In this paper, we introduce a method of threshold secret sharing scheme (TSSS) in which secret reconstruction is based on Babai's nearest plane algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there are no quantum threats to these channels. A solution to this problem can be utilization of lattice-based cryptosystems for these channe...

Secret Sharing from the perspective of threshold schemes has been wellstudied over the past decade. Threshold schemes, however, can only handle a small fraction of the secret sharing functions which we may wish to form. For example, if it is desirable to divide a secret among four participants A , B: C, and D in such a way that either A together with B can reconstruct the secret or C together w...

Weighted threshold secret sharing was introduced by Shamir in his seminal work on secret sharing. In such settings, there is a set of users where each user is assigned a positive weight. A dealer wishes to distribute a secret among those users so that a subset of users may reconstruct the secret if and only if the sum of weights of its users exceeds a certain threshold. A secret sharing scheme ...

We present group signature schemes that distribute group management using threshold encryption. To our best knowledge, we are the first to construct and analyze such schemes in detail. The threshold encryption schemes we employ to distribute group management are based on Shamir secret sharing and monotone span programs. We analyze our schemes not only in a static scenario, but also under group ...

A secret sharing scheme starts with a secret and then derives from it certain shares (or shadows) which are distributed to users. The secret may be recovered only by certain predetermined groups. In case of compartmented secret sharing, the set of users is partitioned into compartments and the secret can be recovered only if the number of participants from any compartment is greater than a fixe...

Visual cryptography (VC) has been developed extensively based on its practicability. These schemes can encode a black-and-white secret image into several shadow images, and, by stacking a certain number of shadow images, can retrieve the secret image through the human visual system. In this paper, we employ Hsu et al.’s ideal multi-threshold secret sharing scheme based on monotone span programs...

Recently, two novel schemes have been proposed for hierarchical threshold secret sharing, one based on Birkoff interpolation and another based on bivariate Lagrange interpolation. In this short paper, we propose a much simpler solution for this problem.

Abstract In the history of secret sharing schemes many constructions are based on geometric objects. this paper we investigate generalizations threshold and related finite structures. particular, analyse compartmented hierarchical schemes, deduce some more general results, especially bounds for special arcs novel conjunctive 2-level 3-level schemes.

In this paper, we propose a class of new threshold secret sharing schemes with repairing function between shares. Specifically, each share, when it is broken or lost, can be repaired by some others without the help of the dealer. Further, a construction of such repairable threshold secret sharing schemes is designed by applying linearized polynomials and regenerating codes in distributed storag...