Erika Andersson

Oblivious transfer (OT) is a cryptographic primitive which is universal for multiparty computation. Unfortunately, perfect information-theoretically secure (ITS) quantum oblivious transfer is impossible. Imperfect information-theoretically secure quantum oblivious transfer is possible, but the smallest possible cheating probabilities are not known. We present an imperfect information-theoretically secure quantum oblivious transfer protocol with no restrictions on dishonest parties, and its experimental implementation. The cheating probabilities are 0.75 and 0.729 for sender and receiver respectively, which is lower than in existing protocols. Using a photonic test-bed, we have implemented the protocol with honest parties, as well as optimal cheating strategies.

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.

Oblivious transfer (OT) is a cryptographic primitive which is universal for multiparty computation. Unfortunately, perfect information-theoretically (IT) secure quantum oblivious transfer is impossible (except with restrictions on cheating parties). Imperfect IT secure quantum oblivious transfer remains possible, but the smallest possible cheating probabilities are not known. Informally, in 1-out-of-2 oblivious transfer, a sender Alice has two bits x0, x1. A receiver Bob obtains one of these, xb, where b= 0 or b= 1. Alice should not be able to guess b, and Bob should not be able to guess the bit value he did not obtain. Bounds on cheating probabilities in quantum oblivious transfer have previously been investigated for complete protocols. “Complete” means that if sender Alice and receiver Bob both follow the protocol, the bit value Bob obtains correctly matches Alice’s bit value. Here we instead investigate incomplete protocols, where Bob obtains an incorrect bit value with probability pf. For complete protocols, both “classical” and quantum, it holds that if one party can cheat no better than with a random guess, then the other party can cheat perfectly. For incomplete protocols, in contrast, even with no restrictions on cheating parties, and when one party can cheat no better than with random guess, it is possible that the other party still cannot cheat perfectly; their cheating probability can be lower than in complete protocols. We find the optimal non-interactive protocols where Alice’s bit values are represented by four symmetric pure quantum states, and where Alice cannot cheat better than with a random guess. “Optimal” means that for a given pf, Bob’s cheating probability pr is as low as possible, and vice versa. We also show that quantum protocols can outperform classical non-interactive protocols. Our results also provide a lower bound on Bob’s cheating probability in interactive quantum protocols. An advantage of the non-interactive protocols we investigate is that they require neither entanglement nor quantum memory. The optimal protocols could be readily implemented using standard optical components.

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.

Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart from being of fundamental interest, quantum state elimination may find uses in quantum communication and quantum cryptography. We consider unambiguous elimination of a pair of quantum states, and present a possible optical realisation of the scheme.