Threshold construction from specific cases in visual cryptography without the pixel expansion

•Three general threshold construction methods from specific cases are proposed.•The proposed VCS has superior performance that previous PVSS fails to have.•The proposed methods are also progressive VCSs without the pixel expansion.

Unexpanded shares can decrease the bandwidth and save storage in a visual cryptography scheme (VCS). To avoid the pixel expansion, some previous VCSs without the pixel expansion were given. However, most of them are only for specific cases other than general threshold (case). In this paper, three general threshold construction methods from specific cases are proposed. The constructed threshold VCSs are also progressive VCS without the pixel expansion. Analyses and experiments are conducted to evaluate the security and efficiency of the proposed methods.