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We propose a new distance bounding protocol, which builds upon the private RFID authentication protocol by Peeters and Hermans [25]. In contrast to most distance-bounding protocols in literature, our construction is based on public-key cryptography. Public-key cryptography (specifically Elliptic Curve Cryptography) can, contrary to popular belief, be realized on resource constrained devices such as RFID tags. Our protocol is wide-forward-insider private, achieves distance-fraud resistance and near-optimal mafia-fraud resistance. Furthermore, it provides strong impersonation security even when the number of time-critical rounds supported by the tag is very small. The computational effort for the protocol is only four scalar-EC point multiplications. Hence the required circuit area is minimal because only an ECC coprocessor is needed: no additional cryptographic primitives need to be implemented.