ONE-WAY FUNCTIONS AND (IM)PERFECT OBFUSCATION\ast

A program obfuscator takes a program and outputs a ``scrambled"" version of it, where the goal is that the obfuscated program will not reveal much about its structure beyond what is apparent from executing it. There are several ways of formalizing this goal. Specifically, in indisresults of obfuscating any two functionally equivalent programs (circuits) will be computationally indistinguishable. In 2013, a fascinating candidate construction for indistinguishability obfuscation was ACM, 2013, pp. 467--476]. This has led to a flurry of discovery of intriguing constructions of primitives and protocols whose existence was not previously known (for instance, fully deniable encryption 484]). Most of them explicitly rely on additional hardness assumptions, such as one-way functions. Our goal is to get rid of this extra assumption. We cannot argue that indistinguishability obfuscation of all polynomial-time circuits implies the existence of one-way functions, since if P = NP, then program obfuscation (under the indistinguishability notion) is possible. Instead, the ultimate goal is to argue that if P NP and program obfuscation is possible, then one-way functions exist. Our main result is that if NP g io-BPP and there is an efficient (even imperfect) indistinguishability obfuscator, then there are one-way functions. In addition, we show that the existence of an indistinguishability vides an alternative version of our main result, based on the assumption of hard-on-the-average NP problems. To get some of our results we need obfuscators for simple programs such as 3CNF circuits.