Abstract
In some particular situations, participants need to recover different secrets both within a group (i.e., intragroup) and between two groups (i.e., intergroup). However, most of the existing multilevel secret sharing (MLSS) and multigroup secret sharing (MGSS) schemes mainly focus on how to protect a secret between one or more groups. In this paper, we propose a polynomial-based scheme to share multiple secret images both within a group and between groups. The random elements’ utilization model of integer linear programming is used to find polynomial coefficients that meet certain conditions so that each participant holds only one shadow image and some of them can recover secrets of both intergroup and intragroup. In addition, our scheme based on polynomials has the advantage of low computational complexity. Theoretical analysis and experiments show that the proposed scheme is feasible and effective.
Highlights
With the popularization of digital media technology, the transmission of information is more and more convenient and fast
At least k participants are needed to recover the secret, while less than k participants cannot obtain any information of the secret. e Lagrange interpolation method is used to recover the secret. e SS scheme based on polynomial can be applied to secret image sharing (SIS) for grayscale images and color images
Shamir proposed a (k, n) threshold secret sharing scheme based on the polynomial and it can be applied to SIS. e polynomial-based SIS (PSIS) scheme shares a secret image into n shadow images and distributes them to n participants
Summary
With the popularization of digital media technology, the transmission of information is more and more convenient and fast. Wu et al [24] proposed a hierarchical SIS scheme with multigroup joint management In their scheme, participants in different groups have to meet different threshold conditions to recover the secret, while all of the shadow images have the same weight. Ey constructed a base matrix to embed the information of multiple secret images into the coefficients of m polynomials Participants in their scheme are required to hold more than one shadow image. In order to realize MSIS within one group and between groups and to transmit and save shadow images more conveniently in practical application, we propose an intragroup and intergroup MSIS scheme with each participant holding one shadow image.
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