In this work, we show that (subexponentially secure) secret-key functional encryption is powerful enough to construct indistinguishability obfuscation if we additionally assume the existence of (subexponentially secure) plain public-key encryption. In other words, secret-key functional encryption provides a bridge from cryptomania to obfustopia.
On the technical side, our result relies on two main components. As our first contribution, we show how to use secret key functional encryption to get ``exponentially-efficient indistinguishability obfuscation'' (\XIO), a notion recently introduced by Lin et al. (PKC '16) as a relaxation of \IO. Lin et al. show how to use \XIO and the \LWE assumption to build \IO. As our second contribution, we improve on this result by replacing its reliance on the \LWE assumption with any plain public-key encryption scheme.
Lastly, we ask whether secret-key functional encryption can be used to construct public-key encryption itself and therefore take us all the way from minicrypt to obfustopia. A result of Asharov and Segev (FOCS '15) shows that this is not the case under black-box constructions, even for exponentially secure functional encryption. We show, through a non-black box construction, that subexponentially secure-key functional encryption indeed leads to public-key encryption. The resulting public-key encryption scheme, however, is at most quasi-polynomially secure, which is insufficient to take us to obfustopia.Category / Keywords: Indistinguishability Obfuscation, Functional Encryption. Original Publication (with minor differences): IACR-TCC-2016 Date: received 2 Jun 2016, last revised 24 Aug 2016 Contact author: alain passelegue at ens fr Available format(s): PDF | BibTeX Citation Note: Correcting typos and adding some remarks for clarity (08/24/2016). This is the full version of the paper that appears at TCC 2016-B. Version: 20160824:092622 (All versions of this report) Short URL: ia.cr/2016/558 Discussion forum: Show discussion | Start new discussion