This paper introduces a new approach to a problem of data sharing among multiple parties, without disclosing the data between the parties. Our focus is data sharing among parties involved in a data mining task. We study how to share private or confidential data in the following scenario: multiple parties, each having a private data set, want to collaboratively conduct association rule mining without disclosing their private data to each other or any other parties. To tackle this demanding problem, we develop a secure protocol for multiple parties to conduct the desired computation. The solution is distributed, i.e., there is no central, trusted party having access to all the data. Instead, we define a protocol using homomorphic encryption techniques to exchange the data while keeping it private.