International Association
for Cryptologic Research

A program obfuscator takes a program and outputs an \"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

indistinguishability obfuscation, first defined by Barak et al. (CRYPTO 2001), the requirement is that the results of obfuscating any two

functionally equivalent programs (circuits) will be computationally indistinguishable. Recently, a fascinating candidate construction for

indistinguishability obfuscation was proposed by Garg et al. (FOCS 2013). 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 by Sahai and Waters, STOC 2014). 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 $P \\neq NP$ and program obfuscation is possible, then one-way functions exist.

Our main result is that if $NP \\not\\subseteq ioBPP$ 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 obfuscator implies (unconditionally) the existence of SZK-

arguments for NP. This, in turn, provides 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 CNF formulas.