On the round complexity of covert computation
Vipul Goyal, Abhishek Jain · 2010
In STOC'05, von Ahn, Hopper and Langford introduced the notion of covert computation. In covert computation, a party runs a secure computation protocol over a covert (or steganographic) channel without knowing if the other parties are participating as well or not. At the end of the protocol, if all parties participated in the protocol and if the function output is "favorable" to all parties, then the output is revealed (along with the fact that everyone participated). All covert computation protocols known so far require a large polynomial number of rounds. In this work, we first study the question of the round complexity of covert computation and obtain the following results: 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.) By relying on the two slot non-black-box simulation technique of Pass (STOC'04) and techniques from cryptography in NC0 (Applebaum et al, FOCS'04), we obtain a construction of a constant round covert multi-party computation protocol.