Z.Shao提出了两种签名方案,并宣称它们的安全性是基于大数分解问题和离散对数问题的。其实,这两种签名方案在代换攻击下是不安全的。本文给出了伪造签名的公式,同时还提出了几种带有信息恢复功能的签名方案,它们的安全性是基于上述两个难题的,并且,它们在实施中的效率要比现有的方案好。 Z.Shao proposed two signature schemes and claimed that their security was based on the problem of large number decomposition and discrete logarithm. In fact, these two signature schemes are not safe under the substitution attack. This paper presents a formula for forging signatures. At the same time, several signature schemes with information restoration are proposed. Their security is based on the above two problems, and they are more efficient in implementation than the existing schemes it is good.