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椭圆曲线公钥密码体制(ECC)具有最高的位安全强度,将是对现有公钥密码体制的替代。文章描述了代数几何与ECC的数学基础,讨论了椭圆曲线离散对数困难性问题及ECC在电子商务中的安全应用。利用仿射坐标与射影坐标的映射关系,设计了一种有限素整数域上ECC快速算法,使得ECC在电子商务中实际安全应用成为可能。
Elliptic Curve Public Key Cryptosystems (ECC) have the highest bit security and will be an alternative to existing public-key cryptosystems. The paper describes the mathematical basis of algebraic geometry and ECC, discusses the difficulty of discrete logarithm of elliptic curve and the security application of ECC in e-commerce. By using the mapping relationship between affine coordinates and projective coordinates, an ECC fast algorithm is designed on integer field of finite element, which makes ECC practical application in e-commerce possible.