**Mixture Differential Cryptanalysis and Structural Truncated Differential Attacks on round-reduced AES**

*Lorenzo Grassi*

**Abstract: **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 AES-like 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.

As a second contribution, we show how to combine this new 4-round distinguisher with a modified version of a truncated differential distinguisher in order to set up new 5-round distinguishers, that exploit properties which are independent of the secret key, of the details of the S-Box and of the MixColumns matrix. As a result, while a “classical” truncated differential distinguisher exploits the probability that a couple of texts satisfies or not a given differential trail independently of the others couples, our distinguishers work with sets of N >> 1 (related) couples of texts. In particular, our new 5-round AES distinguishers exploit the fact that such sets of texts satisfy some properties with a different probability than a random permutation.

Even if such 5-round distinguishers have higher complexity than e.g. the “multiple-of-8” one present in the literature, one of them can be used as starting point to set up the first key-recovery attack on 6-round AES that exploits directly a 5-round secret-key distinguisher. The goal of this paper is indeed to present and explore new approaches, showing that even a distinguisher like the one presented at Eurocrypt -- believed to be hard to exploit - can be used to set up a key-recovery attack.

**Category / Keywords: **secret-key cryptography / AES - Secret-Key Distinguisher - Key-Recovery Attack - Mixture Differential Cryptanalysis - Truncated Differential - Subspace Trail Cryptanalysis

**Date: **received 30 Aug 2017, last revised 1 Jul 2019

**Contact author: **lorenzo grassi at iaik tugraz at

**Available format(s): **PDF | BibTeX Citation

**Note: **New name for the proposed distinguishers and attacks

**Version: **20190701:125900 (All versions of this report)

**Short URL: **ia.cr/2017/832

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