Optimal Security Bounds for Quantum Oblivious Transfer

Oblivious transfer is a fundamental cryptographic primitive in which Bob transfers one of two bits to Alice in such a way that Bob cannot know which of the two bits Alice has learned. We present an optimal security bound for quantum oblivious transfer protocols, in the information theoretic setting, under a natural and arguably demanding definition of what it means for Alice to cheat. Our lower bound is a smooth tradeoff between the probability P Bob with which Bob can guess Alice's bit choice and the probability P Alice with which Alice can guess both of Bob's bits given that she learns one of the bits with certainty. We prove that 2P Bob + P Alice 2 in any quantum protocol for oblivious transfer, from which it follows that one of the two parties must be able to cheat with probability at least 2/3. We prove that this bound is optimal by exhibiting a family of protocols whose cheating probabilities can be made arbitrarily close to any point on the tradeoff curve.