Exact maximum expected differential and linear probability for $2$-round Kuznyechik

This paper presents the complete description of the best differentials and linear hulls in $2$-round Kuznyechik. We proved that $2$-round maximal expected differential probability equals $2^{-86.66\dots}$ and maximal expected linear probability equals $2^{-76.739\dots}$. A comparison is made with similar results for the AES cipher.