Secret Sharing Based on a Hard-on-Average Problem

TL;DR

This paper introduces a novel secret sharing scheme based on a hard-on-average computational problem, enhancing cryptographic security by leveraging the Distributional Matrix Representability Problem's complexity.

Contribution

It presents a new secret sharing protocol grounded in a hard-on-average problem, expanding the cryptographic toolkit for secure key management.

Findings

Scheme's security relies on a Discrete NP-Complete problem.

Provides a multiparty protocol for network key management.

Enhances security by using average-case hardness of a problem.

Abstract

The main goal of this work is to propose the design of secret sharing schemes based on hard-on-average problems. It includes the description of a new multiparty protocol whose main application is key management in networks. Its unconditionally perfect security relies on a discrete mathematics problem classiffied as DistNP-Complete under the average-case analysis, the so-called Distributional Matrix Representability Problem. Thanks to the use of the search version of the mentioned decision problem, the security of the proposed scheme is guaranteed. Although several secret sharing schemes connected with combinatorial structures may be found in the bibliography, the main contribution of this work is the proposal of a new secret sharing scheme based on a hard-on-average problem, which allows to enlarge the set of tools for designing more secure cryptographic applications.