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2020 | OriginalPaper | Chapter

Method and Application of Homomorphic Subtraction of the Paillier Cryptosystem in Secure Multi-party Computational Geometry

Authors : Meng Liu, Yun Luo, Chi Yang, Dongliang Xu, Taoran Wu

Published in: Cloud Computing, Smart Grid and Innovative Frontiers in Telecommunications

Publisher: Springer International Publishing

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Abstract

A secure two-party computation protocol for the problem of the distance between two private points is important and can be used as the building block for some secure multi-party computation (SMC) problems in the field of geometry. Li’s solution to this problem is inefficient based on \(OT_m^1\) oblivious transfer protocol and some drawbacks still remain while applied to compute the relationship between a private circle and a private point. Two protocols are also proposed based on the Paillier cryptosystem by Luo et al. and more efficient than Li’s solution, but there also remain some drawbacks. In this paper, we propose an idea to improve the efficiency of secure protocol by using its homomorphic subtraction based on the Paillier cryptosystem. Then we apply it to solve the secure two-party computation problem for the distance between two private points. Using our solution, the SMC protocol to the relationship between a private point and a private circle area is more efficient and private than Li’s solution. In addition, we also find that our solution is also more efficient than the BGN-based solution and much better while the plaintext can be in some large range.

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Title: Method and Application of Homomorphic Subtraction of the Paillier Cryptosystem in Secure Multi-party Computational Geometry
Authors: Meng Liu
Yun Luo
Chi Yang
Dongliang Xu
Taoran Wu
Publisher: Springer International Publishing
Book: Cloud Computing, Smart Grid and Innovative Frontiers in Telecommunications
Print ISBN: 978-3-030-48512-2

Electronic ISBN: 978-3-030-48513-9

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-48513-9_45

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