Lossless and Efficient Secret Image Sharing Based on Matrix Theory Modulo 256

Abstract

Most of today’s secret image sharing (SIS) schemes are based on Shamir’s polynomial-based secret sharing (SS), which cannot recover pixels larger than 250. Many exiting methods of lossless recovery are not perfect, because several problems arise, such as large computational costs, pixel expansion and uneven pixel distribution of shadow image. In order to solve these problems and achieve perfect lossless recovery and efficiency, we propose a scheme based on matrix theory modulo 256, which satisfies ( k , k ) and ( k , k + 1 ) thresholds. Firstly, a sharing matrix is generated by the filter operation, which is used to encrypt the secret image into n shadow images, and then the secret image can be obtained by matrix inverse and matrix multiplication with k or more shadows in the recovery phase. Both theoretical analyses and experiments are conducted to demonstrate the effectiveness of the proposed scheme.