We propose a novel authentication scheme that ensures privacy of the provers. Our scheme is based on symmetric-key cryptography, and therefore, it is well-suited to resource constrained applications in large scale environments. A typical example for such an application is an RFID system, where the provers are low-cost RFID tags, and the number of the tags can potentially be very large. We analyze the proposed scheme and show that it is superior to the well-known key-tree based approach for private authentication both in terms of privacy and efficiency.