CP-PSIS: CRT and polynomial-based progressive secret image sharing

•A novel progressive SIS scheme is proposed by combining polynomial and CRT.•Homomorphism of CRT in Lagrange interpolation operation is utilized.•The proposed CP-PSIS scheme is general and flexible.•Security is guaranteed by CRT and polynomial-based secret sharing technique. In (k, n) Progressive Secret Image Sharing (PSIS) schemes, n shares are obtained by sharing a secret image. With k to n shares, the secret image can be recovered progressively. No information of the secret image can be constructed by k-1 or fewer shares. Many Secret Image Sharing (SIS) schemes have been developed to achieve the progressive reconstruction property. However, such property is usually based on the pre-processing of the secret image which is inconvenient and would increase the cost of the algorithm. Moreover, in existing PSIS schemes, only if all of n shares are involved, the secret image can be completely reconstructed. That makes the schemes not fault-tolerant. Thus, a solution for the flexible and extendable PSIS scheme is required. In this paper, we propose a Chinese Remainder Theorem (CRT) and Polynomial-based Progressive Secret Image Sharing (CP-PSIS) scheme and a modified version of CP-PSIS scheme. The proposed schemes are the first to utilize the homomorphism of CRT in the Lagrange interpolation operation. The progressive property of the schemes is achieved by CRT. In the (k, n) threshold SIS, any k participants can obtain different versions of the secret image by choosing different parameters. Our proposed schemes achieve a high security based on CRT and polynomial. Theoretical analyses and experimental results have demonstrated that the proposed schemes are general, flexible and extendable for different PSIS applications.