Abstract
Abstract Secure multi-party computation (SMC) is a research focus in international cryptographic community. At present' there is no SMC to the intersection problem of sets. In this paper' we first propose a SMC solution to this problem. Applying Cantor encoding method to computational geometry problems' and based on the solution to set-intersection problem' we further propose solutions to points inclusion problem and intersection problem of rectangles and further prove their privacy-preserving property with widely accepted simulation paradigm. Compared with the known solutions' these new solutions are of less computational complexity and less communication complexity' and have obvious superiority in computational and communication complexity. * Supported by National Natural Science Foundation of China (Grant No.90304014) and Hi-tech Research and Development Program of china (Grant No 2005AA114160)
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