An ideal multi-secret sharing scheme based on minimal privileged coalitions

TL;DR

This paper introduces an algorithm to construct ideal multi-secret sharing schemes for general access structures, addressing an open problem, and demonstrates that many existing schemes are imperfect, proposing a more versatile scheme.

Contribution

It provides an algorithm for privileged coalitions of any length and designs an improved ideal multi-secret sharing scheme for diverse access structures.

Findings

Most existing schemes are not perfect due to privileged coalitions.

The proposed algorithm can identify privileged coalitions of any length.

The new scheme supports more authorized sets than traditional threshold schemes.

Abstract

How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, we solve an open problem proposed by Spiez et al.recently [Finite Fields and Their Application, 2011(17) 329-342], namely to design an algorithm of privileged coalitions of any length if such coalitions exist. Furthermore, in terms of privileged coalitions, we show that most of the existing multi-secret sharing schemes based on Shamir threshold secret sharing are not perfect by analyzing Yang et al.'s scheme and Pang et al.'s scheme. Finally, based on the algorithm mentioned above, we devise an ideal multi-secret sharing scheme for families of access structures, which possesses more vivid authorized sets than that of the threshold scheme.