  Oblivious transfer is a fundamental primitive in cryptography. While perfect
information theoretic security is impossible, quantum oblivious transfer
protocols can limit the dishonest players' 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 coin flipping protocol and conclude by using
Kitaev's coin flipping lower bound. 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.
