A note on the impossibility of obfuscation

In this note we show that indistinguishability obfuscation implies that all functions with sufficient "pseudo-entropy" cannot be obfuscated under a virtual black box definition with a universal simulator. Let F={f_s} be a circuit family with super-polynomial pseudo-entropy, and suppose O is a candidate obfuscator with universal simulator S. We demonstrate the existence of an adversary A that, given the obfuscation O(f_s), learns a predicate the simulator S cannot learn from the code of A and black-box access to f_s. Furthermore, this is true in a strong sense: for any secret predicate P that is not learnable from black-box access to f_s, there exists an adversary that given O(f_s) efficiently recovers P(s), whereas given oracle access to f_s and given the code of the adversary, it is computationally hard to recover P(s). We obtain this result by exploiting a connection between obfuscation with a universal simulator and obfuscation with auxiliary inputs, and by showing new impossibility results for obfuscation with auxiliary inputs.