A novel approach for multilevel multi-secret image sharing scheme

Multi-secret sharing (MSS) is an effective technique that securely encodes multiple secrets to generate shares and distributes them among the participants in such a way that these shares can be used later to reconstruct the secrets. MSS schemes have a considerable advantage over the single-secret sharing schemes for secure multimedia data transmission. This paper presents a novel secret image sharing approach, namely ‘(n, m, l)-Multilevel Multi-Secret Image Sharing (MMSIS) scheme.’ The proposed MMSIS scheme encodes ‘n’ distinct secret images to generate ‘m’ shares and distributes them among ‘m’ participants allocated to ‘l’ distinct levels. The paper proposes two variants of the MMSIS scheme. The first variant is an (n,n+1,l)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n,n+1,l)$$\end{document}-MMSIS scheme which encodes ‘n’ secret images each having a unique level id Lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_k$$\end{document} into (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+1)$$\end{document} shares. The image shares are then distributed among (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+1)$$\end{document} participants assigned to ‘l=n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l=n$$\end{document}’ different levels. With the increase in level id, the number of shares required to reconstruct the secret image also increases. To reconstruct a secret image of a particular level Lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_k$$\end{document}, all the shares at level Lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_k$$\end{document} and its preceding levels need to be acquired, which requires the consensus of all participants holding the shares up to level Lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_k$$\end{document}. The second variant, namely extended-MMSIS (EMMSIS) scheme is a generalized (n, m, l) version of the former scheme that allows to generate more shares for a specific secret image at a particular level in accordance with the consensus requirements for its reconstruction. The multilevel structure of the scheme makes it useful for multi-secret distribution in a multilevel organizational structure.