Weak coin flipping is the cryptographic task where Alice and Bob remotely flip a coin but want opposite outcomes. This work studies this task in the device-independent regime where Alice and Bob neither trust each other, nor their quantum devices. The best protocol was devised over a decade ago by Silman, Chailloux, Aharon, Kerenidis, Pironio, and Massar with bias $\varepsilon \approx 0.33664$, where the bias is a commonly adopted security measure for coin flipping protocols. This work presents two techniques to lower the bias of such protocols, namely self-testing and abort-phobic compositions. We apply these techniques to the SCAKPM '11 protocol above and, assuming a continuity conjecture, lower the bias to $\varepsilon \approx 0.29104$. We believe that these techniques could be useful in the design of device-independent protocols for a variety of other tasks. Independently of weak coin flipping, en route to our results, we show how one can test $n-1$ out of $n$ devices, and estimate the performance of the remaining device, for later use in the protocol. The proof uses linear programming and, due to its generality, may find applications elsewhere.

翻译：弱势硬币翻转是一种密码学任务，其中Alice和Bob远程翻转一枚硬币，但希望得到相反的结果。本研究在设备无关体系下探讨此任务，在该体系中，Alice和Bob既不信任彼此，也不信任他们的量子设备。十余年前，Silman、Chailloux、Aharon、Kerenidis、Pironio和Massar设计了最佳协议，其偏差ε≈0.33664，偏差是硬币翻转协议中常用的安全度量指标。本文提出了两种降低此类协议偏差的技术，即自测试和避中止组合。我们将这些技术应用于上述SCAKPM '11协议，并在假设连续性猜想成立的前提下，将偏差降低至ε≈0.29104。我们相信，这些技术对于设计其他多种任务的设备无关协议将具有实用价值。独立于弱势硬币翻转，在推导结果的过程中，我们还展示了如何测试n个设备中的n-1个，并估算剩余设备的性能，以便后续在协议中使用。该证明采用线性规划方法，因其通用性，可能在其他领域找到应用。