International Association
for Cryptologic Research

Multi-party computation (\textsf{MPC}) is a major research interest in modern cryptography, and Privacy Set Intersection (\textsf{PSI}) is an important research topic within \textsf{MPC}. Its main function is to allow two parties to compute the intersection of their private sets without revealing any other information. Therefore, \textsf{PSI} can be applied to various real-world scenarios, such as the Industrial Internet of Things (\textsf{IIOT}). Chase and Miao presented a paper on ``Light-weight PSI'' at CRYPTO 2020, highlighting its convenient structure and optimal communication cost. However, the drawback is that this protocol is deterministically encrypted and it was discovered through simulation that it is not resistant to probabilistic attacks. Building upon the ideas from CM20, this paper introduces the concept of a {\em perturbed pseudorandom generator}, constructs and proves its security, and replaces one of the hash functions (originally there were two) from CM20. In order to demonstrate the security of the \textsf{PSI} protocol proposed in this paper, a dedicated definition of Chosen Plaintext Attack (\textsf{CPA}) security model for this \textsf{PSI} protocol is provided. The paper then proceeds to prove that the \textsf{PSI} protocol satisfies this defined security model. Efficiency analysis shows that the \textsf{PSI} in this paper is comparable to CM20's \textsf{PSI}, whether on PC, pad, or phone.