Two protocols for computing the sub-polygon's areas divided by a line

Abstract

Secure Multi-party Computation (SMC) plays an important role in information security under the circumstance of cooperation calculation, so SMC on privacy-preservation is of great interest. In this paper we discuss an issue which is a special SMC problem. Based on Scalar Product Protocol, Monte Carlo Method and Oblivious Transfer, we give two solutions to the problem about how to decide the areas. That is, a polygon is divided into two parts by a line: S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . Furthermore, we analyze the security and computational complexity, as well as the comparison of these two protocols. The results of analysis show that the proposed protocols are secure and efficient. We believe the two protocols will be useful in other geometric and combinatorial problems.