# Does there exist a universal one-way permutation?

Leonid Levin constructed a universal one-way function, i.e. a function which is one-way as long as there exists at least one one-way function.

But my question is, does there exist a universal one-way permutation, i.e. a function which is a one-way permutation as long as there exists at least one one-way permutation? Would a modification of Levin’s construction achieve this?