An application of the O'Nan-Scott theorem to the group generated by the round functions of an AES-like cipher

TL;DR

This paper applies the O'Nan-Scott theorem to prove that the permutation group generated by the round functions of an AES-like cipher is the alternating group, enhancing understanding of its algebraic structure.

Contribution

It is the first to use the O'Nan-Scott classification to identify the permutation group as the alternating group in this context.

Findings

The group generated by the cipher's round functions is primitive.

The permutation group is proven to be the alternating group.

This result provides insights into the cipher's algebraic properties.

Abstract

In a previous paper, we had proved that the permutation group generated by the round functions of an AES-like cipher is primitive. Here we apply the O'Nan Scott classification of primitive groups to prove that this group is the alternating group.