Abstract-Radio Frequency IDentification (RFID) systems are steadily becoming paramount due to their vast applications such as supply chains, inventory, tolling, baggage management, access control etc. While they have potentials to improve our lives, they also present a privacy risk. Privacy is often overlooked in many applications, but due to pervasiveness of RFIDs the issue has to be taken into account. However, additional security always comes at price and the scarceness of resources on a tag makes conventional privacy-preserving protocols infeasible.In this paper we propose several authentication protocols that are all made of the same building blocks. More precisely, we first revise the EC-RAC (Elliptic Curve Based Randomized Access Control) protocol and we expand it into several authentication protocols. All the proposed protocols satisfy the basic requirements, which are the system scalability, un-traceability and security against cloning attacks and replay attacks, but each protocol has different security properties. The security proofs are implied by means of cryptographic reductions, i.e. they are based on the security of the Schnorr protocol and the hardness of the decisional Diffie-Hellman problem.