Structure Evaluation of AES-like Ciphers against Mixture Differential Cryptanalysis

Abstract

In ASIACRYPT 2017, Rønjom et al. analyzed AES with yoyo attack. Inspired by their 4-round AES distinguisher, Grassi proposed the mixture differential cryptanalysis as well as a key recovery attack on 5-round AES, which was shown to be better than the classical square attack in computation complexity. After that, Bardeh et al. combined the exchange attack with the 4-round mixture differential distinguisher of AES, leading to the first secret-key chosen plaintext distinguisher for 6-round AES. Unlike the attack on 5-round AES, the result of 6-round key-recovery attack on AES has extremely large complexity, which implies the weakness of mixture difference to a certain extent. Our work aims at evaluating the security of AES-like ciphers against mixture differential cryptanalysis. We propose a new structure called a boomerang struncture and illustrate that a differential distinguisher of a boomerang struncture just corresponds to a mixture differential distinguisher for AES-like ciphers. Based on the boomerang structure, it is shown that the mixture differential cryptanalysis is not suitable to be applied to AES-like ciphers with high round number. In specific, we associate the primitive index with our framework built on the boomerang structure and give the upper bound for the length of mixture differentials with probability 1 on AES-like ciphers. It can be directly deduced from our framework that there is no mixture differential distinguisher for 6-round AES