In STOC'05, Luis von Ahn, Nicholas Hopper and John Langford introduced the notion of covert computation. A covert computation protocol is one in which parties can run a protocol without knowing if other parties are also participating in the protocol 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. Ahn, Hopper and Langford proposed a protocol for covert two-party computation in the random oracle model. In this work, we first point out some subtle (but important) problems with their construction. We show how to correct these problems and perform covert two-party computation in the standard model, and give a construction for covert multi-party computation in the standard model.
This is joint work with Vipul Goyal, Amit Sahai and Rafail Ostrovsky