Considerate Ramp Secret Sharing

TL;DR

This paper introduces considerate ramp secret sharing schemes that enhance security by focusing on second layer protections, based on revisiting and extending fundamental information transfer principles in linear ramp schemes.

Contribution

It proposes a new construction of ramp secret sharing schemes emphasizing second layer security, based on insights from monomial-Cartesian codes and revisiting foundational information transfer results.

Findings

New construction ensures second layer security in ramp schemes

Largest possible sets cannot determine any information about the secret

Provides a structured example of considerate ramp secret sharing

Abstract

In this work we revisit the fundamental findings by Chen et al. in [5] on general information transfer in linear ramp secret sharing schemes to conclude that their method not only gives a way to establish worst case leakage [5, 25] and best case recovery [5, 19], but can also lead to additional insight on non-qualifying sets for any prescribed amount of information. We then apply this insight to schemes defined from monomial-Cartesian codes and by doing so we demonstrate that the good schemes from Sec.\ IV in [14] have a second layer of security. Elaborating further, when given a designed recovery number, in a new construction the focus is entirely on ensuring that the access structure possesses desirable second layer security, rather on what is the worst case information leakage in terms of number of participants.The particular structure of largest possible sets being not able to determine any amount of information suggests that we coin the concept of considerate ramp secret sharing schemes of which the proposed new construction is a well-structured example