An Unconditionally Secure Protocol for Multi-Party Set Intersection

Existing protocols for private set intersection are based on homomorphic public-key encryption and the technique of representing sets as polynomials in the cryptographic model. Based on the ideas of these protocols and the two-dimensional verifiable secret sharing scheme, we propose a protocol for private set intersection in the informationtheoretic model. By representing the sets as polynomials, the set intersection problem is converted into the task of computing the common roots of the polynomials. By sharing the coefficients of the polynomials among parties, the common roots can be computed out using the shares. As long as more than 2n/3 parties are semi-honest, our protocol correctly computes the intersection of n sets, and reveals no other information than what is implied by the intersection and the secrets sets controlled by the active adversary. This is the first specific protocol for private set intersection in the information-theoretic model as far as we know.