Revisiting the Multiple-of Property for SKINNY: The Exact Computation of the Number of Right Pairs

At EUROCRYPT 2017, Grassi et al. proposed the multiple-of-8 property for 5-round AES, where the number n of right pairs is a multiple of 8. At ToSC 2019, Boura et al. generalized the multiple-of property for a general SPN block cipher and applied it to block cipher SKINNY. In this paper, we present that n is not only a multiple but also a fixed value for SKINNY. Unlike the previous proof of generalization of multiple-of property using equivalence class, we investigate the propagation of the set to compute the exact number n. We experimentally verified that presented property holds. We extend this property one round more using the lack of the whitening key on the SKINNYand use this property to construct 6-round distinguisher on SKINNY-64 and SKINNY-128. The probability of success of both distinguisher is almost 1 and the total complexities are 216 and 232 respectively. We verified that this property only holds for SKINNY, not for AESand MIDORI, and provide the conditions under which it exists for AES-like ciphers.