Research On Several Secure Multiparty Computation Problems

As science and technology fast develop,more and more people perform cooperative computation on their private date to explore the relationship between data,to make full use of data and to develop the value of data.Cooperative computation threats and challenges the participants' privacy seriously while benefiting the participants.In the distrusted network environment,privacy may disclose due to careless.To prevent privacy disclosing in cooperative computation process,secure multiparty computation was introduced.The rapid development of secure multiparty computation makes the private data play their roles while preserving the privacy.Therefore,secure multiparty computation attracts more and more attention of international cryptographic community.Secure multiparty computation makes distrusted participants perform cooperative computation on their private data.Secure multiparty computation guarantees that the inputs of participants are independent and the computation result is correct while preserving the data privacy.Secure multiparty computation has become a key privacy-preserving technology and is of great theoretical and practical significance.It has been a focus of the international cryptographic community in recent years.In this paper,we focus on the secure Manhattan distance computation,secure generation of histogram chart and pie chart and secure feasible solution determination.We thoroughly studied these problems and propose solutions to them.Our contributions are as follows.To privately compute the Manhattan distance between two private points,we first design a new encoding scheme.Then we use the Paillier cryptosystem,combining with the encrypt-and-choose technology,to design an efficient protocol to privately compute the absolute value of the difference of two private numbers.Using the protocol of absolute value problem as a building block,we further design a protocol to privately compute the Manhattan distance between two private points.We prove that these protocols are secure in the semi-honest model by using the simulation paradigm.We analyze and test the efficiency of our protocols.Theoretical analysis and simulation show that our protocols are efficient.Finally,we show how to use our protocol to solve other secure multiparty computation problems.To privately generate histogram or pie chart,we first propose another new encoding scheme.Based on the Paillier cryptosystem and the new encoding scheme,we design a protocol to privately generate a histogram or pie chart.Then we propose a more efficient and more secure protocol based on Elliptic curve threshold cryptosystem.Finally,we prove that these protocols are secure in the semi-honest model by using the simulation paradigm.We also analyze the computational complexities and communication complexities of the proposed protocols.Theoretical analysis and simulation show that these protocols are efficient.To privately determine feasible solution to an optimization problem,we use Elliptic curve cryptosystem to design a specific protocol to privately determine a feasible solution involving two participants with a constraint,and prove the correctness and security of the protocol.Besides,we use Elliptic curve cryptosystem and threshold cryptosystem to privately determine a feasible solution involving two participants with multiple constraints and multiple participants with multiple constraints.The efficiency analysis shows that these schemes are simple and efficient.In the end,we show some applications of these protocols.