Weak coin flipping is an important cryptographic primitive$\unicode{x2013}$it is the strongest known secure two-party computation primitive that classically becomes secure only under certain assumptions (e.g. computational hardness), while quantumly there exist protocols that achieve arbitrarily close to perfect security. This breakthrough result was established by Mochon in 2007 [arXiv:0711.4114]. However, his proof relied on the existence of certain unitary operators which was established by a non-constructive argument. Consequently, explicit protocols have remained elusive. In this work, we give exact constructions of related unitary operators. These, together with a new formalism, yield a family of protocols approaching perfect security thereby also simplifying Mochon's proof of existence. We illustrate the construction of explicit weak coin flipping protocols by considering concrete examples (from the aforementioned family of protocols) that are more secure than all previously known protocols.

翻译：弱掷币是一种重要的密码学原语——它是目前已知的最强大的安全两方计算原语，在经典条件下仅能在特定假设（如计算复杂性）下实现安全，而量子领域已存在可达到任意接近完美安全性的协议。这一突破性成果由Mochon于2007年确立[arXiv:0711.4114]。然而，其证明依赖于特定酉算子的存在性，该存在性通过非构造性论证确立，导致显式协议长期缺失。本工作通过精确构造相关酉算子，结合新形式化体系，提出了一族逼近完美安全性的协议，从而简化了Mochon的存在性证明。我们通过分析该协议族中的具体实例，展示了显式弱掷币协议的构造方法，这些实例的安全性均超越所有已知协议。