论文标题
用QRT地图分解ECM
ECM factorization with QRT maps
论文作者
论文摘要
Quispel-Roberts-Thompson（QRT）地图是平面的生育地图家族，它提供了可集成的哈密顿系统的最简单的离散类似物，并且与椭圆形纤维相关。 QRT图的每个通用轨道对应于椭圆曲线上的点序列。在这项初步研究中，我们探索椭圆曲线方法（ECM）的版本，以基于迭代的三个不同的QRT图和特定初始数据的迭代分解。简要讨论了伪随机数和其他可能的应用。
Quispel-Roberts-Thompson (QRT) maps are a family of birational maps of the plane which provide the simplest discrete analogue of an integrable Hamiltonian system, and are associated with elliptic fibrations in terms of biquadratic curves. Each generic orbit of a QRT map corresponds to a sequence of points on an elliptic curve. In this preliminary study, we explore versions of the elliptic curve method (ECM) for integer factorization based on iterating three different QRT maps with particular initial data. Pseudorandom number generation and other possible applications are briefly discussed.
