1) There does not exist a constant round covert computation protocol with respect to black box simulation even for the case of two parties. (In comparison, such protocols are known even for the multi-party case if there is no covertness requirement.)
2) By relying on the two slot non-black-box simulation technique of Pass (STOC'04) and techniques from cryptography in NC^0 (Applebaum et al, FOCS'04), we obtain a construction of a constant round covert multi-party computation protocol.
Put together, the above adds one more example to the growing list of tasks for which non-black-box simulation techniques (introduced in the work of Barak in FOCS'01) are necessary.
Finally, we study the problem of covert multi-party computation in the setting where the parties only have point to point (covert) communication channels. We observe that our covert computation protocol for the broadcast channel inherits, from the protocol of Pass, the property of secure composition in the bounded concurrent setting. Then, as an application of this protocol, somewhat surprisingly we show the existence of covert multi-party computation with point to point channels (assuming that the number of parties is a constant).Category / Keywords: Publication Info: To appear at STOC 2010. This is the full version. Date: received 11 May 2010, last revised 12 May 2010 Contact author: abhishek at cs ucla edu Available format(s): PDF | BibTeX Citation Version: 20100512:164719 (All versions of this report) Short URL: ia.cr/2010/279 Discussion forum: Show discussion | Start new discussion