Analysis of Rotation-Based Diffusion Functions

ARX-based crypto-designs are gaining popularity nowadays because of their simplicity and efficiency. Rotation-based diffusion functions are used as building blocks in such designs. Invertibility or bijectivity of a diffusion function is a foremost requirement for the crypto-designs. In this paper, we analyse this aspect of diffusion functions. We consider a class of rotation-based linear diffusion functions and derive a necessary condition under which a diffusion function of this class is invertible. Further, we find a particular case where this necessary condition is sufficient also.