No reduction from TDP to OT

A reduction of class unstated from TDP to OT would imply a contradiction.

Statement

Migrated verbatim from trapdoor-permutation § Enhanced trapdoor permutations:

An enhanced TDP additionally requires that the TDP remain hard to invert even when given a random coin $r$ and a random element $y=\mathsf{Eval}(f,x)$ sampled using $r$ in a specific way. This stronger property is necessary for constructing OT from TDPs.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• ‘necessary for constructing OT from TDPs’ is a negative claim (plain TDPs do not suffice) stated with NO citation; the relevant results are Goldreich’s enhanced-TDP note and Haitner’s separations.
• Typed as a barrier because it asserts the non-existence of a construction from plain TDP, but the reduction class and the exact Q are unstated — low confidence.
• The word ‘necessary’ may be intended loosely (‘needed for the known proof’), in which case it is not a barrier at all.