$(t,n)$ 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 ($m\ge t$) 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.

$（Ť，ñ）$阈值秘密共享（SS）是一种重要的加密原语，其中将秘密分为n个份额，然后任何t个或更多的股东都可以交换份额以重建秘密，而无需任何可信任的第三方的帮助。但是，如果没有任何有效份额的非法参与者假冒股东以m（$米\ge Ť$）传统的合法股东 $（Ť，ñ）$阈值SS方案，它可以获得秘密。因此，本文利用双变量对称多项式提出了一种基本的阈值可变秘密共享（TCSS）方案，该方案具有欺骗性免疫功能，可以阻止上述非法参与者的攻击。在基本的TCSS方案中，在秘密重建期间，允许阈值从t增加到所有参与者的确切人数。这样，仅当所有参与者都具有有效共享时，才可以恢复秘密。但是，每个股东必须保留其份额的t系数。然后，提出了一种基于单变量多项式和双变量对称多项式的改进的TCSS方案，以减少每个股东的股票系数。