Threshold changeable secret sharing with secure secret reconstruction

•Firstly, a basic TCSS scheme based on a bivariate polynomial is proposed to thwart illegal participant attack.•Secondly, an improved TCSS scheme is proposed to reduce coefficients of shares for each shareholder.•Thirdly, both the two schemes are dealer-free, non-interactive and cheating immune. (t,n) threshold secret sharing (SS) is an important cryptographic primitive in which a secret is divided into n shares, and then any t or more shareholders can exchange shares to reconstruct the secret without help of any trusted third party. However, if an illegal participant, without any valid share, impersonates a shareholder to recover the secret with m (m≥t) legal shareholders in a traditional (t,n) threshold SS scheme, it may obtain the secret. Therefore, this paper utilizes a bivariate symmetry polynomial to propose a basic threshold changeable secret sharing (TCSS) scheme which is cheating immune and thwarts the above illegal participant attack. In the basic TCSS scheme, threshold is allowed to increase from t to the exact number of all participants during secret reconstruction. In this way, the secret can be recovered only if all the participants have valid shares. However, each shareholder has to keep t coefficients of its share. Then, an improved TCSS scheme based on both univariate polynomial and bivariate symmetry polynomial is proposed to reduce coefficients of shares for each shareholder.