We give combinatorial characterizations of the SSFE functions $f$ that have passive-secure protocols, and those which are protocols secure in the standalone setting. With respect to universally composable security (for unbounded parties), we show that there is an infinite hierarchy of increasing complexity for SSFE functions, That is, we describe a family of SSFE functions $f_1, f_2, \ldots$ such that there exists a UC-secure protocol for $f_i$ in the $f_j$-hybrid world if and only if $i \le j$.
Our main technical tool for deriving complexity separations is a powerful protocol simulation theorem which states that, even in the strict setting of UC security, the canonical protocol for $f$ is as secure as any other protocol for $f$, as long as $f$ satisfies a certain combinatorial characterization. We can then show intuitively clear impossibility results by establishing the combinatorial properties of $f$ and then describing attacks against the very simple canonical protocols, which by extension are also feasible attacks against {\em any} protocol for the same functionality.
Category / Keywords: foundations / multi-party computation, universal composition, secure function evaluation Date: received 28 Oct 2008, last revised 3 Nov 2010 Contact author: rosulek at uiuc edu Available format(s): PDF | BibTeX Citation Version: 20101104:043916 (All versions of this report) Short URL: ia.cr/2008/454