[aidenn0]

IIRC, if P=NP then trapdoor functions do not exist, so proving that one existed would be a huge deal even outside of cryptography.

[Dylan16807]

Only if your definitions of "easy" and "hard" are based entirely on complexity classes.

If you show me a setup where "easy" is n^3 and "hard" is n^15 I will happily call that a trapdoor function.