We define several variants of pIO, using different approaches to formalizing the above security requirement, and study non-trivial relations among them. Moreover, we give a construction of one of our pIO variants from sub-exponentially hard indistinguishability obfuscation (for deterministic circuits) and one-way functions, and conjecture this construction to be a good candidate for other pIO variants.
We then move on to show a number of applications of pIO:
* We give a general and natural methodology to achieve leveled homomorphic encryption (LHE) from variants of semantically secure encryption schemes and of pIO. In particular, we propose instantiations from lossy and re-randomizable encryption schemes, assuming the two weakest notions of pIO.
* We enhance the above constructions to obtain a full-fledged (i.e., non-leveled) FHE scheme under the same (or slightly stronger) assumptions. In particular, this constitutes the first construction of full-fledged FHE that does not rely on encryption with circular security.
* Finally, we show that assuming sub-exponentially secure puncturable PRFs computable in NC1, sub-exponentially-secure indistinguishability obfuscation for (deterministic) NC1 circuits can be bootstrapped to obtain indistinguishability obfuscation for arbitrary (deterministic) poly-size circuits.Category / Keywords: foundations / Obfuscation, IO, FHE Date: received 25 Oct 2014 Contact author: rachel lin at cs ucsb edu Available format(s): PDF | BibTeX Citation Version: 20141028:191841 (All versions of this report) Short URL: ia.cr/2014/882 Discussion forum: Show discussion | Start new discussion