There is no Indistinguishability Obfuscation in Pessiland

We show that if NP , co−RP then the existence of efficient indistinguishability obfuscation (iO) implies the existence of one-way functions. Thus, if we live in “Pessiland”, where NP problems are hard on the average but one-way functions do not exist, or even in “Heuristica”, where NP problems are hard in the worst case but easy on average, then iO is impossible. Our result makes it redundant to explicitly assume the existence of one-way functions in most “cryptographically interesting” applications of iO.