A Study Of New Secure Multiparty Set Operations Based On Lattice

The main research of secure multiparty computation is that how many participants to obtain a common goal without revealing their own secret information. Secure multiparty computation plays an important role in electronic voting, electronic auctions and threshold signature scene and has been a hot topic in cryptography field in recent years. But most secure multiparty computation protocols are made based on the difficult problems such as discrete logarithm or Decomposition of large number. There are some disadvantages of these solutions, such as using of complex logarithmic, modular exponentiation and that they cannot resist quantum attack and so on. However, the lattice has become an important tool for solving secure multiparty computation problems due to its so many advantages such as high efficiency, the simple algebraic structure, that it can resist quantum attacks and provable security, etc.This thesis studies the set problems in the field of secure multiparty computation, including the problems of judging weather multi-party sets equal each other, calculating their intersect and merge. Currently solutions for the problems of the calculation on the set are mostly for the case of two parties, and few of them are suit for multi-party sets. In addition, most secure multi-party computation on set schemes use encryption algorithms based on the problems of decomposition of large numbers, discrete logarithm or, etc. The calculation process is complex. To solve those problems, this paper presented a scheme of LWE-based encryption algorithm under semi-honest model to solve the practical problems associated with the set.The main contributions of this thesis are as follows:1. We constructed a solution for problem that judging weathere multi sets equal. By using the LWE encryption algorithm, I changed the data of each participant’s collection into each participant’s private key.Then I encrypted and decrypted a random string. Then I solved the problem of judging weather multiple sets equal.In addition, introducing of a trusted third party ensured the efficiency of the scheme and the fairness between the participants2. We researched and analysize the problem of calculating intersection of multi-set. Then I presented the design process and design model of solution. This paper proposed a program for determining weather an element belong to a set and presented a flow chart for calculating the intersection of two sets. Finally, I changed the number of participants from two to many and further constructed the scheme for calculating intersection of multi-stakeholder.3. Based on above schemes solving problem of calculating intersection of multi-stakeholder, I further proposed a scheme for solving problem of calculating union set of multi-stakeholder. At first all participants send their key-value pairs with plaintext and ciphertext to the third trusted party.Then the third party handled these key-value pairs and send them to all participants.At last all participants decoded all key-value pairs and get the union set with intersection calculated before.The three solutions in this thesis can be applied to the set operation problems with any number of participants, make the scheme applicable range is wider; In addition, Changing the data of participants into the private key and omiting the selection process of the private key in the encryption algorithm made these schemes easy. Introducing a third trusted party into scheme reduced the rounds of communication and made it fair between all participants. At last, the security of schemes were all based on LWE difficulty hypothesis, making these schemes can resist the leak of private key. The disadvantage of the two schemes is that introduced the outside trusted third party, but so far, the security of the trusted third party is still a bottleneck problem in practical application.