Lara Stroh

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.

Oblivious transfer (OT) is an important cryptographic primitive for transmitting information between two non-trusting parties and can be used as basic building block to implement any two-party computation. One variant of OT is XOR oblivious transfer (XOT), where the sender Alice has two bits and sends them to the receiver Bob. Bob will obtain either the first bit, the second bit, or their XOR. In an honest run of the protocol, Bob should not learn anything more than this, and Alice should not be able to tell what Bob has learned. Unfortunately, perfect quantum OT is impossible with information-theoretic security, so we focus on obtaining the smallest possible cheating probabilities for dishonest parties, when there are no restrictions imposed on them. We present a non-interactive quantum XOT protocol with classical post-processing, where the cheating probabilities are 1/2 for Alice and 3/4 for Bob. Reversing this protocol, so that Bob becomes the sender of a quantum state and Alice the receiver who measures it, while still implementing oblivious transfer from Alice to Bob, we show that the cheating probabilities for both parties stay the same as for the unreversed protocol. The reversed protocol is even easier to implement. The quantum XOT protocol outperforms classical XOT protocols. Lastly, we are in the process of implementing both the unreversed and the reversed protocol experimentally.