Abstract
Multipartite secret sharing schemes are those that have multipartite access structures. The set of the participants in those schemes is divided into several parts, and all the participants in the same part play the equivalent role. One type of such access structure is the compartmented access structure, and the other is the hierarchical access structure. We propose an efficient compartmented multisecret sharing scheme based on the linear homogeneous recurrence (LHR) relations. In the construction phase, the shared secrets are hidden in some terms of the linear homogeneous recurrence sequence. In the recovery phase, the shared secrets are obtained by solving those terms in which the shared secrets are hidden. When the global threshold is t , our scheme can reduce the computational complexity of the compartmented secret sharing schemes from the exponential time to polynomial time. The security of the proposed scheme is based on Shamir’s threshold scheme, i.e., our scheme is perfect and ideal. Moreover, it is efficient to share the multisecret and to change the shared secrets in the proposed scheme.
Highlights
Shamir [1] and Blakley [2] proposed the threshold secret sharing schemes in 1979. eir schemes were based on the Lagrange interpolation algorithm and the linear projective geometry, respectively
In the (t, n) threshold secret sharing scheme, the secrets can be shared among n participants, and any t or more participants can recover the shared secrets by pooling their shares since greater than or equal to t participants can construct a qualified subset
In this paper, based on the linear homogeneous recurrence relations, we propose a compartmented multisecret sharing scheme
Summary
Shamir [1] and Blakley [2] proposed the threshold secret sharing schemes in 1979. eir schemes were based on the Lagrange interpolation algorithm and the linear projective geometry, respectively. Brickell proposed a method to construct an ideal secret sharing scheme for the multilevel and compartmented access structures [7], but it is not efficient. One of the key contributions is to introduce the LHR relations into the compartmented access structure, which divides the degree t of a polynomial into the low degrees of some polynomials, and each low degree equals to a fixed compartment threshold minus one. The compartmented access structure is realized by using the linear homogeneous recurrence (LHR) relations. E LHR relations are suitable for the compartmented access structure since it has the ability to associate each compartment with a different polynomial Another key contribution is to reduce the computational complexity of the compartmented secret sharing schemes from exponential time to polynomial time (O(nmax(ti−1)log n)).
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