cryptoGPS has been promoted as a public-key technology suitable for UHF RFID tag authentication. Since it is a classical commitment-challenge-response (CCR) scheme, it can be converted into a signature scheme using the transformation proposed by Fiat and Shamir. Previously this signature variant has not been considered for RFID, but in this paper we show how to achieve this transformation in a way that yields a compact and efficient scheme. Further, the three-pass CCR scheme is turned into a regular challenge-response scheme with the attendant protocol and implementation improvements. Since we use a block cipher rather than a hash function for the transformation, we justify our approach using results in the ideal cipher model and the net result is a variant of cryptoGPS that offers asymmetric UHF tag authentication with reduced communication and protocol complexity.