Mixture Differential Cryptanalysis: a New Approach to Distinguishers and Attacks on round-reduced AES

• Published in: IACR Transactions on Symmetric Cryptology pp. 133 - 160
• Main Author: Lorenzo Grassi
• Format: Journal Article
• Language: English
• Published: Ruhr-Universität Bochum 01.06.2018
• Subjects: AES; Key-Recovery Attack; Mixture Differential Cryptanalysis; Secret-Key Distinguisher; Subspace Trail Cryptanalysis; Truncated Differential
• ISSN: 2519-173X
• DOI: 10.13154/tosc.v2018.i2.133-160

At Eurocrypt 2017 the first secret-key distinguisher for 5-round AES - based on the “multiple-of-8” property - has been presented. Although it allows to distinguish a random permutation from an AES-like one, it seems rather hard to implement a key-recovery attack different than brute-force like using such a distinguisher. In this paper we introduce “Mixture Differential Cryptanalysis” on round-reduced AESlike ciphers, a way to translate the (complex) “multiple-of-8” 5-round distinguisher into a simpler and more convenient one (though, on a smaller number of rounds). Given a pair of chosen plaintexts, the idea is to construct new pairs of plaintexts by mixing the generating variables of the original pair of plaintexts. Here we theoretically prove that for 4-round AES the corresponding ciphertexts of the original pair of plaintexts lie in a particular subspace if and only if the corresponding pairs of ciphertexts of the new pairs of plaintexts have the same property. Such secret-key distinguisher - which is independent of the secret-key, of the details of the S-Box and of the MixColumns matrix (except for the branch number equal to 5) - can be used as starting point to set up new key-recovery attacks on round-reduced AES. Besides a theoretical explanation, we also provide a practical verification both of the distinguisher and of the attack.