In this paper, we introduce a randomized bit encoding scheme that can strengthen the privacy protection on RFID tags. This scheme is used together with the backward channel protection method proposed by Choi and Roh in [1], which serves to protect the unique identifier of an RFID tag from disclosure to close-range eavesdroppers. Choi and Roh's method faces the `same-bit' problem, in which some bits of the unique identifier could be disclosed, thereby revealing critical information. Our proposed scheme alleviates the `same-bit' problem to a negligible level. Furthermore, we propose an enhanced system model that can protect the unique tag identifier from disclosure not only against eavesdroppers, but against unauthorized interrogators as well. A metric based on entropy was defined and used to measure the amount of protection offered by the scheme. A method to construct an optimal randomized n-bit encoding scheme was also described. In addition, theoretical analysis and si...