STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Robust efficient distributed RSA-key generation
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
Communications of the ACM
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Private Information Retrieval Based on the Subgroup Membership Problem
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Privacy Preserving Set Intersection Protocol Secure against Malicious Behaviors
PDCAT '07 Proceedings of the Eighth International Conference on Parallel and Distributed Computing, Applications and Technologies
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Efficient protocols for privacy preserving matching against distributed datasets
ICICS'06 Proceedings of the 8th international conference on Information and Communications Security
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Privacy-preserving set operations
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Honest-verifier private disjointness testing without random oracles
PET'06 Proceedings of the 6th international conference on Privacy Enhancing Technologies
Efficient and secure protocols for privacy-preserving set operations
ACM Transactions on Information and System Security (TISSEC)
Proceedings of the 9th annual ACM workshop on Privacy in the electronic society
Privacy-preserving disjunctive normal form operations on distributed sets
Information Sciences: an International Journal
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We propose a more efficient privacy preserving set intersection protocol which improves the previously known result by a factor of O(N) in both the computation and communication complexities (N is the number of parties in the protocol). Our protocol is obtained in the malicious model, in which we assume a probabilistic polynomial-time bounded adversary actively controls a fixed set of t (t N/2) parties. We use a (t + 1,N)-threshold version of the Boneh-Goh-Nissim (BGN) cryptosystem whose underlying group supports bilinear maps. The BGN cryptosystem is generally used in applications where the plaintext space should be small, because there is still a Discrete Logarithm (DL) problem after the decryption. In our protocol the plaintext space can be as large as bounded by the security parameter τ, and the intractability of DL problem is utilized to protect the private datasets. Based on the bilinear map, we also construct some efficient non-interactive proofs. The security of our protocol can be reduced to the common intractable problems including the random oracle, subgroup decision and discrete logarithm problems. The computation complexity of our protocol is O(NS2τ3) (S is the cardinality of each party's dataset), and the communication complexity is O(NS2τ) bits. A similar work by Kissner et al. (2006) needs O(N2S2τ3) computation complexity and O(N2S2τ) communication complexity for the same level of correctness as ours.