One-Way Functions
A function f is one-way if, given x it is easy to compute f(x), but given f(x) it is hard to compute x (superpolynomial, or exponential time).
Trapdoor one-way functions: easy to compute f(x) given x, hard to compute x given f(x). But there is some secret information y, s.t. given f(x) and y, easy to compute x.