Abstract Division property is a cryptanalysis method that proves to be very efficient on block ciphers. Computer-aided techniques such as MILP have been widely and successfully used to study various cryptanalysis techniques, and it especially led to many new results for the division property. Nonetheless, we claim that the previous techniques do not consider the full search space. We show that even if the previous techniques fail to find a distinguisher based on the division property over a given function, we can potentially find a relevant distinguisher over a linearly equivalent function. We show that the representation of the block cipher heavily influences the propagation of the division property, and exploiting this, we give an algorithm to efficiently search for such linear mappings. As a result, we exhibit a new distinguisher over 10 rounds of , while the previous best was over 9 rounds, and rule out such a distinguisher over more than 9 rounds of . We also give some insight about the construction of an S-box to strengthen a block cipher against our technique. We prove that using an S-box satisfying a certain criterion is optimal in term of resistance against classical division property. Accordingly, we exhibit stronger variants of and , improving the resistance against division property based distinguishers by 2 rounds.

The majority of current attacks on reduced-round variants of block ciphers seeks to maximize the number of rounds that can be broken, using less data than the entire codebook and less time than exhaustive key search. In this paper, we pursue a different approach, restricting the data available to the adversary to a few plaintext/ciphertext pairs. We argue that consideration of such attacks (which received little attention in recent years) improves our understanding of the security of block ciphers and of other cryptographic primitives based on block ciphers. In particular, these attacks can be leveraged to more complex attacks, either on the block cipher itself or on other primitives (e.g., stream ciphers, MACs, or hash functions) that use a small number of rounds of the block cipher as one of their components. As a case study, we consider the Advanced Encryption Standard (AES)-the most widely used block cipher. The AES round function is used in many cryptographic primitives, such as the hash functions Lane, SHAvite-3, and Vortex or the message authentication codes ALPHA-MAC, Pelican, and Marvin. We present attacks on up to four rounds of AES that require at most three known/chosen plaintexts. We then apply these attacks to cryptanalyze an AES-based stream cipher (which follows the leak extraction methodology), and to mount the best known plaintext attack on six-round AES.