A Note on Black-Box Complexity of Indistinguishability Obfuscation

Mahmoody et al. (TCC 2016-A) showed that basing indistinguishability obfuscation (IO) on a wide range of primitives in a semi-black-box way is as hard as basing public-key cryptography on one-way functions. The list included any primitive P that can be realized relative to random trapdoor permutations or degree-O(1) graded encoding model for any finite ring secure against computationally unbounded polynomial-query attackers. In this note, we rely on the recent result of Brakerski, Brzuska, and Fleischhacker (ePrint 2016/226) and rule out fully black-box constructions of IO from any such primitive P , assuming the existence of one-way functions and NP 6⊆ coAM. At a technical level, we show that attacks in idealized (randomized) oracle models that succeed with constant advantage over the trivial bound (e.g., guessing the obfuscated circuit with probability 1/2 + 1/10) would remain successful for an infinite sequence of security parameters for a non-zero measure of the oracles.