Efficient Private Set Intersection Using Point-Value Polynomial Representation

Ou Ruan,Hao Mao

doi:10.1155/2020/8890677

Abstract

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.

Highlights

Private set intersection (PSI) can be described that participants complete computation based on their private inputs and cannot learn additional information other than the set intersection
PSI has a wide range of applications such as privacy-preserving contact tracing for infection detection [1, 2], private contact discovery [3], similar document detection [4], suspects detection [5], relationship path discovery in social networks [6], and satellite collisions matching [7]
According to cryptographic techniques involved, PSI protocols are mainly divided into the following three categories: (1) PSI based on the public-key technology: the main cryptographic technique was homomorphic encryption. e protocols were designed in such a way that the sender encrypted sets and the receiver performed some operations on the ciphertexts using the property of homomorphic encryption; the sender decrypted them by using his private key and got the intersection

Summary

Introduction

Private set intersection (PSI) can be described that participants complete computation based on their private inputs and cannot learn additional information other than the set intersection. PSI protocols based on symmetric cryptosystem have higher efficiency, but negotiating or secure transferring of secret keys leads to additional computations and communications. We transform the problem of the intersection of sets into the problem of finding the roots of polynomials by using pointvalue polynomial representation and propose an efficient PSI protocol without any cryptosystem. We transform the problem of the intersection of sets into the problem of finding roots of polynomials by using point-value polynomial representation and propose a new approach to PSI protocol without any cryptosystem. We propose a new approach for designing PSI protocol based on point-value polynomial representation and pseudorandom function. We optimize the new PSI protocol using the permutation-based hashing method, which converts the hashed elements into shorter strings without collisions and reduces the degree of polynomials.

Related Work

Preliminaries

Hashing Techniques

Efficient PSI Protocol Using Hashing

Evaluation

Conclusion and Future Work