Computing k-nearest-neighbor graphs constitutes a fundamental operation in a variety of data-mining applications. As a prominent example, user-based collaborative-filtering provides recommendations by identifying the items appreciated by the closest neighbors of a target user. As this kind of applications evolve, they will require KNN algorithms to operate on more and more sensitive data. This has prompted researchers to propose decentralized peer-to-peer KNN solutions that avoid concentrating all information in the hands of one central organization. Unfortunately , such decentralized solutions remain vulnerable to malicious peers that attempt to collect and exploit information on participating users. In this paper, we seek to overcome this limitation by proposing H&S (Hide & Share), a novel landmark-based similarity mechanism for decentralized KNN computation. Landmarks allow users (and the associated peers) to estimate how close they lay to one another without disclosing their individual profiles. We evaluate H&S in the context of a user-based collaborative-filtering recommender with publicly available traces from existing recommendation systems. We show that although landmark-based similarity does disturb similarity values (to ensure privacy), the quality of the recommendations is not as significantly hampered. We also show that the mere fact of disturbing similarity values turns out to be an asset because it prevents a malicious user from performing a profile reconstruction attack against other users, thus reinforcing users' privacy. Finally, we provide a formal privacy guarantee by computing an upper bound on the amount of information revealed by H&S about a user's profile.