Optimal Quantum Strong Coin Flipping

Coin flipping is a fundamental cryptographic primitive that enables two distrustful and far apart parties to create a uniformly random bit. Quantum information allows for protocols in the information theoretic setting where no dishonest party can perfectly cheat. The previously best-known quantum protocol by Ambain is achieved a cheating probability of at most 3/4. On the other hand, Kitaev showed that no quantum protocol can have cheating probability less than 1/¿2. Closing this gap has been one of the important open questions in quantum cryptography. In this paper, we resolve this question by presenting a quantum strong coin flipping protocol with cheating probability arbitrarily close to 1/¿2. More precisely, we show how to use any weak coin flipping protocol with cheating probability 1/2 + ¿ in order to achieve a strong coin flipping protocol with cheating probability 1/¿2 + O(¿). The optimal quantum strong coin flipping protocol follows from our construction and the optimal quantum weak coin flipping protocol described by Mochon.