The upsurge in the number of web users over the last two decades has resulted in a significant growth of online information. This information growth calls for recommenders that personalize the information proposed to each individual user. Nevertheless, personalization also opens major privacy concerns. This paper presents D2P, a novel protocol that ensures a strong form of differential privacy, which we call distance-based differential privacy, and which is particularly well suited to recommenders. D2P avoids revealing exact user profiles by creating altered profiles where each item is replaced with another one at some distance. We evaluate D2P analytically and experimentally on MovieLens and Jester datasets and compare it with other private and non-private recommenders.