Equivalence Classes in AES -- Part 1

TL;DR

This paper explores the properties of equivalence classes in AES related to its core operations, aiming to understand their structure and potential implications for cryptanalysis.

Contribution

It analyzes how AES operations affect equivalence classes, laying groundwork for future key recovery attacks based on these classes.

Findings

Properties of equivalence classes under AES operations

Impact of MixColumns and InvMixColumns on classes

Potential for key recovery attacks using class pairs

Abstract

We investigate properties of equivalence classes in AES which arise naturally from properties of MixColumns and InvMixColumns. These two operations have the property that the XOR of the 4 input bytes equals the XOR of 4 output bytes. We examine the effect on equivalence classes due to the operation of SubBytes, ShiftRows, MixColumns and AddRoundKey. The next phase of research is to find a key recovery attack using known (plaintext, ciphertext) equivalence class pairs. Keywords: AES, Equivalence, Class, MixColumns, ShiftRows, SubBytes, AddRoundKey, Schedule, State, XOR