Are there one-way functions?

A one-way function is easy to compute but hard to invert. The existence of one-way functions is essentially equivalent to the existence of most symmetric-key cryptography — yet whether they really exist is unknown.

A proof that one-way functions exist would imply P ≠ NP; a proof that they don't would break essentially all of modern cryptography. Most cryptographers conjecture they do exist but cannot prove it.