A Study Of Three Secure Multiparty Computation Problems

With the rapid development of information technology and network technologies such as the Internet,cloud computing,big data,the Internet of Things,global informatization has become an inevitable trend.In this era,it is becoming more and more popular for different entities to share data to perform cooperative computation.However,the data owned by different entities may be private or confidential data.If the data is directly shared without proper protection,the private or confidential information will be leaked,which will bring huge economic and credibility losses to the entities.Therefore,how to carry out cooperative computation while preserving the privacy to maximize the value of data is an urgent problem to be solved.Secure multi-party computation(SMC)is a powerful tool for addressing this problem.SMC enables all participants to cooperatively compute on their private data without disclosing the privacy of the data while ensuring the correctness of the computation results.SMC is a key privacy preserving technology of data sharing.It is of great practical significance to study SMC problems arising in various practical applications.In this thesis,we study the secure multiparty location relationship determination,secure absolute value computation in the semi-honest model and secure maximum(minimum)computation in malicious model.The main contents of this thesis are as follows.1.Using the encrypt-and-choose method,we design two protocols based on the Lifted ElGamal threshold decryption cryptosystem and a new encoding scheme.The first protocol privately determine the relationship between multiple private points and a private interval.And the second protocol privately determine the relationship between the overlap length of multiple private intervals and a private threshold.We also give some examples to illustrate the extensive application of the protocols in real life.2.To privately compute absolute value of private numbers,we first design a protocol to compute and output the absolute value on ciphertext inputs.The protocol is efficient and very simple,and is applicable to many application scenarios.Then,we propose a protocol to privately compute and output the ciphertext of absolute value on plaintext inputs.Using this protocol as a building block,we design two protocols to privately compute Chebyshev distance,determine location relationship between rational number and rational interval.We prove that the protocol is secure by the simulation paradigm.Theoretical analysis and experimental results show that our protocols are efficient.3.To privately compute maximum(minimum)when the scenarios may have malicious adversaries,we first design a protocol which is secure in the semi-honest model.The protocol does not compute maximum by pairwise comparing.We analyze all possible attacks that a malicious adversary may launch.To resist those possible attacks,we use threshold decryption ElGamal cryptosystem,zero-knowledge proof of discret logarithm and secure shuffling as building blocks to design a protocol which is secure in the malicious model.We also prove its correctness and security.Experimental results show that the protocol is feasible.