Cube distinguisher extraction using division property in block ciphers

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Cube attack, a simplified type of algebraic attack, is widely utilised to cryptanalyse ciphers. However, since the cube attack works without considering the cipher structure, it is highly complex. In 2017, division property, a successful approach to finding integral distinguishers, was used to extract cube distinguishers in a non-blackbox manner for stream ciphers, which led to a significant improvement of the previous results. This is the first paper employing division property for cube distinguisher extraction in block ciphers. To do this, first, an approach relying on Boolean satisfiability problem (SAT) is presented to evaluate the propagation of division property. Indeed, extraction of zero-sum distinguisher is mapped on a SAT problem and SAT solvers are used to finding division trails efficiently and automatically. Then, this approach is extended and adapted to extract cube distinguishers in block ciphers. However, there are similarities between our contribution and others but the different structure of block and stream ciphers lead to disparity in applying division property to extract cube distinguisher for block ciphers. To prove the efficiency of the presented approach, it is applied to the lightweight block cipher Katan and the cube distinguishers are extended to a higher round in comparison with previous results.