In other settings throughout cryptography, black-box constructions invariably lead to better practical efficiency than comparable non-black-box constructions. Could secure computation protocols similarly be made more practical by eliminating their dependence on a circuit representation of the target function? Or, in other words, {\em must one know the code of $f$ to securely evaluate $f$?}
In this work we initiate the theoretical study of this question. We show the following:
1. A complete characterization of the 2-party tasks which admit such security against semi-honest adversaries. The characterization is inspired by notions of {\em autoreducibility} from computational complexity theory. From this characterization, we show a class of pseudorandom functions that {\em cannot} be securely evaluated (when one party holds the seed and the other holds the input) without ``knowing'' the code of the function in question. On the positive side, we show a class of functions (related to blind signatures) that can indeed be securely computed without ``knowing'' the code of the function.
2. Sufficient conditions for such security against malicious adversaries, also based on autoreducibility. We show that it is not possible to prove membership in the image of a one-way function in zero-knowledge, without ``knowing'' the code of the one-way function.
Category / Keywords: foundations / secure computation, black-box protocols Publication Info: Revised version of work appearing in CRYPTO 2012 Date: received 10 Aug 2012 Contact author: mikero at cs umt edu Available format(s): PDF | BibTeX Citation Version: 20120813:150346 (All versions of this report) Short URL: ia.cr/2012/455 Discussion forum: Show discussion | Start new discussion