Paper 2017/919 Original: eprint.iacr.org/2017/919 ↗
Improving the Linear Programming Technique in the Search for Lower Bounds in Secret Sharing
Abstract
We present a new improvement in the linear programming technique to derive lower bounds on the information ratio of secret sharing schemes. We obtain non-Shannon-type bounds without using information inequalities explicitly. Our new technique makes it possible to determine the optimal information ratio of linear secret sharing schemes for all access structures on 5 participants and all graph-based access structures on 6 participants. In addition, new lower bounds are presented also for some small matroid ports and, in particular, the optimal information ratios of the linear secret sharing schemes for the ports of the Vamos matroid are determined.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2022-03-30: last updated
- 2017-09-24: published
- Short URL
- https://ia.cr/2017/919
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2017/919,
author = {Oriol Farràs and Tarik Kaced and Sebastià Martín and Carles Padró},
title = {Improving the Linear Programming Technique in the Search for Lower Bounds in Secret Sharing},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/919},
year = {2017},
url = {https://eprint.iacr.org/2017/919}
}