A class of optimal authentication codes with secrecy

TL;DR

This paper introduces a new class of linear authentication codes with secrecy, featuring simple encoding, based on Weil sums, and proven to be asymptotically optimal against certain attacks.

Contribution

It constructs a novel class of authentication codes with secrecy that are easy to implement and asymptotically optimal, using Weil sums.

Findings

Codes have simple encoding rules and are easy to implement.

Maximum success probabilities for attacks are calculated.

Codes are proven asymptotically optimal with respect to certain bounds.

Abstract

In this paper, a class of linear authentication codes with secrecy are constructed, which have simple encoding rules and are easy to implement. Based on the special Weil sum, the maximum success probabilities of substitution attack and impersonation attack are calculated, and these codes are proven to be asymptotically optimal with respect to certain bounds.