We show how to construct indistinguishability obfuscation (iO) for circuits from any non-compact functional encryption (FE) scheme with sub-exponential security against unbounded collusions. We accomplish this by giving a generic transformation from any such FE scheme into a compact FE scheme. By composing this with the transformation from sub-exponentially secure compact FE to iO (Ananth and Jain [CRYPTO'15], Bitansky and Vaikuntanathan [FOCS'15]), we obtain our main result.
Our result provides a new pathway to iO. For example, by combining our result with the FE scheme of Garg et al. [ePrint 2014/666], we obtain a new construction of iO based on the sub-exponential GGHZ assumption over composite-order multilinear maps.
We also identify a "simple" function family for FE that suffices for our general result. We show that the function family F is complete, where every f in F consists of three evaluations of a Weak PRF followed by finite operations. We believe that this may be useful for realizing iO from weaker assumptions in the future.
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