Paper 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.
Metadata
- Available format(s)
-
PDF
- Publication info
- Preprint. MINOR revision.
- Keywords
- obfuscationmultilinear maps
- Contact author(s)
- amitsahai @ gmail com
- History
- 2015-08-13: last of 2 revisions
- 2015-08-10: received
- See all versions
- Short URL
- https://ia.cr/2015/791
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/791,
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{https://eprint.iacr.org/2015/791}},
url = {https://eprint.iacr.org/2015/791}
}
