Welcome to the resource topic for 2015/791
Title:
On the Equivalence of Obfuscation and Multilinear Maps
Authors: Omer Paneth, 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.
ePrint: https://eprint.iacr.org/2015/791
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