Recently, a new type of Radio Frequency IDentification (RFID) system with mobile readers is introduced. In such a system, it is more desirable for mobile readers to identify tags without a back-end server, and thus it is frequently referred as a serverless mobile RFID system. In this paper, we formalize a serverless mobile RFID system model and propose a new encryption-based system that preserves the privacy of both tags and readers in the model. In addition, we define a new adversary model for the system model and show the security of the proposed system. Throughout comparisons between ours and the other alternatives, we show that our proposed system provides a stronger reader privacy and robustness against a reader forgery attack than the competitors.