Analysis of rotation and shift based diffusion functions

Abstract ‘Rotation and shift’ based diffusion functions are used in modern ciphers especially in ARX (Addition, Rotation, and XOR) based designs. They are preferred over other alternatives as they are efficient and lightweight. Usually, such diffusion functions map an n-bit block to another n-bit block. One of the requirements for an n-bit to n-bit diffusion function is that, it should be invertible. In this paper, we present mathematical models for different classes of ‘rotation and shift’ based diffusion functions and explore their invertibility. We derive sufficient conditions under which diffusion functions of these classes are invertible.