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

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