Abstract
Two parties, wishing to establish a shared random bit at a distance, must solve a problem known as coin flipping. Classical two-party secure computations such as coin flipping are impossible in the information theoretic setting. However quantum information allows for the possibility of unconditional security. Mochon defines a model of secure two-party computations, point games, to show the existence of optimal quantum weak coin flipping protocols in [29]. His ground-breaking result is widely accepted, but its proof is very complicated, has never been validated, and remains poorly understood despite the efforts of several researchers [12,25,35].
In this thesis we use analytical and mathematical methods to study point games. We discover several new primitives, and construct new building blocks to define a new family of point games. We present a new truncation technique that is simpler, more efficient, is more intuitive, and achieves better results than the best previously known. We provide concrete examples of these point games. We analyze Mochon's optimal point games, and we identify the key elements of their construction that are not specified. We also provide a new recursion technique that achieves better results than the one proposed by Mochon. Furthermore, we construct simple and elegant point games using binomial coefficients. Our point games are simpler than Mochon's, since his point games are constructed using techniques in mathematical analysis. Studying point games with new techniques may lead to a simpler formalism of two-party secure computations, and to more efficient protocols.
