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Distributed online social networks (DOSN) have emerged recently. Nevertheless, recommending friends in the distributed social networks has not been exploited fully. We propose BCE (Bloom Filter based Common-Friend Estimation), a scalable and privacy-preserving common-friend estimation scheme that estimates the set of common friends without the need of cryptography techniques. First, BCE denotes each user using the identifiers created by the Peer-to-Peer underlay that are robust against the dictionary attacks. Second, BCE uses a Bloom filter to represent a friend list for scalability. Third, BCE estimates common friends of two users using the intersection of Bloom filters computed by one of their common friends, which ensures the privacy of friend lists against unknown users. Our privacy analysis shows that BCE hides the privacy of each user with a high probability. Simulations over real-world social-network data sets confirms that BCE is both accurate and scalable.