In this paper, we consider personalized recommendation systems in which before publication, the profile of a user is sanitized by a non-interactive mechanism compliant with the concept of differential privacy. We consider two existing schemes offering a differentially private representation of profiles: BLIP (BLoom-and-flIP) and JLT (Johnson-Lindenstrauss Transform). For assessing their security levels, we play the role of an adversary aiming at reconstructing a user profile. We compare two inference attacks named single and joint decoding. The first one decides of the presence of a single item in the profile, and sequentially browses all the item set. The latter strategy decides whether a subset of items is likely to be the user profile, and browses all the possible subsets. Our contributions are a theoretical analysis and practical implementations of both attacks tested on datasets composed of real user profiles revealing that joint decoding is the most powerful attack. This also gives useful insights on the setting the differential privacy parameter $\epsilon$.