In peer to peer social networking systems, the list of neighbors is a valuable privacy information. However, sometimes, it needs to compute the common neighbors between two nodes without revealing the list of neighbors. For that matter, recently a Bloom filter based approach has been proposed, where the probability of filter errors of the Bloom filter is the key factor for the privacy of the neighbor lists and the accuracy of the common neighbor computation. Thus, with the given target probability of filter error p, it is critical to design a Bloom filter that provides exact p probability of filter errors. The existing design method only uses an approximation of the filter errors. In this paper, we propose an iterative algorithm that computes the size of the Bloom filters to provide p probability of filter errors. We show that the given algorithm finds a better Bloom filter size to provide the target probability of filter errors.
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