Number Theory And Arithmetic Geometry

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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.