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On Partial Anonymity in Secret Sharing

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Public Key Infrastructure (EuroPKI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4582))

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Abstract

Anonymous secret sharing schemes allow a secret to be recovered from shares regardless of the identity of shareholders. Besides being interesting in its own right, this property is especially appealing to guarantee the anonymity of participants when secret sharing is used as a building block of more general distributed protocols (e.g. to anonymously share the secret key corresponding to a public key). However, current constructions of anonymous secret sharing schemes are not very efficient (because of the number of shares that every participant must hold) and existing bounds do not leave much room for optimism. In this paper we propose to weaken the anonymity condition to partial anonymity, where by partial anonymity we mean that the identity of the participant is not made public, but he is known to belong to some subset. That is, the search for a participant narrows down to one in a set of possible candidates. Furthermore, we propose a general construction of partial anonymous secret sharing schemes.

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References

  1. Beimel, A., Franklin, M.: Weakly-private secret sharing. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 253–272. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  2. Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, American Federation of Information, Processing Societies Proceedings, vol. 48, pp. 313–317 (1979)

    Google Scholar 

  3. Blundo, C., Giorgia Gaggia, A., Stinson, D.R.: On the dealer’s randomness required in secret sharing schemes. Designs, Codes and Cryptography 11, 107–122 (1997)

    Article  MATH  Google Scholar 

  4. Blundo, C., Stinson, D.R.: Anonymous secret sharing schemes. Discrete Applied Mathematics 77, 13–28 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Brickell, E.F.: Some ideal secret sharing schemes. J. Math. Combin. Comput. 6, 105–113 (1989)

    MATH  MathSciNet  Google Scholar 

  6. Carpentieri, M.: A perfect threshold secret sharing scheme to identify cheaters. Designs, Codes and Cryptography 5, 183–188 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cramer, R., Damgård, I., Nielsen, J.: Multiparty computation from threshold homomorphic encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–299. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)

    Google Scholar 

  9. Farràs, O., Martí-Farré, J., Padró, C.: Ideal multipartite secret sharing schemes. In: Eurocrypt 2007. LNCS, Springer, Heidelberg (to appear, 2007)

    Google Scholar 

  10. Gehrmann, C.: Topics in Authentication Theory, Ph.D. Thesis, Lund University (1997)

    Google Scholar 

  11. Ghodosi, H., Pieprzyk, J., Safavi-Naini, R.: Secret sharing in multilevel and compartmented groups. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 367–378. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  12. Guillermo, M., Martin, K.M., O’Keefe, C.M.: Providing anonymity in unconditionally secure secret sharing schemes. Designs, Codes and Cryptography 28, 227–245 (2004)

    Article  MathSciNet  Google Scholar 

  13. Herranz, J., Sáez, G.: New results on multipartite access structures. IEE Proceedings of Information Security 153-4 (December 2006)

    Google Scholar 

  14. Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing any access structure. In: Proc. IEEE Globecom 1987, pp. 99–102 (1987)

    Google Scholar 

  15. Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Transactions on Information Theory 29(1), 35–41 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kishimoto, W., Okada, K., Kurosawa, K., Ogata, W.: On the bound for anonymous secret sharing schemes. Discrete Applied Mathematics 121(1-3), 193–202 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Phillips, S.J., Phillips, N.C.: Strongly ideal secret sharing schemes. Journal of Cryptology 5, 185–191 (1992)

    Article  MATH  Google Scholar 

  18. Samarati, P., Sweeney, L.: Protecting privacy when disclosing information: k-anonymity and its enforcement through generalization and suppression. Tech. rep., SRI International (1998)

    Google Scholar 

  19. Shamir, A.: How to share a secret. Communications of the ACM 22, 612–613 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  20. Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  21. Simmons, G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1990)

    Google Scholar 

  22. Stinson, D.R., Vanstone, S.A.: A combinatorial approach to threshold schemes. SIAM J. Disc. Math. 1, 230–236 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  23. von Ahn, L., Bortz, A., Hopper, N.J.: k-anonymous message transmission. In: Proc. of the 10th ACM Conference on Computer and Communications Security, pp. 122–130. ACM Press, New York (2003)

    Chapter  Google Scholar 

  24. Xu, S., Yung, M.: k-anonymous secret handshakes with reusable credentials. In: Proc. of the 11th ACM Conference on Computer and Communications Security, pp. 158–167. ACM press, New York (2004)

    Chapter  Google Scholar 

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Javier Lopez Pierangela Samarati Josep L. Ferrer

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Daza, V., Domingo-Ferrer, J. (2007). On Partial Anonymity in Secret Sharing. In: Lopez, J., Samarati, P., Ferrer, J.L. (eds) Public Key Infrastructure. EuroPKI 2007. Lecture Notes in Computer Science, vol 4582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73408-6_14

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  • DOI: https://doi.org/10.1007/978-3-540-73408-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73407-9

  • Online ISBN: 978-3-540-73408-6

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