Paper 2023/398

A New Linear Distinguisher for Four-Round AES

Abstract

In SAC’14, Biham and Carmeli presented a novel attack on DES, involving a variation of Partitioning Cryptanalysis. This was further extended in ToSC’18 by Biham and Perle into the Conditional Linear Cryptanalysis in the context of Feistel ciphers. In this work, we formalize this cryptanalytic technique for block ciphers in general and derive several properties. This conditional approximation is then used to approximate the inv : GF(2^8) → GF(2^8) : x → x^254 function which forms the only source of non-linearity in the AES. By extending the approximation to encompass the full AES round function, a linear distinguisher for four-round AES in the known-plaintext model is constructed; the existence of which is often understood to be impossible. We furthermore demonstrate a key-recovery attack capable of extracting 32 bits of information in 4-round AES using 2^125.62 data and time. In addition to suggesting a new approach to advancing the cryptanalysis of the AES, this result moreover demonstrates a caveat in the standard interpretation of the Wide Trail Strategy — the design framework underlying many SPN-based ciphers published in recent years.