In this paper we propose an efficient forward-private RFID mutual authentication protocol. The protocol is secure under standard assumptions. It builds over a recent work, extends it to achieve mutual authentication, and improves it by introducing a resynchronization mechanism between tag and reader, through which the server-side computation from O(N ω) is reduced to O(N + ω), where N is the total number of tags in the system, and ω is the maximum number of authentications each single tag can afford during its lifetime. Moreover, the protocol enables the server to control how many times a tag has been read by legitimate and fake readers.