Study and realization on secure elliptic curve over optimal extension fields
最佳扩域上的安全椭圆曲线的研究与实现

Concerning the deficiency that the study on elliptic curve cryptosystem over Optimal Extension Fields (OEF) mainly focuses on the operation about addition, subtraction, multiplication and inverse of field's element, the preparative base point method was presented and a simple algorithm of computing the order on elliptic curve was designed. Making use of the methods and the algorithm, a fast generating algorithm of secure elliptic curve over optimal extension fields was implemented on general PC. Experiments show that the efficient is preferable.