论文标题
关于椭圆曲线的小组法的基本线性地球式证明，没有计算机辅助论证
An Elementary Linear-Algebraic Proof without Computer-Aided Arguments for the Group Law on Elliptic Curves
论文作者
论文摘要
椭圆曲线的理性点上的小组结构在数学中以及最近在其他领域（例如密码学）中扮演了多个重要角色。但是，集体财产的著名证据（尤其是其协会法律）需要一定的高级数学，因此非数学家不容易获得。另一方面，文献中已经尝试提供基本证据，但是那些依赖于计算机辅助计算的证据。在本文中，我们仅在基本的线性代数级别上，而不需要计算机辅助论点的数学知识，给出了该操作的关联定律的独立证明。
The group structure on the rational points of elliptic curves plays several important roles, in mathematics and recently also in other areas such as cryptography. However, the famous proofs for the group property (in particular, for its associative law) require somewhat advanced mathematics and therefore are not easily accessible by non-mathematician. On the other hand, there have been attempts in the literature to give an elementary proof, but those rely on computer-aided calculation for some part in their proofs. In this paper, we give a self-contained proof of the associative law for this operation, assuming mathematical knowledge only at the level of basic linear algebra and not requiring computer-aided arguments.
