We address a concrete secure multi-party computational (MPC) problem related to a triangle, of which the coordinates of the three vertexes 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 protocol employs weaker assumptions of the existence of pseudorandom generators. Especially, unlike massive secure MPC protocols that mainly rely on the primitive of oblivious transfer (OT), ours utilizes a new computing idea named round summation to avoid this burdensome obstacle. Finally, we provide a proof of the protocol by a series of security reductions of our newly-defined games, which seems somewhat stronger than the previous simulation-based proofs.
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