Improved Linear Differential Attacks on CubeHash

This paper presents improved collision attacks on round-reduced variants of the hash function CubeHash, one of the SHA-3 second round candidates. We apply two methods for finding linear differential trails that lead to lower estimated attack complexities when used within the framework introduced by Brier,.Khazaei, Meier and Peyrin at ASIA-CRYPT 2009. The first method yields trails that are relatively dense at the beginning and sparse towards the end. In combination with the condition function concept; such trails lead to much faster collision attacks. We demonstrate this by providing a. real collision for CubeHash-5/96. The second method randomizes the search for highly probable linear differential trails and leads to significantly better attacks for up to eight rounds.