If there are two people Alice and Bob, and each has one set. They want to know whether their sets have intersect or not. Is there any Private Set Intersection scheme that only leak whether intersect or not without the real intersection value? Thank you!
What you are asking for is also known as a test for disjointness of private datasets.
Kiayias, who introduced this problem in 2005, called a protocol solution the Private Intersection Predicate Evaluation (PIPE) protocol.
Reference: Kiayias, Aggelos, and Antonina Mitrofanova. "Testing disjointness of private datasets." In International Conference on Financial Cryptography and Data Security, pp. 109-124. Springer, Berlin, Heidelberg, 2005