Essential secret image sharing scheme with the same size of shadows

• An essential secret image sharing scheme is proposed based on derivative polynomial.
• The essential shadows are more important than non-essential shadows.
• All shadows have the same size.
• No concatenation operation is needed in generation of shadows.

Secret image sharing is a method to decompose a secret image into shadow images (shadows) so that only qualified subset of shadows can be used to reconstruct the secret image. Usually all shadows have the same importance. Recently, an essential SIS (ESIS) scheme with different importance of shadows was proposed. All shadows are divided into two group: essential shadows and non-essential shadows. In reconstruction, the involved shadows should contain at least a required number of shadows, including at least a required number of essential shadows. However, there are two problems in previous ESIS scheme: unequal size of shadows and concatenation of sub-shadow images. These two problems may lead to security vulnerability and complicate the reconstruction. In this paper, we propose a novel ESIS scheme based on derivative polynomial and Birkhoff interpolation. A single shadow with the same-size is generated for each essential and non-essential participant. The experimental results demonstrate that our scheme can avoid above two problems effectively.