Secret image sharing with smaller shadow sizes for general access structures

In the area of secret image sharing (SIS), most papers focused on the schemes for threshold or some special access structures. Regarding general access structures (GAS), few results have been found in the literature. Two SIS schemes for GAS were proposed in 2001 and 2010, both are based on qualified sets. However, one distorts the reconstructed secret image, and some extra information is needed in both schemes. Here, we propose three polynomial based SIS schemes for GAS. Considering either qualified or forbidden sets, these schemes can reconstruct the secret image perfectly without any extra information needed. Some proof and analysis on the shadow sizes of the three schemes are given to lead us to choose the one with the smallest size. In addition, we also give some comparisons with two existing schemes, and security issue is also addressed in conclusion.