Cryptomania is usually presented as the Impagliazzo's world, which gives us public-key cryptography under the assumption that trapdoor OWFs exist. For purposes of constructing public-key cryptography we also want the underlying problem to be in $NP \cap coNP$ as described in here. Are there any papers, which explore this particular requirement in relation to Impagliazzo's worlds?
Edit 02/04/2021: After some more digging I managed to find the answer, which describes the $NP \cap coNP$ requirement, as such I am restructuring this question, to only ask about results on impagliazzo's 5 worlds in relation to this property.