Title: Lower Bounds on Indistinguishability Obfuscation from Zero-One Encryption

Abstract: Indistinguishability Obfuscation (IO) has recently emerged as a central primitive in cryptography, enabling many heretofore out-of-reach applications. However, currently all known constructions of IO are based on multilinear maps which are poorly understood. With the hope of basing IO on more standard assumptions, in this work we ask whether IO could be based on any of powerful (and recently realized) encryption primitives such as attribute-based/predicate encryption, fully homomorphic encryption, and witness encryption. What connects these primitives is that they are zero-one: either the message is revealed fully by the “right key” or it remains completely hidden.

Our main result is a negative one: we prove there is no black-box construction of IO from any of the above list of “zero-one” encryptions. We note many IO constructions are in fact non-black-box and e.g., results of Anath-Jain’15 and Bitansky-Vaikuntanathan’15 of basing IO on functional encryption is non-black-box. In fact, we prove our separations in an extension of the black-box framework of Impagliazzo-Rudich’89 and Reingold-Trevisan-Vadhan’04 which allows such non-black-box techniques as part of the model by default. Thus, we believe our extended model is of independent interest as a candidate for the new “standard” for cryptographic separations.