Weak coin flipping is an important cryptographic primitive -- 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：弱硬币翻转是一种重要的密码学原语——它是已知最强的安全两方计算原语，在经典计算中仅在某些假设（如计算复杂性假设）下才具有安全性，而在量子计算中则存在可实现任意接近完美安全性的协议。这一突破性结果由Mochon于2007年建立[arXiv:0711.4114]。然而，他的证明依赖于特定酉算子的存在性，该存在性是通过非构造性论证建立的。因此，显式协议一直难以实现。在本工作中，我们给出了相关酉算子的精确构造。这些构造结合新形式化方法，产生了一族趋近完美安全性的协议，同时简化了Mochon的存在性证明。我们通过考虑具体实例（来自上述协议族）来展示显式弱硬币翻转协议的构造过程，这些实例比所有先前已知的协议具有更高的安全性。