Research On Secure Two-Party Polynomial Data Computation Based On NTRUEncrypt

In the current era of rapid development of the electronic information industry,”data islands”have become a major issue in the information era.Data is stored separately by multiple parties,and it is impossible to establish actual connections.The emergence of secure multi-party computation provides a good solution to the ”data island” problem,achieving joint operations of private data while ensuring individual data privacy,and promoting security cooperation between parties.On the other hand,with the development of quantum computers,lattice based post quantum cryptography algorithms achieve a better balance between security,key size,and computational speed compared to other cryptography systems.NTRUEncrypt is a lattice based anti quantum attack encryption algorithm.This thesis is inspired by the secure two-party computing of AES and RSA cryptosystems to achieve distributed key management.This thesis takes two-party computing and NTRUEncrypt as the starting point,and the main innovation points are as follows:1.A secure two-party computation scheme for implementing NTRUEncrypt is proposed.The entire process of NTRUEncrypt is implemented by using the basic modules of secure multiparty computation,such as oblivious transfer and privacy set intersection,through the collaborative generation of keys and joint decryption by two participants.The security proof of this scheme in a semi honest model is given.2.For polynomial operations,this thesis uses the Chinese Remainder Theorem to encode numeric data into polynomial form data.Its coding rules meet the homomorphic characteristics of the data,reduce coding overhead,and implement two common secure bipartite polynomial type data operations schemes,namely,polynomial addition and multiplication operations under privacy computation.3.A general polynomial data verification scheme based on NTRUEncrypt is proposed to prove the correctness of the polynomial to ensure the correct execution of subsequent protocols.At the same time,this scheme can also be used to protect keys.The main idea is to split the keys.In summary,this thesis has well expanded the calculation of data,elevating data operations to the polynomial level.Due to the high security of NTRUEncrypt and direct ciphertext computation under homomorphic encryption,both parties can effectively ensure data security,and also provide the feasibility of implementing multi-party computation under cryptosystems.