Just wanted to emphasize your point about "worst case hardness" -- even if 3SAT turns out to be hard (due to P != NP), it is only hard in the worst case (for a very small subset of all possible 3SAT problems). Most 3sat problem instances are (probably?) easy.
In crypto, we need to sample "average case hard" problems, where on average, a random problem that we sample is hard. This is in contrast to, for instance, uniformly sampling from the set of all 3SAT instances, which gives an easy problem on average.
A continuation of this line of research essentially looks at turning worst case hard problems into average case hard problems. Asymptotics are already way on the backburner since we are in theory world.
(Note that a One way function is average case hard)
In crypto, we need to sample "average case hard" problems, where on average, a random problem that we sample is hard. This is in contrast to, for instance, uniformly sampling from the set of all 3SAT instances, which gives an easy problem on average.
A continuation of this line of research essentially looks at turning worst case hard problems into average case hard problems. Asymptotics are already way on the backburner since we are in theory world.
(Note that a One way function is average case hard)