Paper 2015/791

On the Equivalence of Obfuscation and Multilinear Maps

Omer Paneth and Amit Sahai


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.

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Preprint. MINOR revision.
obfuscationmultilinear maps
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amitsahai @ gmail com
2015-08-13: last of 2 revisions
2015-08-10: received
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      author = {Omer Paneth and Amit Sahai},
      title = {On the Equivalence of Obfuscation and Multilinear Maps},
      howpublished = {Cryptology ePrint Archive, Paper 2015/791},
      year = {2015},
      note = {\url{}},
      url = {}
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