Elliptic curve cryptosystem has becoming the popular public-key cryptosystem gradually,thus it is important for us to comprehend its security state. Firstly, it has researched the definition of ECC and ECDLP. And then according to the selecting of elliptic curve as well as the application and the disverfied attacks of elliptic curve cryptosystem, the security analysis of elliptic curve cryptosystem was proposed in detail. Compared with other public-key cryptosystem,conclude that elliptic curve cryptosystem wiil be popularity in the future for the characters of short key, high security, fast encryption, little computation and small storage space. Therefore elliptic curve cryptosystem has important theoretical value and wide application prospect.%椭圆曲线密码体制已成为当前最流行的公钥加密体制.为明确椭圆曲线密码的当前总体安全形势,首先研究椭圆曲线的定义及椭圆曲线离散对数问题,然后分别从安全椭圆曲线的选择方法、椭圆曲线密码的应用和针对椭圆曲线密码的攻击等几个方面,着重分析了椭圆曲线密码的安全性问题.根据与其它公钥密码体制的安全强度分析比较表明:椭圆曲线密码体制具有许多优点,主要包括密钥短、安全强度高、加密快、运算量小、占用存储空间少等.因此椭圆曲线密码体制的研究具有重要的理论价值和广阔的应用前景.
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