Lower bounds for quantum oblivious transfer (pp0158-0177)
          Andre Chailloux, Iordanis Kerenidis, and Jamie Sikora
          doi: https://doi.org/10.26421/QIC13.1-2-9
Abstracts: Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest player�s cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat with probability bounded below by a constant strictly larger than 1/2. Alice�s cheating is defined as her probability of guessing Bob�s index, and Bob�s cheating is defined as his probability of guessing both input bits of Alice. In our proof, we relate these cheating probabilities to the cheating probabilities of a bit commitment protocol and conclude by using lower bounds on quantum bit commitment. Then, we present an oblivious transfer protocol with two messages and cheating probabilities at most 3/4. Last, we extend Kitaev�s semidefinite programming formulation to more general primitives, where the security is against a dishonest player trying to force the outcome of the other player, and prove optimal lower and upper bounds for them.
Key words: quantum cryptography, oblivious transfer, bit commitment, coin flipping, semidefinite programming.