One-Way Function

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, “easy” and “hard” are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient for a function to be called one-way (see Theoretical definition, below).

The existence of such one-way functions is still an open conjecture. Their existence would prove that the complexity classes P and NP are not equal, thus resolving the foremost unsolved question of theoretical computer science.[1]: ex. 2.2, page 70  The converse is not known to be true, i.e. the existence of a proof that P≠NP would not directly imply the existence of one-way functions