椭圆曲线密码是公钥密码体制,它的安全基础是椭圆曲线上的离散对数问题。研究表明,椭圆曲线密码是目前唯一无法用亚指数算法破解的公钥密码。通过详细介绍ECC的数学基础的基础,分析针对椭圆曲线离散对数问题的常见攻击算法,并在最后给出一种完整的安全椭圆曲线选择方法。
Elliptic curves cryptosystem (ECC) is a kind of public-key cryptosystem whose security is based on the discrete logarithm problem in finite field. By far, studies have shown that no effective attacking algorithm has not been founded which can invert the elliptic curves discrete logarithm problem (ECDLP) in sub-exponential time. After an introduction to the mathematic concepts of ECC, we proposed a method of choosing an appropriate elliptic curve on the basis of a thorough discussion of all the attacking algorithms to ECC.