Ideal homomorphic secret sharing schemes over cyclic groups

For a cyclic groupG and an access structureA, the sufficient and necessary condition under whichA isG-ideal homomorphic is given by using the fine-representation of the corresponding matroid over the ring\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{Z}_m $$ \end{document}. Furthermore, the clasification ofG-ideal homomorphic graphic access structures is shown.