Abstract
In this paper we propose a new publicly verifiable secret sharing scheme using pairings with close relations to Shoenmakers’ scheme. This scheme is efficient, multiplicatively homomorphic and with unconditional verifiability in the standard model. We formalize the notion of Indistinguishability of Secrets and prove that out scheme achieves it under the Decisional Bilinear Square (DBS) Assumption that is a natural variant of the Decisional Bilinear Diffie Hellman Assumption. Moreover, our scheme tolerates active and adaptive adversaries.
This research was partially supported by the Centre de Recerca Matemàtica (CRM).
Chapter PDF
Similar content being viewed by others
References
Boldyreva, A.: Threshold signatures, multisignatures and blind signatures based on the gap-diffie-hellman-group signature scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 31–46. Springer, Heidelberg (2002)
Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: Proc. 26th IEEE Symp. on Found. of Comp. Sci., pp. 383–395 (1985)
Feldman, P.: A Practical Scheme for Non-interactive Verifiable Secret Sharing. In: Proceedings 28th IEEE Symp. on Found. of Comp. Sci., pp. 427–437 (1987)
Fiat, A., Shamir, A.: How to prove yourself: Practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Fujisaki, E., Okamoto, T.: A practical and provably secure scheme for publicly verifiable secret sharing and its applications. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 32–46. Springer, Heidelberg (1998)
Goldwasser, S., Tauman, Y.: On the (In)security of the Fiat-Shamir Paradigm. In: Proc. 44th Annual IEEE Symp. on Found. of Comp. Sci., pp. 102–115 (2003)
Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006)
Joux, A.: A One Round Protocol for Tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000)
Libert, B., Vergnaud, D.: Unidirectional chosen-ciphertext secure proxy re-encryption. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 360–379. Springer, Heidelberg (2008)
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Ruiz, A., Villar, J.L.: Publicly Verifiable Secret Sharing from Paillier’s Cryptosystem. In: WEWoRC 2005. LNI P-74, pp. 98–108 (2005)
Sadeghi, A.-R., Steiner, M.: Assumptions related to discrete logarithms: Why subtleties make a real difference. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 243–260. Springer, Heidelberg (2001)
Schoenmakers, B.: A simple publicly verifiable secret sharing scheme and its application to electronic voting. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 148–164. Springer, Heidelberg (1999)
Shamir, A.: How to share a secret. Commun. of the ACM 22, 612–613 (1979)
Stadler, M.A.: Publicly verifiable secret sharing. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 190–199. Springer, Heidelberg (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heidarvand, S., Villar, J.L. (2009). Public Verifiability from Pairings in Secret Sharing Schemes. In: Avanzi, R.M., Keliher, L., Sica, F. (eds) Selected Areas in Cryptography. SAC 2008. Lecture Notes in Computer Science, vol 5381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04159-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-04159-4_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04158-7
Online ISBN: 978-3-642-04159-4
eBook Packages: Computer ScienceComputer Science (R0)