AFAIK, we don’t even know whether trapdoor functions exist.
https://en.wikipedia.org/wiki/Trapdoor_function:
“As of 2004, the best known trapdoor function (family) candidates are the RSA and Rabin families of functions”
Also note that the ‘examples’ section starts with:
“In the following two examples, we always assume it is difficult to factorize a large composite number (see Integer factorization).”
If you show me a setup where "easy" is n^3 and "hard" is n^15 I will happily call that a trapdoor function.
AFAIK, we don’t even know whether trapdoor functions exist.
https://en.wikipedia.org/wiki/Trapdoor_function:
“As of 2004, the best known trapdoor function (family) candidates are the RSA and Rabin families of functions”
Also note that the ‘examples’ section starts with:
“In the following two examples, we always assume it is difficult to factorize a large composite number (see Integer factorization).”