Efficient Multiparty Protocols via Log-Depth Threshold Formulae

We put forward a new approach for the design of ecient multiparty protocols: 1. Design a protocol for a small number of parties (say, 3 or 4) which achieves security against a single corrupted party. Such protocols are typically easy to construct, as they may employ techniques that do not scale well with the number of corrupted parties. 2. Recursively compose with itself to obtain an ecient n-party protocol which achieves security against a constant fraction of corrupted parties. The second step of our approach combines the \player emulation" technique of Hirt and Maurer (J. Cryptology, 2000) with constructions of logarithmic-depth formulae which compute threshold functions using only constant fan-in threshold gates. Using this approach, we simplify and improve on previous results in cryptography and distributed computing. In particular: We provide conceptually simple constructions of ecient protocols for Secure Multiparty Computation (MPC) in the presence of an honest majority, as well as broadcast protocols from point-to-point channels and a 2-cast primitive. We obtain new results on MPC over blackbox groups and other algebraic structures.

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