AI 中文总结
研究通过半定规划对量子距离界协议进行安全性评估，针对离散变量QDB，将相关博弈简化为凸优化问题求解，分析不同协议的单轮距离欺诈和黑手党欺诈情况；对连续变量QDB，报告高斯攻击模型的估计概率，给出多个协议的新攻击值及概率。
AI 中文摘要
量子距离界（QDB）协议可让验证者检查证明者是否真实且在物理上接近。在量子通信的定时快速阶段，验证者测量往返时间以获取证明者距离的上限。为进行统一比较，我们分离出快速阶段并研究单轮距离欺诈（DF）和黑手党欺诈（MF）博弈。对于离散变量QDB，我们表明这些博弈可简化为凸优化问题，因此可用半定规划精确求解；每个MF值都有一个实现它的显式攻击及一个匹配的证书，证明没有更好的攻击。这与量子位置验证不同，在量子位置验证中，攻击分散在两个分离的方之间，其优化是非凸的，分析依赖于松弛。在我们的MF博弈中，合作对坍缩为单个顺序策略，使博弈保持凸性且其精确值可计算。在所研究的离散变量协议中，最佳单轮DF攻击对每个协议都以相同概率（1/2）成功，而MF则明显区分了协议。对于连续变量QDB，我们报告了校准高斯攻击模型的估计攻击成功概率。该基准涵盖快速阶段本身对证明者进行认证的协议；遵循Brands和Chaum并通过最终认证消息绑定快速阶段的设计，如最早的QDB提议，不在此范围内，需单独处理。在所研究的四个协议中，两个此前没有已知的单轮攻击值，我们报告了首个值；对于另外两个，我们发现MF攻击的成功概率高于此前报道。总体而言，单轮MF抗性取决于攻击者是否能利用证明者早期透露的信息来应对验证者的新挑战。
英文摘要
Quantum distance-bounding (QDB) protocols let a verifier check that a prover is both genuine and physically nearby. During a timed fast phase of quantum communication, the verifier measures round-trip times to obtain an upper bound on the prover's distance. For a uniform comparison, we isolate the fast phase and study one-round distance-fraud (DF) and mafia-fraud (MF) games. For discrete-variable QDB, we show that these games reduce to convex optimization problems and can therefore be solved exactly with semidefinite programming; each MF value comes with an explicit attack achieving it and a matching certificate that no attack does better. This contrasts with quantum position verification, where an attack is split between two separated parties, so its optimization is nonconvex and analyses rely on relaxations. In our MF game, the cooperating pair collapses to a single sequential strategy, which keeps the game convex and its exact value computable. Across the discrete-variable protocols we examine, the best one-round DF attack succeeds with the same probability ($1/2$) for every protocol, whereas MF clearly separates the protocols. For continuous-variable QDB, we report estimated attack success probabilities from a calibrated Gaussian attack model. The benchmark covers protocols whose fast phase itself authenticates the prover; designs that follow Brands and Chaum and instead bind the fast phase with a final authenticated message, like the earliest QDB proposal, fall outside it and are treated separately. Of the four protocols studied, two had no previously known one-round attack values, and we report the first ones; for the other two, we find MF attacks with higher success probability than previously reported. Overall, one-round MF resistance depends on whether an attacker can use information revealed early by the prover to answer a fresh challenge from the verifier.
Comments25 pages, 7 figures
