A Monotone Circuit Construction for Individually-Secure Multi-Secret Sharing
Abstract
In this work, we introduce a new technique for taking a single-secret sharing scheme with a general access structure and transforming it into an individually secure multi-secret sharing scheme where every secret has the same general access structure. To increase the information rate, we consider Individual Security which guarantees zero mutual information with each secret individually, for any unauthorized subsets. Our approach involves identifying which shares of the single-secret sharing scheme can be replaced by linear combinations of messages. When shares are replaced, our scheme obtains an information rate of , where is the set of shares. This provides an improvement over the information rate of in the original single-secret sharing scheme.
Cite
@article{arxiv.2405.06773,
title = {A Monotone Circuit Construction for Individually-Secure Multi-Secret Sharing},
author = {Cailyn Bass and Alejandro Cohen and Rafael G. L. D'Oliveira and Muriel Médard},
journal= {arXiv preprint arXiv:2405.06773},
year = {2024}
}