This thesis focuses on issues related to authentication in low-cost radio frequency identification technology, more commonly referred to as RFID. This technology it is often referred to as the next technological revolution after the Internet. However, due to the very limited resources in terms of computation, memory and energy on RFID tags, conventional security algorithms cannot be implemented on low-cost RFID tags making security and privacy an important research subject today. First of all, we investigate the scalability in low-cost RFID systems by developing a ns-3 module to simulate the universal low-cost RFID standard EPC Class-1 Generation-2 in order to establish a strict framework for secure identification in low-cost RFID systems. We show that, the symmetrical key cryptography is excluded from being used in any scalable low-cost RFID standard. Then, we propose a scalable authentification protocol based on our adaptation of the famous public key cryptosystem NTRU. This protocol is specially designed for low-cost RFID systems, it can be efficiently implemented into low-cost tags. Finally, we consider the zero-knowledge identification i.e. when the no secret sharing between the tag and the reader is needed. Such identification approaches are very helpful in many RFID applications when the tag changes constantly the field of administration. We propose two lightweight zero-knowledge identification approaches based on GPS and randomized GPS schemes. The proposed approaches consist in storing in the back-end precomputed values in the form of coupons. So, the GPS-based variant can be private and the number of coupons can be much higher than in other approaches thus leading to higher resistance to denial of service attacks for cheaper tags