中文摘要：

Yang和Li提出了1个有效的基于离散对数和因子分解的签名方案，其安全性严格基于离散对数和因子分解两大困难问题之上。然而他们的方案需要t＋2对密钥，其中t为1个单向哈希函数输出的比特长度，通常为128或160。为了克服其方案密钥量大的缺陷，通过去掉单向哈希函数，给出1个改进方案。从5种可能的攻击方式对改进方案进行安全性分析。结果显示，在离散对数和因子分解不能同时求解的情况下，改进方案是安全的。从密钥个数、计算复杂性和通信成本3个方面对改进方案与Yang和Li的方案进行比较。改进方案密钥个数下降至3个，计算复杂性明显低于Yang和Li的方案，通信成本相同。

英文摘要：

Yang and Li proposed an efficient signature scheme that is strictly based on two hard problems of discrete logarithms and factoring. However, their scheme requires t＋2 keys for a signing document, where t is the output bit length of a one-way Hash function and is usually equal to 128 or 160. To overcome the weakness of too many keys, we present an improvement of their signature scheme by getting rid of the one-way Hash function. We also consider 5 possible attacks and show that the improved scheme is secure if the discrete logarithms and factoring are simultaneously unsolvable. As compared with the Yang and Li＇s scheme in terms of the number of keys, computational complexity and communication cost, the improved scheme only needs 3 keys, lower computational complexity and same communication cost.