The document proposes a new protocol for securely mining association rules from horizontally distributed databases. It improves on the previous leading protocol from Kantarcioglu and Clifton by offering enhanced privacy, simplicity, and efficiency. The main innovation is a novel secure multi-party algorithm for computing the union of private subsets held by different players, without revealing additional information. This protocol leaks less excess information than the previous approach and only to a few possible coalitions rather than individual players. It also solves the problem of private set inclusion testing in a secure manner.