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中文摘要：
在标准模型下设计高效可证明安全的签名方案具有现实意义。基于Waters和Paterson最近提出的签名方案，提出了两种有效的标准模型下的基于身份的签名方案：一种为（t，n）门限方案，在计算Diffie-Hellman假设（CDH问题）下，方案被证明具有不可伪造性和健壮性；另一种为分级签名方案，该方案签名算法效率高，仅需两次指数运算。在CDH困难问题假设下，该方案被证明是安全的。
英文摘要：
To design a signature scheme which are efficient and provably secure in the standard model is suitable for applications. Two signature schemes based on Paterson＇s and Waters＇s signature schemes are proposed. A（t, n） threshold signature scheme is presented at first and is provable secure in the standard model under CDH assumption. The other contribution in this paper is to construct a new hierarchical identity based signature scheme. It has a highly efficient signing algorithm which requires only two exponentiation operations and is provably secure under CDH assumption in the standard model.
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