We improve on the classical results in information-theoretically secure multiparty computation among a set of n participants, by considering the special case of the computation of the addition function with constant-sized inputs in the secure channels model with a simultaneous broadcast channel. This restricted function is useful as a building block for other applications, including, most notably, voting. The classical results in multiparty computation show that in the case of active corruption, every function can be computed with information-theoretic security if and only if less than n/2 participants are corrupt. We show that, for certain functions in our scenario, this bound can be surpassed, at the cost of decreasing robustness.
This is a joint work with Anne Broadbent, Samuel Ranellucci, and Alain Tapp.