The final nail in the coffin of statistically-secure obfuscator

Abstract

We present an elementary proof of a theorem of Goldwasser and Rothblum [10,11] that the existence of a perfect (or even “slightly” imperfect) statistically-secure obfuscator implies a collapse of the polynomial hierarchy. In fact, our proof gives rise to a more general, quantified version of the theorem exhibiting an (impossible) tradeoff between the correctness and the security of the obfuscator. We also extend the result to a relaxed notion of security.