Symmetric States and their Structure: Improved Analysis of CubeHash

This paper provides three improvements over previous work on analyzing CubeHash, based on its classes of symmetric states: (1) We present a detailed analysis of the hierarchy of symmetry classes. (2) We point out some flaws in previously claimed attacks which tried to exploit the symmetry classes. (3) We present and analyze new multicollision and preimage attacks. For the default parameter setting of CubeHash, namely for a message block size of b = 32, the new attacks are slightly faster than 2 operations. If one increases the size of a message block by a single byte to b = 33, our multicollision and preimage attacks become much faster – they only require about 2 operations. This demonstrates how sensitive the security of CubeHash is, depending on minor changes of the tunable security parameter b.