Abstract
We consider multi-party computation (MPC) in a hierarchical setting, where participants have different capabilities depending on their position in the hierarchy. First, we give necessary conditions for multiplication of secrets in a hierarchical threshold linear secret sharing scheme (LSSS). Starting with known ideal constructions, we then propose a modified scheme with improved multiplication properties. We give sufficient conditions for the new scheme to be (strongly) multiplicative and show that our construction is almost optimal in the number of required participants. Thus, we obtain a new class of strongly multiplicative LSSS with explicit ideal constructions. Such LSSS are also useful outside the MPC setting, since they have an efficient algorithm for reconstructing secrets in the presence of errors.
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References
Brickell, E.F.: Some ideal secret sharing schemes. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 468–475. Springer, Heidelberg (1990)
Chen, H., Cramer, R.: Algebraic geometric secret sharing schemes and secure multi-party computations over small fields. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 521–536. Springer, Heidelberg (2006)
Cramer, R., Damgård, I., Maurer, U.M.: General secure multi-party computation from any linear secret-sharing scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)
Cramer, R., Daza, V., Gracia, I., Urroz, J.J., Leander, G., Martí-Farré, J., Padró, C.: On codes, matroids and secure multi-party computation from linear secret sharing schemes. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 327–343. Springer, Heidelberg (2005)
Farràs, O., Martí-Farré, J., Padró, C.: Ideal multipartite secret sharing schemes. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 448–465. Springer, Heidelberg (2007)
Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fact-track multiparty computations with applications to threshold cryptography. In: ACM Symposium on Principles of Distributed Computing, pp. 101–111 (1998)
Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. In: IEEE Goblecom 1987 (1987)
Karchmer, M., Wigderson, A.: On span programs. In: Structure in Complexity Theory Conference, pp. 102–111 (1993)
Martin, K.M.: New secret sharing schemes from old. Journal of Combinatorial Mathematics and Combinatorial Computing 14, 65–77 (1993)
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Simmons, G.J.: How to (really) share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1990)
Tassa, T.: Hierarchical threshold secret sharing. Journal of Cryptology 20(2), 237–264 (2007)
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Käsper, E., Nikov, V., Nikova, S. (2009). Strongly Multiplicative Hierarchical Threshold Secret Sharing. In: Desmedt, Y. (eds) Information Theoretic Security. ICITS 2007. Lecture Notes in Computer Science, vol 4883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10230-1_13
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DOI: https://doi.org/10.1007/978-3-642-10230-1_13
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