Multilinear Maps from Obfuscation

We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the DDH assumption hold for them. Our first construction is symmetric and comes with a κ-linear map e : Gκ −→ GT for prime-order groups G and GT . To establish the hardness of the κ-linear DDH problem, we rely on the existence of a base group for which the (κ − 1)-strong DDH assumption holds. Our second construction is for the asymmetric setting, where e : G1 × · · · × Gκ −→ GT for a collection of κ + 1 prime-order groups Gi and GT , and relies only on the standard DDH assumption in its base group. In both constructions the linearity κ can be set to any arbitrary but a priori �...

• Type: Journal
• Year: 2016
• Where: TCC
• Authors: Martin R. Albrecht, Pooya Farshim, Dennis Hofheinz, Enrique Larraia, Kenneth G. Paterson
• Keywords: Cryptology, TCC 2016