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.
Highlights
A secret sharing scheme is one of cryptographies
Adachi [12] studies a secret sharing scheme with two keys based on Hermite interpolation
We describe our new scheme, that is, a multi-secret sharing scheme based on Hermite interpolation in the case p ≤ t, where p is the number of keys, and t is the number of necessary participants who can reconstruct keys
Summary
A secret sharing scheme is one of cryptographies. A secret sharing scheme was introduced by Shamir in 1979 [1] and Blakley in 1979 [2] independently. (2014) A Multi-Secret Sharing Scheme with Many Keys Based on Hermite Interpolation. A multi-secret sharing scheme by utilizing a one-way function is studied by He and Dawson [6] in 1994, and by Harn [7] in 1995. A multi-secret sharing scheme by utilizing a two variables one-way function is studied by He and Dawson [8] in 1995. A multi-secret sharing scheme by utilizing a linear block code is studied by Chien et al [9] in 2000, and by Pang and Wang [10] in 2005. Adachi [12] studies a secret sharing scheme with two keys based on Hermite interpolation. We give a scheme of a (t, n) multi-secret sharing based on Hermite interpolation, in the case of p ≤ t. The goal of this paper is 1) to find system parameters, 2) to construct secret distribution, and 3) to complete secret reconstruction, for a multi-secret sharing, by utilizing Hermite interpolation
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