Practical Secret Image Sharing Based on the Chinese Remainder Theorem

Abstract

Compared with Shamir’s original secret image sharing (SIS), the Chinese-remainder-theorem-based SIS (CRTSIS) generally has the advantages of a lower computation complexity, lossless recovery and no auxiliary encryption. However, general CRTSIS is neither perfect nor ideal, resulting in a narrower range of share pixels than that of secret pixels. In this paper, we propose a practical and lossless CRTSIS based on Asmuth and Bloom’s threshold algorithm. To adapt the original scheme for grayscale images, our scheme shares the high seven bits of each pixel and utilizes the least significant bit (LSB) matching technique to embed the LSBs into the random integer that is generated in the sharing phase. The chosen moduli are all greater than 255 and the share pixels are in the range of [0, 255] by a screening operation. The generated share pixel values are evenly distributed in the range of [0, 255] and the selection of (k,n) threshold is much more flexible, which significantly improves the practicality of CRTSIS. Since color images in RGB mode are made up of three channels, it is easy to extend the scheme to color images. Theoretical analysis and experiments are given to validate the effectiveness of the proposed scheme.

Keywords

• secret image sharing
• Chinese remainder theorem
• (<i>k</i>, <i>n</i>) threshold
• practical
• lossless