I like the approach of showing the assumption that "factoring is hard" implies a statement that at first blush has nothing to do with computational difficulty.

I like the approach of showing the assumption that "factoring is hard" implies a statement that at first blush has nothing to do with computational difficulty. That is, the number of solutions for a particular Diophantine equation doesn't immediately look like it should have anything to do with the running time of an algorithm. Wonder if the approach could be pushed further to other areas of mathematics that are even further afield, e.g. analysis?