A Multi-Secret Sharing Scheme with Many Keys Based on Hermite Interpolation

A secret sharing scheme is one of cryptographies. A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange's interpolation formula. A secret sharing scheme has one key. On the other hand, a multi-secret sharing scheme has more than one keys; that is, a multi-secret sharing scheme has p (2) keys. Dealers distribute shares of keys among n participants. Gathering t (n) participants, keys can be reconstructed. In this paper, we give a scheme of a (t,n) multi-secret sharing based on Hermite interpolation, in the case of pt.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Adachi, T. and Okazaki, C. (2014) A Multi-Secret Sharing Scheme with Many Keys Based on Hermite Interpolation. Journal of Applied Mathematics and Physics, 2, 1196-1201. doi: 10.4236/jamp.2014.213140.

 [1] Shamir, A. (1979) How to Share a Secret. Communications of the ACM, 22, 612-613. http://dx.doi.org/10.1145/359168.359176 [2] Blakley, G.R. (1979) Safeguarding Cryptographic Keys. AFIPS Conference Proceedings, 48, 313-317. [3] Feldman, P. (1987) A Practical Scheme for Non-Interactive Verifiable Secret Sharing. Proceedings of 28th IEEE Symposium on Foundations of Computer Science, Los Angeles, 12-14 October 1987, 427-437. [4] Pedersen, T.P. (1992) Non-Interacive and Information-Theoretic Secure Verifiable Secret Sharing. Advances in Cryptology CRYPTO ’91, 129-140. [5] Jackson, W.A., Martin, K.M. and O’Keefe, C.M. (1995) On Sharing Many Secrets. Advances in Cryptology— ASIACRYPT’94, 917, 42-54. [6] He, J. and Dawson, E. (1994) Multistage Secret Sharing Based on One-Way Function. Electronics Letters, 30, 1591-1592. http://dx.doi.org/10.1049/el:19941076 [7] Harn, L. (1995) Comment: Multistage Secret Sharing Based on One-Way Function. Electronics Letters, 31, 262. http://dx.doi.org/10.1049/el:19950201 [8] He, J. and Dawson, E. (1995) Multisecret Sharing Scheme Based on One-Way Function. Electronics Letters, 31, 93-94. http://dx.doi.org/10.1049/el:19950073 [9] Chien, H.Y., Jan, J.K. and Tseng, Y.M. (2000) A Practical (t,n) Multi-Secret Sharing Scheme. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E83, 2762-2765. [10] Pang, L.J. and Wang, Y.M. (2005) A New (t,n) Multi-Secret Sharing Scheme Based on Shamir’s Secret Sharing. Applied Mathematics and Computation, 167, 840-848. http://dx.doi.org/10.1016/j.amc.2004.06.120 [11] Yang, C.C., Chang, T.Y. and Hwang, M.S. (2004) A (t,n) Multi-Secret Sharing Scheme. Applied Mathematics and Computation, 151, 483-490. http://dx.doi.org/10.1016/S0096-3003(03)00355-2 [12] Adachi, T. (Submitted) A Secret Sharing Scheme with Two Keys Based on Hermite Interpolation.