Linear diffusion layer and nonlinear invariants for XSL-algorithms

D. A. Burov

TVP Laboratory

Abstract: In this paper we study the necessary conditions on the linear diffusion layer under which chains of invariants exist for XSL-algorithms. The characteristics of the matrix affecting the existence of such chains have been determined. The obtained results can be used both to prove the non-existence of invariant chains and to construct them. It has been demonstrated that block cipher «Kuznyechik» does not admit invariant chains of the studied type. For MixColumns operation of AES we describe the class of subspaces the cosets of which can form invariant chains Subspaces invariant under the MixColumns transformation of the AES algorithm have been described, and their cosets can form invariant chains.

Keywords: nonlinear invariant attack, invariant subspace attack, linear diffusion layer, «Kuznechik», AES.

UDC: 519.719.2

Received: 31.12.2024

DOI: 10.4213/dm1864