Nonlinearity Properties of the Mixing Operations of the Block Cipher IDEA

In this paper we study the nonlinearity properties of the mixing operations ⊙, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\boxplus$\end{document} and ⊕ used in IDEA. We prove that the nonlinearity of the vector function corresponding to the multiplication operation ⊙ is zero for some key points. The Multiplication-Addition (MA) structure of IDEA is slightly changed to avoid the linearities due to these points and we suggest a new structure called RMA. The nonlinearity of MA, RMA and their composition are compared.