Searching Cubes in Division Property Based Cube Attack: Applications to Round-Reduced ACORN
Recently, division property based cube attack has acheived new progress and some cryptanalytic results against well-known stream ciphers. At EUROCRYPT 2020, Hao et al. proposed a new modeling method for three-subset division property without unknown subset. With this method, the exact expression of the superpoly in cube attack can be recovered. In this paper, we propose a method to search good cubes for both distinguishing attacks and key recovery attacks in the division property based cube attack scenario. Our cube searching procedure is based on the algorithm of degree evaluation of the superpoly and the algorithm of superpoly recovery. In the process of cube searching, we mainly use the embedded property to narrow down the searching space. As a result, we find some new cube testers of dimension 126 on 775-round ACORN. We also find a new key recovery attack on 775-round ACORN with a 126-dimensional cube, whose corresponding superpoly is a 2-degree polynomial with respect to key bits.