Recent breakthroughs in cryptography have positioned indistinguishability obfuscation as a ``central hub'' for almost all known cryptographic tasks, and as an extremely powerful building block for new cryptographic tasks resolving long-standing and foundational open problems. In this paper we prove the first negative results on the power of indistinguishability obfuscation and of the tightly related notion of functional encryption. Our results are as follows:
-- There is no fully black-box construction with a polynomial security loss of a collision-resistant function family from a general-purpose indistinguishability obfuscator.
-- There is no fully black-box construction with a polynomial security loss of a key-agreement protocol with perfect completeness from a general-purpose private-key functional encryption scheme.
-- There is no fully black-box construction with a polynomial security loss of an indistinguishability obfuscator for oracle-aided circuits from a private-key functional encryption scheme for oracle-aided circuits.
Specifically, we prove that any such potential construction must suffer from at least a sub-exponential security loss. Our results are obtained within a subtle framework capturing constructions that may rely on a wide variety of primitives in a non-black-box manner (e.g., obfuscating or generating a functional key for a function that uses the evaluation circuit of a puncturable pseudorandom function), and we only assume that the underlying indistinguishability obfuscator or functional encryption scheme themselves are used in a black-box manner.
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