We investigate an application of RFIDs referred to in the literature as group scanning, in which several tags are "simultaneously" scanned by a reader device. Our goal is to study the group scanning problem in strong adversarial models. We present a security model for this application and give a formal description of the attending security requirements, focusing on the privacy (anonymity) of the grouped tags, and/ or forward-security properties. Our model is based on the Universal Composability framework and supports re-usability (through modularity of security guarantees). We introduce novel protocols that realize the security models, focusing on efficient solutions based on off-the-shelf components, such as highly optimized pseudo-random function designs that require fewer than 2000 Gate-Equivalents.