ONE-WAY FUNCTIONS AND (IM)PERFECT OBFUSCATION

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 indistinguishability obfuscation, first defined by Barak et al. [Advances in Cryptology - CRYPTO, 2001, Lect. Notes Comput. Sci. 2139, Springer, Berlin, Heidelberg, pp. 1-18], the requirement is that the results of obfuscating any two functionally equivalent programs (circuits) will be computationally indistinguishable. In 2013, a fascinating candidate construction for indistinguishability obfuscation was proposed by Garg et al. [Proceedings of the Symposium on Theory of Computing Conference, STOC, 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 by Sahai and Waters [Proceedings of the Symposium on Theory of Computing, 2014, STOC, pp. 475-484]). Most of them explicitly rely on additional hardness assumptions, such as one-way functions. Our goal is to get rid of this extra assumption.