Take your favorite hash function, and view it as inducing a directed graph on the set of its possible outputs. Finding a cycle is hard! (except, most hash functions map 0->0 for "nothing up my sleeves" appeal)
But also, it's ridiculously hard to answer simple questions about such graphs, such as listing its nodes.
But also, it's ridiculously hard to answer simple questions about such graphs, such as listing its nodes.