David Reichmuth, Heriot-Watt University
One-out-of-two (1-2) oblivious transfer is a cryptographic primitive, in which a sender holds two bits, x0 and x1, and a receiver receives one of them, in such a way that the receiver does not know both bits, and the sender does not know which bit the receiver obtained. While information-theoretical security for quantum versions of such protocols is not possible, it is of interest to examine possible security bounds, which previous work has shown to be set at 0.749 in “complete” protocols employing pure symmetric states. Protocol completeness means that the protocol is executed without an inherent probability for failure.
By considering incomplete protocols using coherent states and measuring them using homodyne detection, we show that it is possible to improve on that bound and, further, construct a protocol with security against one of the parties, which is not possible for complete protocols. While the use of coherent states in this manner allows for comparatively easy implementation, it also gives rise to high protocol failure probabilities, P_F≥24%, in the regions in which the security bounds of the complete protocol are beaten.