International Association
for Cryptologic Research

We define a notion of semantic security of multi-linear

(a.k.a. graded) encoding schemes: roughly speaking, we require that if

an algebraic attacker (obeying the multi-linear restrictions) cannot tell

apart two constant-length sequences $\\vec{m}_0$, $\\vec{m}_1$ in the

presence of some other elements $\\vec{z}$, then

encodings of these sequences should be indistinguishable.

Assuming the existence of semantically secure multi-linear encodings

and the LWE assumption, we demonstrate the existence of

indistinguishability obfuscators for all polynomial-size circuits.

Additionally, if we assume an strengthening of

semantic security, our construction yields extractatability

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 (ePrint\'13) 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

semantical security of multi-linear encoding (which trivially holds in

the generic multilinear encoding model).