Group properties of block ciphers of the Russian standards GOST R 34.11-2012 and GOST R 34.12-2015

A group generated by the set of the round functions is often used to describe properties of a block cipher. The results obtained by A. S. Maslov in 2007 are used to prove that round functions of Kuznyechik and Stribog generate the alternating groups. We prove a theorem on the mixing properties of linear transformations and apply this theorem to the family of Stribog-like ciphers (Stribog, Anubis, etc.).