STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The round complexity of secure protocols
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Efficient oblivious transfer protocols
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Non-Malleable Non-Interactive Zero Knowledge and Adaptive Chosen-Ciphertext Security
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Universal Arguments and their Applications
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
How to Go Beyond the Black-Box Simulation Barrier
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Bounded-concurrent secure multi-party computation with a dishonest majority
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Covert Multi-Party Computation
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
On Pseudorandom Generators with Linear Stretch in NC0
Computational Complexity
Secure computation without authentication
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Constant round non-malleable protocols using one way functions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Non-black-box simulation in the fully concurrent setting
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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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. 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).