On the equivalence of authentication codes and robust (2,2)-threshold schemes

TL;DR

This paper establishes a direct equivalence between authentication codes and robust (2,2)-threshold secret sharing schemes, providing new insights into their relationship and introducing the concept of key-substitution attacks.

Contribution

It introduces a direct equivalence between authentication codes and robust secret sharing schemes, and explores the implications of key-substitution attacks within this framework.

Findings

Established a direct equivalence between authentication codes and robust secret sharing schemes.

Analyzed key-substitution attacks in the context of dual authentication codes.

Provided new methods to prove properties and generalizations of existing constructions.

Abstract

In this paper, we show a "direct" equivalence between certain authentication codes and robust secret sharing schemes. It was previously known that authentication codes and robust secret sharing schemes are closely related to similar types of designs, but direct equivalences had not been considered in the literature. Our new equivalences motivate the consideration of a certain "key-substitution attack." We study this attack and analyze it in the setting of "dual authentication codes." We also show how this viewpoint provides a nice way to prove properties and generalizations of some known constructions.