The Optimal Linear Secret Sharing Scheme for Any Given Access Structure

Tang Chunming; Gao Shuhong; Zhang Chengli

Paper 2011/147 Original: eprint.iacr.org/2011/147 ↗

The Optimal Linear Secret Sharing Scheme for Any Given Access Structure

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.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
History: 2011-03-27: last updated; 2011-03-27: published
Short URL: https://ia.cr/2011/147
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2011/147,
      author = {Tang Chunming and Gao Shuhong and Zhang Chengli},
      title = {The Optimal Linear Secret Sharing Scheme for Any Given Access Structure},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/147},
      year = {2011},
      url = {https://eprint.iacr.org/2011/147}
}