In this talk I will present new techniques for proving the security of
witness encryption and indistinguishability obfuscation cryptosystems.
Witness encryption and indistinguishability obfuscation are powerful
primitives that give rise to many cryptographic applications including
attribute-based encryption for circuits, functional encryption and
deniable encryption. Recently, the first candidate constructions for
these primitives were proposed using multilinear encodings. However,
to this point security proofs of these primitives were limited to arguing
security in an idealized generic group model or using assumptions closely
related to these generic group arguments.
I will present constructions of witness encryption and indistinguishability
obfuscation along with security reductions to the multilinear subgroup
elimination assumption. This assumption is a natural multilinear extension
of the subgroup decision assumptions used in bilinear groups.