algorithm is a candidate of the Lightweight Cryptography standardization process started by the National Institute of Standards and Technology (NIST) of the USA that passed the first round and successfully entered the second round. It is designed to achieve a balance between hardware cost and software efficiency for both authenticated encryption with associated data (AEAD) and hashing functionalities. This paper focuses on the impossible differential attack against the ACE
permutation, which is the core component of the ACE
algorithm. Based on the method of characteristic matrix, we build an automatic searching algorithm that can be used to search for structural impossible differentials and give the optimal permutation for ACE
permutation and other SPN ciphers. We prove that there is no impossible differential of ACE
permutation longer than 9 steps and construct two 8-step impossible differentials. In the end, we give the optimal word permutation against impossible differential cryptanalysis, which is
, and a safer word XOR structure of ACE permutation.
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