Indistinguishability obfuscation from semantically-secure multilinear encodings

Abstract

We define a notion of semantic security of multilinear (a.k.a. graded) encoding schemes, which stipulates security of a class of algebraic "decisional" assumptions: roughly speaking, we require that for every nuPPT distribution D over two constant-length sequences m0,m 1 and auxiliary elements z such that all arithmetic circuits (respecting the multilinear restrictions and ending with a zero-test) are constant with overwhelming probability over (mb, z), b ∈ {0,1}, we have that encodings of m0, z are computationally indistinguishable from encodings of m1, z. Assuming the existence of semantically secure multilinear encodings and the LWE assumption, we demonstrate the existence of indistinguishability obfuscators for all polynomial-size circuits. © 2014 International Association for Cryptologic Research.