Abstract: The paper analyses a signature scheme with message recovery based on elliptic curves, and finds the original scheme is insecure in message recovery. An improved scheme is presented in this paper to solve the problem that anyone can restore original message. An attack, named birthday attack, to a signature scheme with message recovery based on elliptic curves is introduced. When attackers use birthday attack to attack the signature information the secret key is easily exposed in original scheme, in this regard, an improved scheme is put forward and the new scheme can fully resist birthday attack.

Key words: digital signature, elliptic curve, message recovery, birthday attack

摘要： 通过分析一个基于椭圆曲线的具有消息恢复的数字签名方案，发现原方案的消息恢复存在安全性的缺陷，并针对此问题给出了改进的方案，解决了任何人都能恢复消息的缺陷。介绍了基于椭圆曲线的具有消息恢复的数字签名方案的一种攻击方法：生日攻击。原方案在攻击者使用生日攻击对签名信息进行攻击使得密钥信息容易暴露，对原方案作了改进，使得改进后的方案完全能够抵抗生日攻击。

关键词: 数字签名, 椭圆曲线, 消息恢复, 生日攻击