Abstract: Combining the advantages of Elliptic Curve Cryptosystem with the concept of forward security, the method of system time division is introduced to reduce the loss caused by key leakage on the basis of Elliptic Curve Digital Signature Algorithm（ECDSA）, and a forward security signature scheme（improved scheme） based on elliptic curve is constructed. Security analysis shows that the scheme is not only robust to random number attacks, but also forward secure based on Elliptic Curve Discrete Logarithm Problem（ECDLP） under the random oracle model. The analysis of arithmetic operation shows that the improved scheme has one multiplying points, two modular multiplications and two modular inversion operations less than the ECDSA scheme in signature generation and verification. The results of MATLAB show that the improved scheme is more efficient than ECDSA scheme and Zhou Keyuan scheme with the forward security.

Key words: elliptic curve, key evolution, random oracle model, forward security, digital signature

摘要： 将椭圆曲线密码体制的优势与前向安全的概念相结合，在椭圆曲线数字签名算法（ECDSA）的基础上，引入系统时间划分方法来减少密钥泄露带来的损失，从而构造出一种基于椭圆曲线的前向安全的签名方案（改进方案）。安全性分析表明，该方案不仅可以抗随机数攻击，而且在随机预言模型下基于椭圆曲线离散对数问题（ECDLP）困难性是前向安全的。算法运算量分析表明，在签名生成和验证时，改进方案比ECDSA方案少了1次倍点运算、2次模乘运算和2次模逆运算。MATLAB仿真结果表明，在签名效率上，改进方案比ECDSA方案以及同样具有前向安全性的周克元方案都要高。

关键词: 椭圆曲线, 密钥演化, 随机预言模型, 前向安全, 数字签名