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 JAMP  Vol.2 No.13 , December 2014
A Multi-Secret Sharing Scheme with Many Keys Based on Hermite Interpolation
Abstract: 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 p≤t.
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.
References

[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.

 
 
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