Secure multi-party computation tolerating faulty majority
Jonathan Katz, Rafail Ostrovsky, Adam Smith
We consider the round complexity of multi-party computation in the presence of a static adversary who controls a majority of the parties. Here, n players wish to securely compute some functionality and up to n-1 of these players may be arbitrarily malicious. Previous protocols for this setting (when a broadcast channel is available) require O(n) rounds. We present two protocols with improved round complexity: The first assumes only the existence of trapdoor permutations and dense cryptosystems, and achieves round complexity O(\log n) based on a proof scheduling technique of Chor and Rabin; the second requires a stronger hardness assumption (along with the non-black-box techniques of Barak) and achieves O(1) round complexity.
comment: Appeared in Proceedings of Advances in Cryptology, (EUROCRYPT-2003) Springer-Verlag/IACR Lecture Notes in Computer Science.
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