Research On Several Secure Multi-party Computation Protocols

Information is important resource to promote social development,economic growth and scientific and technological progress.It is also important wealth and strategic asset of a country.Information exists in form of data.Efficient algorithms can work on sufficient data to produce valuable information to benefit our work.However,no entity even if an internet giant can collect all data it needs.Therefore,it has to share data collected by other entities to obtain the information it wants.That is,perform cooperative computation on their private data to achieve what they want.In real life,data often contains ample private or confidential information.If the data is shared unprotected,serious privacy disclosure will occur.It is an important and basic cryptographic problem to share data through the Internet while preserving the privacy of data.It is also an important problem of information security practice.Secure multi-party computation(SMC)makes a group of distrusted parties perform cooperative computation on their private data without disclosing the privacy of data.As the key technology of privacy-preserving data sharing,SMC plays an important role in electronic commerce,scientific research,intelligent medical care,outsourcing computing etc.This paper focuses on the problems of privately determining whether the ranks of a matrix and its augmented matrix are equal,of secure multiparty multi-data ranking,and of privately determining whether two rational numbers are equal.The main research is as follows.To privately determine whether the rank of a matrix equals that of its augmented matrix,we design an efficient protocol using matrix transformation.Our protocol does not use public key encryption system.It can be used as a basic building block to construct many secure multiparty computation protocols.We further use it to solve other SMC problems including privately determining the relationship between two lines,determining whether a polynomial divides another one etc.For secure multiparty multi-data ranking problem,we mainly study the secure ranking when there is repeated element in multi-party arrays and union arrays.We first design new encoding schemes to hide private numbers.Based on the new encoding schemes and threshold decryption elliptic curve cryptosystem,we design secure ranking protocols for three ranking problems:the ranking that the same numbers have the same order and the order of next number increase by 1;the ranking that the same numbers have the same order,but if there are k same numbers,the order of next number will increase by k;the ranking that the same numbers have different orders.These new encoding schemes are of independent interest to be used as building blocks to address other SMC problems.We also design a ranking protocol in the malicious model.To privately determine whether two rational numbers are equal,we use the Paillier cryptosystem to design a protocol which is secure in the semi-honest model.We further modify it such that it is secure in the malicious model.Theoretical analysis indicates that these protocols are efficient.Finally,we program and test the protocols in our PC.The experimental results show that the three protocols,that is,the private matrix rank equality test protocol,secure multiparty multi-data ranking protocol and private equality test of rational numbers are efficient.