Research Article
Method and Application of Homomorphic Subtraction of the Paillier Cryptosystem in Secure Multi-party Computational Geometry
@INPROCEEDINGS{10.1007/978-3-030-48513-9_45, author={Meng Liu and Yun Luo and Chi Yang and Dongliang Xu and Taoran Wu}, title={Method and Application of Homomorphic Subtraction of the Paillier Cryptosystem in Secure Multi-party Computational Geometry}, proceedings={Cloud Computing, Smart Grid and Innovative Frontiers in Telecommunications. 9th EAI International Conference, CloudComp 2019, and 4th EAI International Conference, SmartGIFT 2019, Beijing, China, December 4-5, 2019, and December 21-22, 2019}, proceedings_a={CLOUDCOMP}, year={2020}, month={6}, keywords={Secure multi-party computation Homomorphic cryptosystem Computational geometry Subtraction}, doi={10.1007/978-3-030-48513-9_45} }- Meng Liu
Yun Luo
Chi Yang
Dongliang Xu
Taoran Wu
Year: 2020
Method and Application of Homomorphic Subtraction of the Paillier Cryptosystem in Secure Multi-party Computational Geometry
CLOUDCOMP
Springer
DOI: 10.1007/978-3-030-48513-9_45
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 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.
