Multilevel Threshold Secret Image Sharing based on the Chinese Remainder Theorem

摘要

(t, n)-threshold secret sharing was first introduced by Shamir and Blakley separately in 1979. Apart from this, there are threshold secret sharing schemes which use the Chinese Remainder Theorem (CRT). The above mentioned are three of the most extensively researched tools used for designing a (t, n)-threshold secret sharing scheme. In this paper we propose a scheme for Multilevel Threshold Secret Image Sharing using the CRT. Multilevel Threshold Secret Sharing (MTSS) is a generalization of the classical secret sharing scheme. In MTSS various participants are classified into levels and the secret is reconstructed from the shares submitted by participants depending on the various levels. Every level has a separate threshold such that a higher level will have a threshold value smaller than that of the threshold of a lower level. Now, participants in each level can reconstruct the secret if the number of shares available is equal to or greater than the threshold of that level. Higher level shares may be used to reconstruct a secret along with lower level shares depending on certain rules. Here, we use Chinese remainder theorem based on Asmuth-Bloom's scheme to perform MTSS in which the secret is an image. The use of Asmuth-Bloom's SS makes this scheme unconditionally secure. Our proposed scheme is the first time the CRT is being used for multilevel threshold secret image sharing.