On asymptotically good ramp secret sharing schemes
Information Theory
2018-02-08 v7 math.IT
Abstract
Asymptotically good sequences of linear ramp secret sharing schemes have been intensively studied by Cramer et al. in terms of sequences of pairs of nested algebraic geometric codes. In those works the focus is on full privacy and full reconstruction. In this paper we analyze additional parameters describing the asymptotic behavior of partial information leakage and possibly also partial reconstruction giving a more complete picture of the access structure for sequences of linear ramp secret sharing schemes. Our study involves a detailed treatment of the (relative) generalized Hamming weights of the considered codes.
Keywords
Cite
@article{arxiv.1502.05507,
title = {On asymptotically good ramp secret sharing schemes},
author = {Olav Geil and Stefano Martin and Umberto Martínez-Peñas and Ryutaroh Matsumoto and Diego Ruano},
journal= {arXiv preprint arXiv:1502.05507},
year = {2018}
}