Abstract A two-polynomial based threshold secret sharing (SS) scheme is proposed by Liu et al., where two functions for detection of share cheating are used. It is found that the scheme is weak as the equations formed by at most (t – 1) dishonest participants in term of unknowns are not equivalent to the cheating detection function, and if one polynomial is kept fixed and other with two cheating detection equations are taken, a set of equations with unknowns exist, and are found to be easily solvable. In this paper, we also propose a two-polynomial based (t, n) threshold SS scheme; however, the polynomials are taken in such a way that they have an arbitrary common coefficient and as a result, both the polynomials are to be modified simultaneously for cheating of shares and incorporates higher cheating detection capability. Some analytical proofs and comparison with other schemes in support of our claims are provided.

中文翻译：

---

基于两个多项式的 (t, n) 阈值秘密共享方案与作弊检测

摘要 Liu 等人提出了一种基于两个多项式的阈值秘密共享（SS）方案，其中使用了两个用于检测共享作弊的函数。发现该方案很弱，因为最多(t-1)个不诚实参与者在未知方面形成的方程不等价于作弊检测函数，如果一个多项式保持不变，另一个有两个作弊检测方程是因此，存在一组带有未知数的方程，并且发现它们很容易求解。在本文中，我们还提出了一种基于两个多项式的(t,n)阈值SS方案；然而，多项式的取法使得它们具有任意的公共系数，因此，这两个多项式都将同时修改以防止股票作弊，并具有更高的作弊检测能力。