Intragroup and intergroup secret image sharing based on homomorphic Lagrange interpolation

Abstract In this paper, a ( k , n , m ) -intragroup and intergroup secret image sharing (I 2 SIS) scheme for the multi-group (i.e., m -group) environment is investigated. ( 2 m − 1 ) secret images are shared within groups (intragroups) and between groups (intergroups). Differing from existing SIS methods, any k or more qualified participants among different groups (i.e., intergroup) can collaboratively recover the respective secret image via the homomorphic Lagrange interpolation. The proposed scheme consists of three major procedures: preprocessing, sharing, and recovering. In the preprocessing procedure, an approach is designed to partition the coefficients in the m ( k − 1 ) -degree polynomials for sharing the ( 2 m − 1 ) secret images. In addition, an optimal algorithm for the preprocessing is given to let all the percentages of recovering secret images be the same as possible. Shadows belonging to all participants in the m groups are generated in the sharing procedure. In the recovering procedure, the secret images can be reconstructed in intragroups and intergroups. Moreover, experiments and comparisons are demonstrated to show the merits of the proposed scheme.