论文标题
奇异立方体的点组
Point-groups over singular cubics
论文作者
论文摘要
在本文中，我们强调说，在具有二次分量的单数立方体上也可以观察到椭圆形曲线的点组结构。从此开始，我们能够以非常一般的方式引入一个小组的结构在任何类型的圆锥上。对于有限场上的圆锥形，我们看到该点群是循环的，并且位于二次。直线组件在点组成的代数描述中扮演的角色可能不明确，但在几何描述中是必不可少的。此外，考虑到锥体的方便参数化，描述了一些对密码学的应用。最后，我们对参数组中涉及的操作的复杂性以及加密应用程序中涉及的操作的复杂性进行评估。
In this paper, we highlight that the point group structure of elliptic curves over finite or infinite fields, may be also observed on singular cubics with a quadratic component. Starting from this, we are able to introduce in a very general way a group's structure over any kind of conics. In the case of conics over finite fields, we see that the point group is cyclic and lies on the quadric; the straight line component plays a role which may be not explicitly visible in the algebraic description of point composition, but it is indispensable in the geometric description. Moreover, some applications to cryptography are described, considering convenient parametrizations of the conics. Finally, we perform an evaluation of the complexity of the operations involved in the parametric groups and consequently in the cryptographic applications.
