We define a notion of semantic security of multilinear
(a.k.a. graded) encoding schemes, which generalizes a multilinear DDH
assumption: roughly speaking, we require that if
two constant-length sequences $\vec{m}_0$, $\vec{m}_1$ are
\emph{pointwise statistically indistinguishable} by algebraic attackers $C$
(obeying the multilinear restrictions) in the
presence of some other elements $\vec{z}$,
then encodings of these sequences should be computationally indistinguishable.
Assuming the existence of semantically secure multilinear encodings
and the LWE assumption, we demonstrate the existence of
indistinguishability obfuscators for all polynomial-size circuits.
We rely on the beautiful candidate obfuscation constructions
of Garg et al (FOCS'13), Brakerski and Rothblum (TCC'14) and Barak et
al (EuroCrypt'14) that were proven secure only in idealized generic
multilinear encoding models,
and develop new techniques for demonstrating security in the standard model, based only on
semantic security of multilinear encodings (which trivially holds in
the generic multilinear encoding model).
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