CoTree: A Side-Channel Collision Tool to Push the Limits of Conquerable Space

By introducing collision information into divide-and-conquer distinguishers, the existing collision-optimized side-channel attacks transform the given candidate space into a significantly smaller collision space, thus achieving more efficient key recovery. However, the candidates of the first several subkeys shared by collision chains are still repeatedly detected, which happens very frequently and brings huge computational overhead. To alleviate this, we propose a highly efficient collision-optimized attack named collision tree (CoTree). This collision detection tool exploits tree structure to store the chains created from the same subchain on the same branch, thus significantly reducing the storage requirements. It then benefits from the properties of both tree and collisions and exploits a top-down tree building procedure and traverses each node only once when detecting their collisions with a candidate of the subkey currently under consideration. Finally, unlike the traditional top-down node removal, CoTree launches a bottom-up branch removal procedure to remove the chains unsatisfying the collision conditions from the tree after traversing all the considered candidates of this subkey, thus avoiding the traversal of the branches satisfying the collision condition. These strategies make our CoTree significantly alleviate the repetitive collision detection, and our experiments verify that it significantly outperforms the existing works.