An Unconditionally Secure Protocol for Multi-Party Set Intersection

Authors:
Ronghua Li;Chuankun Wu
Affiliations:
State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100080, P.R. China and Graduate School of Chinese Academy of Sciences, Beijing 100039, P.R ...;State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100080, P.R. China
Venue:
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Year:
2007

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Abstract

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 information-theoretic 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 nsets, 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.