Computing algebraic formulas with a constant number of registers
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Non-cryptographic fault-tolerant computing in constant number of rounds of interaction
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Comparing information without leaking it
Communications of the ACM
Oblivious transfer and polynomial evaluation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Secure Distributed Linear Algebra in a Constant Number of Rounds
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Modern Computer Algebra
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
On the complexity of computing determinants
Computational Complexity
Privacy-Preserving Distributed Set Intersection
ARES '08 Proceedings of the 2008 Third International Conference on Availability, Reliability and Security
A secure and optimally efficient multi-authority election scheme
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Distributed private matching and set operations
ISPEC'08 Proceedings of the 4th international conference on Information security practice and experience
Testing disjointness of private datasets
FC'05 Proceedings of the 9th international conference on Financial Cryptography and Data Security
Privacy-preserving set operations
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Private itemset support counting
ICICS'05 Proceedings of the 7th international conference on Information and Communications Security
Honest-verifier private disjointness testing without random oracles
PET'06 Proceedings of the 6th international conference on Privacy Enhancing Technologies
Efficient polynomial operations in the shared-coefficients setting
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Syntax-Driven private evaluation of quantified membership queries
ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
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We present efficient protocols for private set disjointness tests. We start from an intuition of our protocols that applies Sylvester matrices. Unfortunately, this simple construction is insecure as it reveals information about the cardinality of the intersection. More specifically, it discloses its lower bound. By using the Lagrange interpolation we provide a protocol for the honest-but-curious case without revealing any additional information. Finally, we describe a protocol that is secure against malicious adversaries. The protocol applies a verification test to detect misbehaving participants. Both protocols require O(1) rounds of communication. Our protocols are more efficient than the previous protocols in terms of communication and computation overhead. Unlike previous protocols whose security relies on computational assumptions, our protocols provide information theoretic security. To our knowledge, our protocols are first ones that have been designed without a generic secure function evaluation. More importantly, they are the most efficient protocols for private disjointness tests for the malicious adversary case.