Statistical Integral Distinguisher with Multi-structure and Its Application on AES

Advanced Encryption Standard (AES), published by NIST, is widely used in data encryption algorithms, hash functions, authentication encryption schemes and so on. Studying distinguishing attacks on (reduced round) AES can help designers and cryptanalysts to evaluate the security of target ciphers. Since integral attack is one of the most powerful tool in the field of symmetric ciphers, in this paper, we evaluate the security of AES by integral cryptanalysis. Firstly we put forward a new statistical integral distinguisher with multiple structures on input and integral properties on output, which enables us to reduce the data complexity comparing to the traditional integral distinguishers under multiple structures. As illustrations, we propose a secret-key distinguisher on 5-round AES with secret S-box under chosen-ciphertext mode. Its data, time and memory complexities are $$2^{114.32}$$ chosen ciphertexts, $$2^{110}$$ encryptions and $$2^{33.32}$$ blocks. This is the best integral distinguisher on AES with secret S-box under secret-key setting so far. Then we present improved known-key distinguishers on 8-round and full 10-round AES-128 with reduced complexities based on Gilbert’s work at ASIACRYPT’14. These distinguishers are the best ones according to the time complexity. Moreover, the proposed statistical integral model could be used to proceed known-key distinguishing attacks on other AES-like ciphers.