Abstract: A threshold digital signature scheme is proposed by Fei Ru-chun and Wang Li-na.Its security is based on the difficulty of solving discrete logarithm in finite field and quadratic residue on some special conditions.The method is constructed to find out the malicious shareholders who disrupt the signature process and forges.Based on number theory，the authors firstly show there are some insufficiencies and potential hazard in the scheme proposed by Fei，et al.That is to say，any t members cannot impersonate another set of group members to sign any message withstand conspiracy attack.Secondly，the authors also propose a new scheme using the idea of Williams to solve the above questions.Compared to the existing threshold signature schemes，the scheme needs not to renew the members’ shadows when the system has renewed and the verification is easy.

摘要： 费如纯、王丽娜等提出了一个安全性基于有限域上求解离散对数的困难性和特定条件下求解二次剩余的困难性的门限数字签名方案。该方案能防止恶意参与者欺诈以阻止签名和伪造攻击。基于数论知识分析指出他们给出的这种实现方案存在不足和安全隐患：t个成员合谋无法假冒其他成员生成有效的数字签名；然后利用Williams体制对上述方案改进，从而解决了以上问题。新方案还具有成员的子密钥可以无限制的使用、验证的简单性等许多良好性质。