Abstract
At ASIACRYPT 2017, Rønjom et al. analyzed AES with the yoyo attack. Similar to their 4-round AES distinguisher, Grassi proposed the 4-round mixture differential cryptanalysis as well as a key recovery attack on 5-round AES at ToSC 2018, 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 structure and illustrate that a differential distinguisher of a boomerang structure 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 numbers. 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 differential distinguisher 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.
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The datasets supporting the conclusions of this article are included within the article and its additional files. The code supporting the conclusions of this article is available in https://github.com/BLOCKCIPHERS702702.
Notes
We have revised the definition of primitive index in [16] since the Type 2 primitive index of P is not used in our work.
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Appendix
Appendix
The truncated differential distinguishers of 6-round Midori64 and 8-round SKINNY64 searched by MILP modeling technique are presented in Figs. 4 and 5, respectively.
A truncated differential distinguisher for boomerang structure of 6-round Midori64
A truncated differential distinguisher for boomerang structure of 8-round SKINNY64
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Xie, X., Tian, T. Structural evaluation of AES-like ciphers against mixture differential cryptanalysis. Des. Codes Cryptogr. 91, 3881–3899 (2023). https://doi.org/10.1007/s10623-023-01277-7
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DOI: https://doi.org/10.1007/s10623-023-01277-7