DSA数字签名的安全性分析

针对目前已知的主要安全攻击直接求取私钥攻击、穷搜索攻击、生日攻击、已知消息的伪造攻击等，对DSA(Digital Signature Algorithm)的安全性进行分析，给出了各种攻击方法需完成的计算。结果表明，其计算量等价或难于求解离散对数问题，一定程度地呈现了DSA的安全强度。指出了DSA可能的弱点存在于随机数 k、与消息无关的签名r、公共模数p与q、Hash函数等处，并给出了相应的解决方案。设计好的随机数生成器选择适宜的随机数，避免低指数和相同随机数攻击；合理选择模p的长度可抵抗共r攻击；在对安全强度要求高而运算速度要求相对较低时，使用DSA素数作为共享模数；使用消息摘要足够长的SHA(Secure Hash Algorithm)，以保证内嵌Hash函数的安全。

Analysis on Security of Digital Signature Algorithm

Extended research and practical application about DSA(Digital Signature Algorithm) are very wide,they are all based on the security of DSA itself.Aiming at the main known attacks of evaluating secret key with the help of public data,exhaustive groping attack,birthday attack and fabrication attack based on known message,security of DSA is analyzed.The computing expressions are given about the attack methods.It is indicated that these attacks are equal to or more difficult than solving the discrete logarithm ...