Indistinguishability obfuscation with non-trivial efficiency

Abstract

It is well known that inefficient indistinguishability obfuscators (iO) with running time poly(|C|, λ) · 2n, where C is the circuit to be obfuscated, λ is the security parameter, and n is the input length of C, exists unconditionally: simply output the function table of C (i. e., the output of C on all possible inputs). Such inefficient obfuscators, however, are not useful for applications. We here consider iO with a slightly “non-trivial” notion of efficiency: the running-time of the obfuscator may still be “trivial” (namely, poly(|C|, λ) · 2n), but we now require that the obfuscated code is just slightly smaller than the truth table of C (namely poly(|C|, λ) · 2n(1−ɛ), where ɛ > 0); we refer to this notion as iO with exponential efficiency, or simply exponentially-efficient iO (Xio). We show that, perhaps surprisingly, under the subexponential LWE assumption, subexponentiallysecure XiO for polynomial-size circuits implies (polynomial-time computable) iO for all polynomial-size circuits.