The Berman-Hartmanis conjecture discusses one-way functions (functions with hard to compute inverse functions).
As a step to solving the conjecture, if one-way functions could be reduced to a canonical or universal one-way function from which all one-way functions could be derived, this would be a major plus...
In a similar way, Turing devised a universal machine and Cook NP-completeness.
The question is then, are there universal one-way functions (discussed in the literature)? Can they be defined through NP-completeness?