Indistinguishability Obfuscation with Non-trivial Efficiency

Abstract

It is well known that inefficient indistinguishability obfuscators (iO) with running time poly(|C|, λ) · 2, 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) · 2), but we now require that the obfuscated code is just slightly smaller than the truth table of C (namely poly(|C|, λ) · 2n(1− , where > 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, subexponentially-secure XiO for polynomial-size circuits implies (polynomialtime computable) iO for all polynomial-size circuits. ∗This paper appears in PKC 2016. †University of California at Santa Barbara, Email: rachel.lin@cs.ucsb.edu. Work supported in part by NSF grants CNS-1528178 and CNS-1514526. ‡Cornell University, rafael@cs.cornell.edu. Work supported in part by a Microsoft Faculty Fellowship, Google Faculty Award, NSF Award CNS-1217821, NSF Award CCF-1214844, AFOSR Award FA9550-15-1-0262 and DARPA and AFRL under contract FA8750-11-2-0211. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the US Government. §Cornell University, Email: karn@cs.cornell.edu. ¶Cornell University, Email: sidtelang@cs.cornell.edu.

DOI: 10.1007/978-3-662-49387-8_17

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@article{Lin2016IndistinguishabilityOW, title={Indistinguishability Obfuscation with Non-trivial Efficiency}, author={Huijia Lin and Rafael Pass and Karn Seth and Sidharth Telang}, journal={IACR Cryptology ePrint Archive}, year={2016}, volume={2016}, pages={6} }