“Updatable” private set intersection (PSI) protocols allow parties that each have an updatable private set to determine the intersection of their sets after an update without the need to compare each element of each set and without compromising privacy. In some protocols, a first party can determine an update to the intersection by determining an intersection of elements that were previously in the first party's set with elements that were added to the second party's set and determining an intersection of elements that were added to the first party's set with elements that are in the second party's (updated) set. In some protocols, both parties can determine the updated intersection.