Efficient Private Set Intersection Using Point-Value Polynomial Representation

• Published in: Security and communication networks Vol. 2020; no. 2020; pp. 1 - 12
• Main Authors: Ruan, Ou, Mao, Hao
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 2020; Hindawi; Hindawi Limited
• Subjects: Communication; Contact tracing; COVID-19; Efficiency; Infections; Linux; Permutations; Polynomials; Privacy; Pseudorandom; Representations; Satellites
• ISSN: 1939-0114; 1939-0122
• DOI: 10.1155/2020/8890677

Private set intersection (PSI) allows participants to securely compute the intersection of their inputs, which has a wide range of applications such as privacy-preserving contact tracing of COVID-19. Most existing PSI protocols were based on asymmetric/symmetric cryptosystem. Therefore, keys-related operations would burden these systems. In this paper, we transform the problem of the intersection of sets into the problem of finding roots of polynomials by using point-value polynomial representation, blind polynomials’ point-value pairs for secure transportation and computation with the pseudorandom function, and then propose an efficient PSI protocol without any cryptosystem. We optimize the protocol based on the permutation-based hash technique which divides a set into multisubsets to reduce the degree of the polynomial. The following advantages can be seen from the experimental result and theoretical analysis: (1) there is no cryptosystem for data hiding or encrypting and, thus, our design provides a lightweight system; (2) with set elements less than 212, our protocol is highly efficient compared to the related protocols; and (3) a detailed formal proof is given in the semihonest model.