论文标题
将水平结构添加到超级椭圆曲线等值映射图
Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs
论文作者
论文摘要
在本文中，我们将级别结构的信息添加到超大的椭圆形曲线中，并以基于同性恋的密码学的动机研究这些对象。带有水平结构映射到四个代数的eichler顺序的超值椭圆形曲线，就像通过经典的deuring对应关系在四元素代数中的超值椭圆曲线映射到最大阶。我们研究这张地图，艾希勒命令自己。我们还查看具有级别结构的超椭圆形曲线的等值图，以及它们与艾希勒订单图的相关性。
In this paper, we add the information of level structure to supersingular elliptic curves and study these objects with the motivation of isogeny-based cryptography. Supersingular elliptic curves with level structure map to Eichler orders in a quaternion algebra, just as supersingular elliptic curves map to maximal orders in a quaternion algebra via the classical Deuring correspondence. We study this map and the Eichler orders themselves. We also look at isogeny graphs of supersingular elliptic curves with level structure, and how they relate to graphs of Eichler orders.
