A New Non-random Property of 4.5-Round PRINCE.

PRINCE is a widely analyzed block cipher proposed in 2012. Subspace trail cryptanalysis is a new cryptanalytic technique to generalize the invariant subspace attack. So far, two subspace trails that exist with probability 1 are known for 2.5 rounds of PRINCE. In this paper, we first describe a new non-random property for 4.5 rounds of PRINCE based on subspace trail with certain probability, which is independent of the secret key, the details of the Linear layer and of the S-Box layer. Then, we obtain that by appropriate choices of difference for a number of input pairs, it is possible to make sure that the number of times that the difference of the resulting output pairs lie in a particular subspace is always a multiple of 8. Later, a detailed proof is given as why it has to exist. Relying on this property, a new distinguisher can be set up to distinguish the 4.5-round PRINCE from a random permutation.