Secure Multi-party Computation of Intersection Potential and Intersection Sum Without Full Set Under the Malicious Model

In the current digital society, data has become a key production factor, however, the contradiction between data privacy protection and effective utilization is increasingly prominent. Secure multi-party computation (MPC), as an important technology in the field of cryptography, can securely compute all kinds of computations in practical applications. Secure computing set intersection potential and sum of intersection elements gradually become one of the research hotpots in the secure computing set problem, which has an important position and role in machine learning, artificial intelligence, privacy matching and other fields. In this paper, we firstly focus on studying and designing the protocol for computing the set intersection potential and intersection sum without full set under the semi-honest model, and then analyze the possible potential malicious attack behaviors under the semi-honest model. For the possible malicious behaviors, the MPC techniques such as homomorphic encryption, zero-knowledge proof, etc., based on the NTRU cryptosystem, are used to design a protocol for computing the set intersection potential and intersection sum of sets without full set under the malicious model, which is proved to be able to effectively improve the computational efficiency and ensure the correctness of the computation while guaranteeing the privacy of the data through detailed theoretical analyses and experimental verifications.