标题： 选择用于使用Shor算法求解ECDLP的坐标形式 显示英文标题

标题： Choosing Coordinate Forms for Solving ECDLP Using Shor's Algorithm

摘要： Shor算法以其能够在多项式时间内解决椭圆曲线离散对数问题（ECDLP）的能力而闻名。 其量子资源的增强仍然是研究的关键焦点。 然而，将投影坐标用于量子资源优化的应用仍是一个未解问题，主要是因为投影坐标的表示在不使用模除运算的情况下缺乏唯一性。 我们的研究表明，当使用Shor方法解决ECDLP时，投影坐标并不像仿射坐标那样具有相同的优势。 显示英文摘要

摘要： Shor's algorithm is well-known for its capability to address the elliptic curve discrete logarithm problem (ECDLP) in polynomial time. The enhancement of its quantum resources continues to be a crucial focus of research. Nevertheless, the application of projective coordinates for quantum resource optimization remains an unresolved issue, mainly because the representation of projective coordinates lacks uniqueness without employing modular division operations. Our study reveals that projective coordinates do not provide the same advantages as affine coordinates when utilizing Shor's method to tackle the ECDLP.