Q₂非分歧扩域上椭圆曲线的近似计算

Q 2 非分歧扩域上椭圆曲线的近似计算 Approximation Calculations on the Elliptic Curves over Unramified Extensions of 2-Adic Number Fields 岳志鸿 YUE Zhihong 1 first-author 徐茂智 XU Maozhi 1 周正华 ZHOU Zhenghua 1 宋承根 SONG Chenggen 1 北京大学数学科学学院 北京大学数学科学学院 School of Mathematical Sciences,Peking University School of Mathematical Sciences,Peking University 研究了Q2的非分歧扩域上椭圆曲线的近似计算问题:椭圆曲线有理点群中元素的有限表示、点加法中的提升算法以及点加法的近似计算等.借助两种提升算法完整地给出椭圆曲线有理点群中加法的近似计算公式,这将为利用无限域上椭圆曲线构造密码的可行性分析提供完善的理论基础. In this paper we address approximation calculations on the elliptic curves defined over unramified extensions of 2-adic number fields,including the finite representation of rational points of an elliptic curve over such fields,lifting algorithms in the point addition and the addition formula with approximation calculations under this representation.Combining with two lifting methods,we get approximation calculation formulas in all conditions for the point addition of the group of rational points on an elliptic curve over these fields.It will be beneficial for the feasibility analysis on the elliptic curve cryptography defined over infinite fields. 椭圆曲线 非分歧扩域 局部域 形式群 elliptic curves unramified extensions local field formal group TN918.1 国家高技术研究发展计划（863）项目（2007AA701315）;国家自然科学基金资助项目（60763009） 2008-05-01 2021-04-01 5