Cryptology ePrint Archive: Report 2015/791

On the Equivalence of Obfuscation and Multilinear Maps

Omer Paneth and Amit Sahai

Abstract: Garg et al. [FOCS 2013] showed how to construct indistinguishability obfuscation (iO) from a restriction of cryptographic multilinear maps called Multilinear Jigsaw Puzzles. Since then, a number of other works have shown constructions and security analyses for iO from different abstractions of multilinear maps. However, the converse question --- whether some form of multilinear maps follows from iO --- has remained largely open.

We offer an abstraction of multilinear maps called Polynomial Jigsaw Puzzles, and show that iO for circuits implies Polynomial Jigsaw Puzzles. This implication is unconditional: no additional assumptions, such as one-way functions, are needed. Furthermore, we show that this abstraction of Polynomial Jigsaw Puzzles is sufficient to construct iO for NC1, thus showing a near-equivalence of these notions.

Category / Keywords: obfuscation, multilinear maps

Date: received 6 Aug 2015, last revised 13 Aug 2015

Contact author: amitsahai at gmail com

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Version: 20150813:170458 (All versions of this report)

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