Authentication and Secrecy Codes for Equiprobable Source Probability Distributions

TL;DR

This paper introduces new combinatorial constructions for authentication and secrecy codes tailored for equiprobable sources, achieving optimal security and secrecy simultaneously, with many being the first of their kind.

Contribution

The paper presents an infinite class of optimal authentication codes that are multi-fold secure and perfectly secret, along with additional new optimal codes with similar properties.

Findings

Constructed an infinite class of optimal authentication codes

Achieved codes that are multi-fold secure against spoofing

Developed codes with perfect secrecy

Abstract

We give new combinatorial constructions for codes providing authentication and secrecy for equiprobable source probability distributions. In particular, we construct an infinite class of optimal authentication codes which are multiple-fold secure against spoofing and simultaneously achieve perfect secrecy. Several further new optimal codes satisfying these properties will also be constructed and presented in general tables. Almost all of these appear to be the first authentication codes with these properties.