James Peat

Rabin oblivious transfer is the cryptographic task where Alice wishes to receive a bit from Bob but it may get lost with probability 1/2. In this work, we provide protocol designs which yield quantum protocols with improved security. Moreover, we provide a constant lower bound on any Rabin oblivious transfer protocol. To quantify the security of this task with asymmetric cheating notions, we introduce the notion of cheating advantage which may be of independent interest in the study of other asymmetric cryptographic primitives as well.

Oblivious transfer is a two-party cryptographic primitive which has been the interest of study as it can be used as a building block for multiparty computation, such as building a voting system between distrusting parties. It has been shown, however, that perfectly secure oblivious transfer is impossible in both the classical and quantum setting. This has pushed the study of oblivious transfer in two directions. The first is applying assumptions about the abilities of a cheating party such as in the bounded storage model. The second is looking for the absolute bounds on a cheating party with no restrictions. We study the latter area, using one version of oblivious transfer known as Rabin oblivious transfer. This is a two-party protocol where the sender holds one bit, and the receiver obtains this bit with a set probability.