Methods and systems for improving homomorphic encryption include: receiving, by a computing device, a data set from at least two or more computing devices, each data set comprising: a plurality of encrypted identifiers, and a number indicating the number of the plurality of encrypted identifiers; creating, by the computing device, a single data set including each of the received data sets; creating, by the computing device, a common identifier vector that indicates each encrypted identifier in the single data set that has underlying unencrypted data that is the same in more than one of the received data sets; and transmitting, by the computing device, the common identifier vector to each of the at least two or more computing devices.