**Indistinguishability Obfuscation with Non-trivial Efficiency**

*Huijia Lin and Rafael Pass and Karn Seth and Sidharth Telang*

**Abstract: **It is well known that *inefficient* indistinguishability obfuscators (iO) with running
time poly(|C|,lambda) . 2^n, where C is the circuit to be
obfuscated, lambda 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|,lambda) . 2^n), but we now require that the obfuscated code is just slightly smaller than the truth table of C (namely poly(|C|,lambda) . 2^{n(1-epsilon)}, where epsilon >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 (polynomial-time computable) iO for all polynomial-size circuits.

**Category / Keywords: **indistinguishability obfuscation

**Original Publication**** (in the same form): **IACR-PKC-2016

**Date: **received 4 Jan 2016

**Contact author: **sidtelang at cs cornell edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20160104:210813 (All versions of this report)

**Short URL: **ia.cr/2016/006

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