Combinatorial Bounds and Characterizations of Splitting Authentication Codes

TL;DR

This paper generalizes splitting authentication codes by establishing combinatorial bounds and characterizations for multi-fold security, introducing new combinatorial designs and necessary conditions for their existence.

Contribution

It provides a combinatorial lower bound on encoding rules and characterizes optimal codes using new design structures, advancing understanding of secure authentication schemes.

Findings

Lower bound on number of encoding rules

Characterization of optimal codes with multi-fold security

Introduction of new combinatorial designs and necessary conditions

Abstract

We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a combinatorial characterization of optimal splitting authentication codes that are multi-fold secure against spoofing attacks. The characterization is based on a new type of combinatorial designs, which we introduce and for which basic necessary conditions are given regarding their existence.