In this paper, we propose an HB-like protocol for privacy-preserving authentication of RFID tags, whereby a tag can remain anonymous and untraceable to an adversary during the authentication process. Previous proposals of such protocols were based on PRF computations. Our protocol can instead be used on low-cost tags that may be incapable of computing standard PRFs. Moreover, since the underlying computations in HB protocols are very efficient, our protocol also reduces reader load compared to PRF-based protocols. We suggest a tree-based approach that replaces the PRF-based authentication from prior work with a procedure such as HB+ or HB#. We optimize the tree- traversal stage through usage of a "light version" of the underlying protocol and shared random challenges across all levels of the tree. This provides significant reduction of the communication resources, resulting in a privacy-preserving protocol almost as efficient as the underlying HB+ or HB#