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Construction If U is friends with A, B, and C, then F1 for U would be a bloom filter with the following contents: F(SA,SB,SC) where F(·) represents a bloom filter. However, U enters a friend X in the bloom filter not using X’s public identity, but using an alias for X (which we denote SX) that is only know to X’s friends. This ensures the privacy of U’s set of friends, since it is impossible to enumerate U’s friends given only the bloom filter and the public identifiers of nodes. Specifically, a user M, given U’s bloom filter, can determine if U is friends with another user only if M is also friends with the other user herself. Moreover, since each user chooses unique parameters, it is impossible to estimate, given two user’s bloom filters, the size of the intersection among the users’ friends. Users construct their two-hop bloom filters by requesting one-hop bloom filters with a specified set of parameters from all of their friends. To construct a two-hop bloom filter, a user then simply perform a bit-wise OR of all of their friends’ responses. Additionally, whenever a user creates or removes links, the user resends its one-hop bloom filter to each of her friends, so that they can update their two-hop bloom filters. Use When a user A wishes to discover a path to user B, A obtains B’s one-hop and two-hop bloom filters using the lookup mechanism of the underlying communication system. A first checks to see if any of her friends appear in B’s one-hop bloom filter. 189PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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