The ElGamal public-key cryptosystem is an international public-key cryptosystem , and also a more effective and secure alogorithm used for secret communication networks and digital signature.It is the foundation of many special-purpose digital signatures.But the ElGamal digital signature algorithm has a security flaw that random numbers cannot repeatedly use. The thesis puts forward an improved method aimed at this security flaw, and makes a security analysis of the improved algorithm , and proves its correctness both in theory and practice.%ElGamal公钥密码体制是一种国际公认的较理想的公钥密码体制,是目前网络上进行保密通信和数字签名的较有效的安全算法,同时也是许多有特殊用途的数字签名的基础.但是ElGamal数字签名算法中存在随机数不能重复使用这一安全缺陷,本文针对这一缺陷提出了一种改进方法,并对改进后的算法进行了安全性分析,对其正确性进行了理论和实际的证明.
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