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

Abstract

At EUROCRYPT 2017, Grassi et al. proposed the multiple-of-8 property for 5-round $\mathtt {AES}$ , 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 $\mathtt {SKINNY}$ . In this paper, we present that $n$ is not only a multiple but also a fixed value for $\mathtt {SKINNY}$ . 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 $\mathtt {SKINNY}$ and use this property to construct 6-round distinguisher on $\mathtt {SKINNY{-}64}$ and $\mathtt {SKINNY{-}128}$ . 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 $\mathtt {SKINNY}$ , not for $\mathtt {AES}$ and $\mathtt {MIDORI}$ , and provide the conditions under which it exists for $\mathtt {AES}$ -like ciphers.

Keywords

• Multiple-of property
• structural-differential property
• SKINNY
• AES-like cipher