# Average case problem and worst case problem in lattice

In Regev's lecture there is "In contrast, virtually all other cryptographic constructions are based on some average-case assumptions. For example, in cryptographic constructions based on factoring, the assumption is that it is hard to factor numbers chosen from a certain distribution. But how should we choose this distribution? Obviously, we should not use numbers with small factors (such as even number), but perhaps there are other numbers that we should avoid? In cryptographic constructions based on worst-case hardness, such questions do not even arise."

I do not understand the meaning of "In cryptographic constructions based on worst-case hardness, such questions do not even arise." According to my understanding, in cryptographic constructions based on worst-case hardness we based the cryptography scheme on hard subsets in which the problem is hard, so we should also avoid we based the cryptography scheme on subsets in which the problem is easy.