Strongly secure ramp secret sharing schemes for general access structures

TL;DR

This paper introduces a method to construct strongly secure ramp secret sharing schemes for any general access structure, addressing a gap in the existing literature and highlighting limitations of threshold schemes.

Contribution

It demonstrates that strong ramp SS schemes can be built from schemes with multiple secrets for all feasible access structures, expanding the design possibilities.

Findings

Strong ramp SS schemes can be constructed from plural secret schemes for any access structure.

Threshold ramp SS schemes based on Shamir's method are not always strong.

The paper provides a general construction method for strong ramp SS schemes.

Abstract

Ramp secret sharing (SS) schemes can be classified into strong ramp SS schemes and weak ramp SS schemes. The strong ramp SS schemes do not leak out any part of a secret explicitly even in the case where some information about the secret leaks from a non-qualified set of shares, and hence, they are more desirable than weak ramp SS schemes. However, it is not known how to construct the strong ramp SS schemes in the case of general access structures. In this paper, it is shown that a strong ramp SS scheme can always be constructed from a SS scheme with plural secrets for any feasible general access structure. As a byproduct, it is pointed out that threshold ramp SS schemes based on Shamir's polynomial interpolation method are {\em not} always strong.