Since the dissemination of Radio Frequency IDentification (RFID) tags is getting larger and larger, the requirement for strong security and privacy is also increasing. Low-cost and ultra-low-cost tags are being implemented on everyday products, and their limited resources constraints the security algorithms to be designed especially for those tags. In this paper, a complete solution providing strong security and high privacy during the whole product lifetime is presented. Combining bit-wise operations and secret keys, the algorithm proposed addresses and solves all the common security attacks.