Oneway functions

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.

For an overview see these slides on one-way functions and the wiki articles:

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. The converse is not known.

Surveys

Key articles

Hash functions

One-Way Functions in Cryptography are used as hash maps.

Constructions of hash functions

Kolmogorov complexity

Quantum computation