[Resource Topic] 2011/147: The Optimal Linear Secret Sharing Scheme for Any Given Access Structure

Welcome to the resource topic for 2011/147

Title:
The Optimal Linear Secret Sharing Scheme for Any Given Access Structure

Authors: Tang Chunming, Gao Shuhong, Zhang Chengli

Abstract:

Any linear code can be used to construct a linear secret sharing scheme. In this paper, it is shown how to decide optimal linear codes (i.e., with the biggest information rate) realizing a given access structure over finite fields. It amounts to solving a system of quadratic equations constructed from the given access structure and the corresponding adversary structure. The system becomes a linear system for binary codes. An algorithm is also given for finding the adversary structure for any given access structure.

ePrint: https://eprint.iacr.org/2011/147

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