Massively deploying RFID systems while preserving people’s privacy and data integrity is a major security challenge of the coming years. Up to now, it was commonly believed that, due to the very limited computational resources of RFID tags, only ad hoc methods could be used to address this problem. Unfortunately, not only those methods generally provide a weak level of security and practicality, but they also require to revise the synopsis of communications between the tag and the reader. In this paper, we give evidence that highly secure solutions can be used in the RFID environment, without substantially impacting the current communication protocols, by adequately choosing and combining low-cost cryptographic algorithms. The main ingredients of our basic scheme are a probabilistic (symmetric or asymmetric) encryption function, e.g. AES, and a coupon-based signature function, e.g. GPS. We also propose a dedicated method allowing the tag to authenticate the reader, which is of independent interest. On the whole, this leads to a privacy-preserving protocol well suited for RFID tags, which is very flexible in the sense that each reader can read and process all and only all the data it is authorized to.