The group generated by the round functions of a GOST-like cipher

TL;DR

This paper investigates the permutation group generated by the round functions of an extended GOST-like cipher, proving it is the alternating group under minimal assumptions, using group theory classifications.

Contribution

It establishes that the group generated by the cipher's round functions is the alternating group, extending understanding of the cipher's algebraic structure.

Findings

The group is primitive.

The group is the alternating group.

The result holds under minimal assumptions.

Abstract

We define a cipher that is an extension of GOST, and study the permutation group generated by its round functions. We show that, under minimal assumptions on the components of the cipher, this group is the alternating group on the plaintext space. This we do by first showing that the group is primitive, and then applying the O'Nan-Scott classification of primitive groups.