Proof of Correspondence between Keys and Encoding Maps in an Authentication Code

TL;DR

This paper proves a one-to-one correspondence between keys and encoding maps in a specific authentication code based on Gray maps over Galois rings, confirming the code's structural integrity.

Contribution

It establishes the theoretical proof of the key-encoding map correspondence for a new authentication code, enhancing understanding of its security framework.

Findings

Proves the bijective relationship between keys and encoding maps.

Confirms the structural soundness of the second authentication code.

Supports the code's potential for secure authentication applications.

Abstract

In a former paper the authors introduced two new systematic authentication codes based on the Gray map over a Galois ring. In this paper, it is proved the one-to-one onto correspondence between keys and encoding maps for the second introduced authentication code.