Qingsong Ye

Efficient Disjointness Tests for Private Datasets

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.

Secure computation of the vector dominance problem

Suppose two parties, holding vectors A = (a1, a2,..., an) and B = (b1, b2,..., bn) respectively, wish to know whether ai > bi for all i, without disclosing any private input. This problem is called the vector dominance problem, and is closely related to the well-studied problem for securely comparing two numbers (Yaos millionaires problem). In this paper, we propose several protocols for this problem, which improve upon existing protocols on round complexity or communication/computation complexity.