Paper 2013/643

There is no Indistinguishability Obfuscation in Pessiland

Tal Moran and Alon Rosen

Abstract

We show that if $\NP \neq co-RP$ 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.