Про неіснування матриць максимального індексу розгалуження над кільцем лишків за модулем n2

S. Yakovlev; V. Didan

On the non-existence of matrices of maximum branch number over ring of residues modulo n2

Authors

S. Yakovlev Department of Mathematical Methods of Information Security, Institute of Physics and Technology, National Technical University of Ukraine “Kyiv Polytechnic Institute”
V. Didan Department of Mathematical Methods of Information Security, Institute of Physics and Technology, National Technical University of Ukraine “Kyiv Polytechnic Institute”

Keywords:

branch number, diffusion layer, modular addition

Abstract

We prove that no matrix over the ring of residues modulo \( n^2 \) has maximal branch number and show how this claim influences the cryptographic properties of algorithms which use modular addition in the linear diffusion layer.