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This paper addresses the problem of data sharing among multiple parties, without disclosing the data between the parties. We focus on sharing of data among parties involved in a data mining task. We study how to share private or confidential data in the following scenario: without disclosing their private data to each other, multiple parties, each having a private data set, want to collaboratively construct support vector machines using a linear, polynomial or sigmoid kernel function. To tackle this 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. We analyze the protocol in the context of mistakes and malicious attacks, and show its robustness against such attacks. All the parties are treated symmetrically: they all participate in the encryption and in the computation involved in learning support vector machines.