Secure three-party computational protocols for triangle area

In this work, we have put forth two different protocols to address a concrete secure multi-party computational (MPC) problem related to a triangle, of which the coordinates of the three vertices are confidentially kept by the three participants, respectively. The three parties wish to collaboratively compute the area of this triangle while preserving their own coordinate privacy. As one of the merits, our protocols employ weaker assumptions of the existence of pseudorandom generators. In particular, unlike massive secure MPC protocols that rely a lot on oblivious transfer, ours utilize a new computing idea called “pseudorandom-then-rounding” method to avoid this burdensome obstacle. The two protocols are based on different theorems, while they both make use of the same underlying idea. At last, we provide a detailed proof for the first protocol by a series of security reductions of our newly defined games, which seems somewhat stronger than the previous simulation-based proofs and a proof sketch for the second one. Analysis and discussion about the reasons are provided as well to round off our work.