Yin, Y.L.: Efficient methods for integrating traceability and broadcast encryption. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 372–387. Springer, Heidelberg (1999)
Goodrich, M.T., Sun, J.Z., Tamassia, R.: Efficient tree-based revocation in groups of low-state devices. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 511–527. Springer, Heidelberg (2004)
Halevy, D., Shamir, A.: The lsd broadcast encryption scheme. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 47–60. Springer, Heidelberg (2002)
Kiayias, A., Yung, M.: On crafty pirates and foxy tracers. In: Sander, T. (ed.) DRM 2001. LNCS, vol. 2320, pp. 22–39. Springer, Heidelberg (2002)
Kiayias, A., Yung, M.: Breaking and repairing asymmetric public-key traitor tracing. In: Feigenbaum, J. (ed.) DRM 2002. LNCS, vol. 2696, pp. 32–50. Springer, Heidelberg (2003)
Kiayias, A., Yung, M.: Traitor tracing with constant transmission rate. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 450–465. Springer, Heidelberg (2002)
Kurosawa, K., Desmedt, Y.: Optimum traitor tracing and asymmetric schemes. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 145–157. Springer, Heidelberg (1998)
Mitsunari, S., Sakai, R., Kasahara, M.: A new traitor tracing. IEICE Trans. Fundamentals E85-A(2), 481–484 (2002)
Naor, D., Naor, M., Lotspiech, J.B.: Revocation and tracing schemes for stateless receivers. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 41–62. Springer, Heidelberg (2001)
Naor, M., Pinkas, B.: Threshold traitor tracing. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 502–517. Springer, Heidelberg (1998)
Naor, M., Pinkas, B.: Efficient trace and revoke schemes. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 1–20. Springer, Heidelberg (2001)
Pfitzmann, B.: Trials of traced traitors. In: Proceedings of Information Hiding Workshop, pp. 49–64 (1996)
Pfitzmann, B., Waidner, M.: Asymmetric fingerprinting for larger collusions. In: Proceedings of the ACM Conference on Computer and Communication Security, pp. 151–160 (1997)
Safavi-Naini, R., Wang, Y.: Sequential traitor tracing. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 316–332. Springer, Heidelberg (2000)
Silverberg, A., Staddon, J., Walker, J.L.: Efficient traitor tracing algorithms using list decoding. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 175–192. Springer, Heidelberg (2001)
Staddon, J.N., Stinson, D.R., Wei, R.: Combinatorial properties of frameproof and traceability codes. Cryptology ePrint 2000/004 (2000)
Stinson, D., Wei, R.: Combinatorial properties and constructions of traceability schemes and frameproof codes. SIAM Journal on Discrete Math 11(1), 41–53 (1998)
Stinson, D., Wei, R.: Key preassigned traceability schemes for broadcast encryption. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, p. 144. Springer, Heidelberg (1999)
Tardos, G.: Optimal probabilistic fingerprint codes. In: Proceedings of STOC 2003, pp. 116–125 (2003)
To, V., Safavi-Naini, R., Zhang, F.: New traitor tracing schemes using bilinear map. In: Proceedings of 2003 DRM Workshop (2003)
Watanabe, Y., Hanaoka, G., Imai, H.: Efficient asymmetric public-key traitor tracing without trusted agents. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 392–407. Springer, Heidelberg (2001)
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Boneh, D., Sahai, A., Waters, B. (2006). Fully Collusion Resistant Traitor Tracing with Short Ciphertexts and Private Keys. In: Vaudenay, S. (eds) Advances in Cryptology - EUROCRYPT 2006. EUROCRYPT 2006. Lecture Notes in Computer Science, vol 4004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11761679_34
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