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
$\mathtt {AES}$
, 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.