Quantum Preimage and Collision Attacks on CubeHash

In this paper we show a quantum preimage attack on CubeHash-512-normal with complexity 2. This kind of attack is expected to cost 2 for a good 512-bit hash function, and we argue that this violates the expected security of CubeHash. The preimage attack can also be used as a collision attack, given that a generic quantum collision attack on a 512-bit hash function require 2 operations, as explained in the CubeHash submission document. This attack only uses very simple techniques, most of which are borrowed from previous analysis of CubeHash: we just combine symmetry based attacks [1,8] with Grover’s algorithm. However, it is arguably the first attack on a second-round SHA-3 candidate that is more efficient than the attacks considered by the designer.