Number Theory and Arithmetic Geometry

离散动力系统由物体的状态在不同时刻的值组成，例如坐标，重量等，其中特定时刻的值根据给定的规则取决于前一时刻的值。本研究的目的是研究动力学中的不可能相交原理，即当两个物体是“随机的”时，它们的相交是小的。求解因子分解问题和离散对数问题的著名的Pollard rho算法依赖于某些动力系统的随机性。这两个问题在数据安全中起着至关重要的作用。

A discrete dynamical system consists of values at different times of the state such as the coordinate, weight, etc. of an object in which the value at a specific time depends on the value at the previous time according to a given rule. This research aims to study the principle of unlikely intersections in dynamics which roughly states that when two objects are "random", their intersection is small. The famous Pollard's rho algorithms for the factorization problem and the discrete logarithm problem rely on the randomness of certain dynamical systems. These two problems play a crucial role in data security.