Threshold changeable secret image sharing using bivariate polynomial

Abstract

In secret image sharing (SIS) scheme, a confidential image is encrypted into multiple shadows, any group of shadows that reaches the threshold, otherwise nothing can be reconstructed at all. Most existing SIS schemes have a fixed threshold, however in this work, we consider more complicated cases that the threshold may be adjusted due to the changeable security environment. In this paper, we construct a $(k\leftrightarrow h,n)$ threshold changeable SIS (TCSIS) scheme using bivariate polynomial, which has $h-k+1$ possible thresholds $k,k+1,...,h$. During image reconstruction, each participant can update the his shadow according to the current threshold $T$ only based on his initial shadow. Comparing with previous TCSIS schemes, the proposed scheme achieves unconditional security, and can overcome the information disclosure problem caused by homomorphism.